2141 lines
421 KiB
Plaintext
2141 lines
421 KiB
Plaintext
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"# CDS: Numerical Methods -- Final Assignment\n",
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"\n",
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"- See lecture notes and documentation on Brightspace for Python and Jupyter basics. If you are stuck, try to google or get in touch via Discord.\n",
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"\n",
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"- Solutions must be submitted <font color=red>**individually**</font> via the Jupyter Hub until <font color=red>**Monday, April 4th, 23:59**</font>.\n",
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"\n",
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"- Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\".\n",
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"\n",
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"- Remember to document your source codes (docstrings, comments where necessary) and to write it as clear as possible.\n",
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"\n",
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"- Do not forget to fully annotate all of your plots.\n",
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"\n",
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"## Submission\n",
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"\n",
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"1. make sure everything runs as expected\n",
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"2. **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart)\n",
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"3. **run all cells** (in the menubar, select Cell$\\rightarrow$Run All)\n",
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"4. Check all outputs (Out[\\*]) for errors and **resolve them if necessary**\n",
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"5. submit your solutions **in time (before the deadline)**"
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]
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},
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}
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"source": [
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"## Tight-Binding Propagation Method Module\n",
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"\n",
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"### Tight-Binding Theory\n",
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"\n",
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"Solid state theory aims to describe crystalline structures defined by periodic arrangements of atomic positions $\\vec{R}_i$ with $i= 1 \\dots n$. To model the electronic properties of such a structure, we can use the so-called tight-binding method. Here one assumes that the problem for a single atom described by the Hamiltonian $H_{at}(\\vec{r})$ has already been solved, so that the atomic wave functions $\\phi_m(\\vec{r})$ are known. The Hamiltonian of the crystalline structure is then constructed from these atomic Hamiltonians as follows \n",
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"\n",
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"\\begin{align*}\n",
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" H(\\vec{r}) = \\sum_{i} H_{at}(\\vec{r} - \\vec{R}_i) + \\Delta V(\\vec{r}),\n",
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"\\end{align*}\n",
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"\n",
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"where $\\Delta V(\\vec{r})$ describes the changes to the atomic potentials due to the periodic arrangement. Solutions to the time-dependent Schrödinger equation $\\psi_n(\\vec{r})$ can then be approximated by linear combinations of the atomic orbitals, i.e. \n",
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"\n",
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"\\begin{align*}\n",
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" \\psi_m(\\vec{r}) = \\sum_{i} \\, c_{i,m} \\, \\phi_m(\\vec{r}-\\vec{R}_i). \n",
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"\\end{align*}\n",
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"\n",
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"Thus, our task is to find the coefficients $c_{i,m}$, which are the eigenfunctions of the tight-binding Hamiltonian $H_{tb}$. In the basis of the atomic orbitals $H_{tb}$ is an $n \\times n$ matrix which describes the \"hopping\" of an electron from one atomic position to the other. In this description the electrons are assumed to be tightly bound to the atomic positions, hence the name of the approach. In summary, we have reduced our original problem $H(\\vec{r})$, described in a continuous space $\\vec{r}$, to a strongly discretized problem $H_{tb}$ in the space of lattice coordinates $\\vec{R}_i$.\n",
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"\n",
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"### Propagation Method\n",
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"\t\n",
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"While this reduction already helps a lot, full diagonalizations of the tight-binding matrix is still not feasible if we need to describe realistic structures with thousands of atoms. For this case we like to have a method which allows us to study the electronic properties, without the need of fully diagonalizing the tight-binding matrix. The tight-biding propagation method allows for exactly this. By analyzing the propagation of an initial electronic state through the crystalline structure we also have access to the full eigenspectrum of $H_{tb}$, without explicit diagonalization.\n",
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"\t\n",
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"### Your Goal\n",
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" \n",
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"In the following you will setup the tight-binding Hamiltonian for a one-dimensional chain of atoms and numerically study its properties using exact diagonalization. Then you will compare it to the results obtained using the tight-binding propagation method. You will need some of the algorithms which you have implemented in the weekly assignments before. Additionally, you will need to implement a few new algorithms, which we have discussed in the last lecture. In principle there will be no need to use Numpy or Scipy (except for Numpy's array handling and a few other exceptions). However, if you encounter any problems with your own implementations of specific functionalities, you can use the Numpy and Scipy alternatives. Therefore you should be able to perform all of the following tasks in any case.\n",
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"\n",
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"Let us start by importing the necessary packages."
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]
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},
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}
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"from matplotlib import pyplot as plt\n",
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"import scipy.linalg"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"solution": false,
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}
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},
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"source": [
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"## Step 1: Crystal Lattice\n",
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"\n",
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"### Task 1.1 [3 points]\n",
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"\n",
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"In the following exercises the atomic positions of the 1D crystal lattice will be fixed to $\\vec{R}_i = x_i = i a$, with $i = 0 \\dots n-1$ and $a$ being the lattice constant.\n",
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"\n",
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"Write a simple Python function that takes the chain length $n$ as an argument and returns the atomic positions $x_i$. Set $a = 1$ for all the following exercises."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"checksum": "bad6e1d563be71de711926b41649c875",
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"grade": true,
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"grade_id": "cell-65a97e8f9f981da1",
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"locked": false,
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"points": 3,
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"schema_version": 3,
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"solution": true,
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}
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},
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"outputs": [],
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"source": [
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"def atomic_positions(n, a=1):\n",
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" \"\"\"\n",
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" Creates an array of atomic position in a 1D crystal lattice\n",
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" for lattice constant a having default value a = 1.\n",
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" \n",
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" Args:\n",
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" n: number of atoms in the 1D lattice string.\n",
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" a: numerical value for the lattice constant.\n",
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"\n",
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" Returns:\n",
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" A 1D array of atomic positions.\n",
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" \"\"\"\n",
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" \n",
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" return np.arange(n)*a"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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}
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"source": [
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"## Step 2: Atomic Basis Functions\n",
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"\n",
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"Our atomic basis functions will be Gaussians of the form\n",
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"$$\n",
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"\\large\n",
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"\\phi(x, \\mu, \\sigma) = \\frac{1}{\\pi^{1/4} \\sigma^{1/2}} e^{-\\frac{1}{2} \\left(\\frac{x-\\mu}{\\sigma}\\right)^2},\n",
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"$$\n",
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"\twhere $\\mu$ is their localization position and $\\sigma$ their broadenings. We also choose to have just one orbital per atom so that we can drop the index $m$ from now on. \n",
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"\t\n",
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"### Task 2.1 [4 points]\n",
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"Implement a Python function which calculates $\\phi(x, \\mu, \\sigma)$ for a whole array of arbitrary $x$, centered at given $\\mu$ with a given broadening $\\sigma$.\n",
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"\n",
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"Plot all the atomic basis functions for a chain with $n = 10$ atoms, using $\\sigma = 0.25$. I.e. plot $\\phi(x, x_i, \\sigma)$ vs $x$, for all atomic positions $x_i$ in the chain."
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]
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},
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"data": {
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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"def atomic_basis(x, mu, sigma):\n",
|
|
" \"\"\"\n",
|
|
" Calculates the atomic basis functions for the 1D chain of atoms.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" x: array of positions to calculate the wavefunction at.\n",
|
|
" mu: atomic position(s) to center Gaussian wavefunction at.\n",
|
|
" sigma: broadening constant for Gaussian function(s).\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" An array of values for the wavefunction over the positions\n",
|
|
" as given by x with shape len(x) by len(mu).\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" return np.pi**(-1/4)*sigma**(-1/2)*np.exp(-1/2*(np.subtract.outer(x, mu)/sigma)**2)\n",
|
|
"\n",
|
|
"n = 10\n",
|
|
"sigma = .25\n",
|
|
"x = np.linspace(-2, 12, 1000)\n",
|
|
"\n",
|
|
"plt.figure()\n",
|
|
"plt.xlabel(\"$x$\")\n",
|
|
"plt.ylabel(\"$\\phi$\")\n",
|
|
"\n",
|
|
"for mu in atomic_positions(n):\n",
|
|
" plt.plot(x, atomic_basis(x, mu, sigma), label=\"n = \" + str(mu))\n",
|
|
"\n",
|
|
"plt.legend()\n",
|
|
"plt.tight_layout()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "e1c7774260f02916e34521c6236638f4",
|
|
"grade": false,
|
|
"grade_id": "cell-e5c9315357a401f9",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 2.2 [6 points]\n",
|
|
"Implement a Python function to calculate numerical integrals (using for example the composite trapezoid or Simpson rule). This one should be general enough to calculate integrals $\\int_a^b f(x) dx$ for arbitrary functions $f(x)$, as you will need it for other tasks as well.\n",
|
|
"\n",
|
|
"Implement a simple unit test for your integration function."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "aecc6d50a1ffd4e4bfbfe3573847edf8",
|
|
"grade": true,
|
|
"grade_id": "cell-d851197b213e5d2d",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def integrate(yk, x):\n",
|
|
" \"\"\"\n",
|
|
" Numerically integrates function yk over [x[0], x[-1]] using Simpson's\n",
|
|
" composite 3/8 rule over the grid provided by x.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" yk: function of one numerical argument that returns a numeric\n",
|
|
" or an array of function values such that x[i] corresponds to yk[i].\n",
|
|
" x: array of numerics as argument to yk.\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" A numeric value for the quadrature of yk over x with error\n",
|
|
" of order -h^4/80*(b - a)*f^(4)(xi) for h the maximum time step\n",
|
|
" and xi such that the fourth derivative of f is maximal.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" # If yk is callable, we use it to determine the function values\n",
|
|
" # over array x.\n",
|
|
" if callable(yk):\n",
|
|
" yk = yk(x)\n",
|
|
" \n",
|
|
" # The distance h_i = x[i + 1] - x[i] is not necessarily constant. The choice of\n",
|
|
" # partitioning of the interval is subject to mathematical considerations I will\n",
|
|
" # not go into.\n",
|
|
" h = x[1:] - x[:-1]\n",
|
|
" \n",
|
|
" # TODO: Check implementation of Simpson's 3/8 rule: is there unnecessary overlap?\n",
|
|
" integral = 0\n",
|
|
" integral += 3/8*(x[1] - x[0])*yk[0]\n",
|
|
" integral += 9/8*h[1::3]@yk[1:-1:3]\n",
|
|
" integral += 9/8*h[2::3]@yk[2:-1:3]\n",
|
|
" integral += 6/8*h[ ::3]@yk[ :-1:3]\n",
|
|
" integral += 3/8*(x[-1] - x[-2])*yk[-1]\n",
|
|
" return integral"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "6ab06c87cf65c73463ed243e46d63b3d",
|
|
"grade": true,
|
|
"grade_id": "cell-59912b2862fbce5a",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def test_integrate():\n",
|
|
" \"\"\"\n",
|
|
" Tests the implementation of Simpson's 3/8 rule in function integrate\n",
|
|
" with two test case integrals.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" # Test integral 1 of f with F its primitive with integration constant 0\n",
|
|
" f = lambda x: x**2\n",
|
|
" F = lambda x: x**3/3\n",
|
|
" x = np.logspace(0, 3, 1000000)\n",
|
|
" assert np.isclose(integrate(f, x), F(x[-1]) - F(x[0]))\n",
|
|
" \n",
|
|
" # Test integral 2 of f with F its primitive with integration constant 0\n",
|
|
" f = lambda x: np.sin(2*x)/(2 + np.cos(2*x))\n",
|
|
" F = lambda x: -.5*np.log(np.cos(2*x) + 2)\n",
|
|
" x = np.linspace(0, 10, 1000)\n",
|
|
" assert np.isclose(integrate(f, x), F(x[-1]) - F(x[0]))\n",
|
|
" \n",
|
|
"test_integrate()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "8c1413a8a11006398e962e8c803ae001",
|
|
"grade": false,
|
|
"grade_id": "cell-86005829da536b5b",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 2.3 [2 points]\n",
|
|
"Use your Python integration function to check the orthogonality of the Gaussian basis functions by verifying the following condition $$\\delta_{ij} = \\int_{-\\infty}^{+\\infty} \\phi(x, x_i, \\sigma) \\, \\phi(x, x_j, \\sigma) \\, dx,$$ where $\\delta_{ii} \\approx 1$ and $\\delta_{ij} \\approx 0$ for $\\sigma = 0.25$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "4751becb5d3cb7663536a0624b3d9c54",
|
|
"grade": true,
|
|
"grade_id": "cell-8a6a8db84dcef484",
|
|
"locked": false,
|
|
"points": 2,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"delta_00 = 1.00000 (self)\n",
|
|
"delta_01 = 0.01832 (nearest neighbours)\n",
|
|
"delta_02 = 0.00000\n",
|
|
"delta_03 = 0.00000\n",
|
|
"delta_04 = 0.00000\n",
|
|
"delta_05 = 0.00000\n",
|
|
"delta_06 = 0.00000\n",
|
|
"delta_07 = 0.00000\n",
|
|
"delta_08 = 0.00000\n",
|
|
"delta_09 = 0.00000\n",
|
|
"delta_10 = 0.01832 (nearest neighbours)\n",
|
|
"delta_11 = 1.00000 (self)\n",
|
|
"delta_12 = 0.01832 (nearest neighbours)\n",
|
|
"delta_13 = 0.00000\n",
|
|
"delta_14 = 0.00000\n",
|
|
"delta_15 = 0.00000\n",
|
|
"delta_16 = 0.00000\n",
|
|
"delta_17 = 0.00000\n",
|
|
"delta_18 = 0.00000\n",
|
|
"delta_19 = 0.00000\n",
|
|
"delta_20 = 0.00000\n",
|
|
"delta_21 = 0.01832 (nearest neighbours)\n",
|
|
"delta_22 = 1.00000 (self)\n",
|
|
"delta_23 = 0.01832 (nearest neighbours)\n",
|
|
"delta_24 = 0.00000\n",
|
|
"delta_25 = 0.00000\n",
|
|
"delta_26 = 0.00000\n",
|
|
"delta_27 = 0.00000\n",
|
|
"delta_28 = 0.00000\n",
|
|
"delta_29 = 0.00000\n",
|
|
"delta_30 = 0.00000\n",
|
|
"delta_31 = 0.00000\n",
|
|
"delta_32 = 0.01832 (nearest neighbours)\n",
|
|
"delta_33 = 1.00000 (self)\n",
|
|
"delta_34 = 0.01832 (nearest neighbours)\n",
|
|
"delta_35 = 0.00000\n",
|
|
"delta_36 = 0.00000\n",
|
|
"delta_37 = 0.00000\n",
|
|
"delta_38 = 0.00000\n",
|
|
"delta_39 = 0.00000\n",
|
|
"delta_40 = 0.00000\n",
|
|
"delta_41 = 0.00000\n",
|
|
"delta_42 = 0.00000\n",
|
|
"delta_43 = 0.01832 (nearest neighbours)\n",
|
|
"delta_44 = 1.00000 (self)\n",
|
|
"delta_45 = 0.01832 (nearest neighbours)\n",
|
|
"delta_46 = 0.00000\n",
|
|
"delta_47 = 0.00000\n",
|
|
"delta_48 = 0.00000\n",
|
|
"delta_49 = 0.00000\n",
|
|
"delta_50 = 0.00000\n",
|
|
"delta_51 = 0.00000\n",
|
|
"delta_52 = 0.00000\n",
|
|
"delta_53 = 0.00000\n",
|
|
"delta_54 = 0.01832 (nearest neighbours)\n",
|
|
"delta_55 = 1.00000 (self)\n",
|
|
"delta_56 = 0.01832 (nearest neighbours)\n",
|
|
"delta_57 = 0.00000\n",
|
|
"delta_58 = 0.00000\n",
|
|
"delta_59 = 0.00000\n",
|
|
"delta_60 = 0.00000\n",
|
|
"delta_61 = 0.00000\n",
|
|
"delta_62 = 0.00000\n",
|
|
"delta_63 = 0.00000\n",
|
|
"delta_64 = 0.00000\n",
|
|
"delta_65 = 0.01832 (nearest neighbours)\n",
|
|
"delta_66 = 1.00000 (self)\n",
|
|
"delta_67 = 0.01832 (nearest neighbours)\n",
|
|
"delta_68 = 0.00000\n",
|
|
"delta_69 = 0.00000\n",
|
|
"delta_70 = 0.00000\n",
|
|
"delta_71 = 0.00000\n",
|
|
"delta_72 = 0.00000\n",
|
|
"delta_73 = 0.00000\n",
|
|
"delta_74 = 0.00000\n",
|
|
"delta_75 = 0.00000\n",
|
|
"delta_76 = 0.01832 (nearest neighbours)\n",
|
|
"delta_77 = 1.00000 (self)\n",
|
|
"delta_78 = 0.01832 (nearest neighbours)\n",
|
|
"delta_79 = 0.00000\n",
|
|
"delta_80 = 0.00000\n",
|
|
"delta_81 = 0.00000\n",
|
|
"delta_82 = 0.00000\n",
|
|
"delta_83 = 0.00000\n",
|
|
"delta_84 = 0.00000\n",
|
|
"delta_85 = 0.00000\n",
|
|
"delta_86 = 0.00000\n",
|
|
"delta_87 = 0.01832 (nearest neighbours)\n",
|
|
"delta_88 = 1.00000 (self)\n",
|
|
"delta_89 = 0.01832 (nearest neighbours)\n",
|
|
"delta_90 = 0.00000\n",
|
|
"delta_91 = 0.00000\n",
|
|
"delta_92 = 0.00000\n",
|
|
"delta_93 = 0.00000\n",
|
|
"delta_94 = 0.00000\n",
|
|
"delta_95 = 0.00000\n",
|
|
"delta_96 = 0.00000\n",
|
|
"delta_97 = 0.00000\n",
|
|
"delta_98 = 0.01832 (nearest neighbours)\n",
|
|
"delta_99 = 1.00000 (self)\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"n = 10\n",
|
|
"sigma = .25\n",
|
|
"\n",
|
|
"positions = atomic_positions(n)\n",
|
|
"infty = 10000\n",
|
|
"x = np.linspace(-infty, infty, 1000000)\n",
|
|
"\n",
|
|
"def ijlabel(i, j):\n",
|
|
" \"\"\"\n",
|
|
" Returns a string label describing the relation between two states in words,\n",
|
|
" if they are close enough.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" if i == j:\n",
|
|
" return \" (self)\"\n",
|
|
" if abs(i - j) == 1:\n",
|
|
" return \" (nearest neighbours)\"\n",
|
|
" # Default:\n",
|
|
" return \"\"\n",
|
|
"\n",
|
|
"for i in range(n):\n",
|
|
" for j in range(n):\n",
|
|
" integrand = lambda x: atomic_basis(x, positions[i], sigma)*atomic_basis(x, positions[j], sigma)\n",
|
|
" print(\"delta_{}{} = {:.5f}{}\".format(i, j, integrate(integrand, x), ijlabel(i, j)))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "e9ccbed5ba3e6b844bcc6e326053d8da",
|
|
"grade": false,
|
|
"grade_id": "cell-3cba7034f4eac62f",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"## Step 3: Tight-Binding Hamiltonian\n",
|
|
"\n",
|
|
"The tight-binding Hamiltonian for our 1D chain should describe the hopping of an electron from all atomic positions to their nearest left and right neighbours (i.e. no long-range hopping). The resulting matrix representation in the basis of the discrete $x_i$ positions is therefore given as a tri-diagonal $n \\times n$ matrix of the form\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" \\mathbf{H}_{tb} =\n",
|
|
" \\left( \\begin{array}{cccc}\n",
|
|
" 0 & t & & 0\\\\\n",
|
|
" t & \\ddots & \\ddots & \\\\\n",
|
|
" & \\ddots & \\ddots & t \\\\\n",
|
|
" 0 & & t & 0\n",
|
|
" \\end{array} \\right),\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"where $t = t_{i,i\\pm1}$ is the nearest-neighbour hopping matrix element. A hopping matrix element $t_{i,j}$ is a measure for the probability of an electron to hop from site $i$ to site $j$. They are defined as\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" t_{i,j} = \\int_{-\\infty}^{+\\infty} \\phi(x, x_i, \\sigma) \\, \\Delta V(x) \\, \\phi(x, x_j, \\sigma) \\, dx,\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"with the potential fixed to\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" \\Delta V(x) = \\sum_i \\frac{-1}{|x - x_i| + 0.001}.\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"### Task 3.1 [3 points]\n",
|
|
"Write a Python function to calculate $t_{i,j}$, using $\\sigma = 0.25$. The function should have as input the indices $i$ and $j$, and the chain length $n$. Verify that the long-range hoppings $t_{i,i\\pm2}$ and $t_{i,i\\pm3}$ are negligible compared to $t_{i,i\\pm1}$.\n",
|
|
"\n",
|
|
"Hint: use your integration function from task 2.2"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "260ae3c806429aee5900599c01cb65c6",
|
|
"grade": true,
|
|
"grade_id": "cell-0abfcd1aa9fad2fa",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def hopping(i, j, n, sigma=.25, a=1):\n",
|
|
" \"\"\"\n",
|
|
" Calculates hopping matrix elements t_ij for sigma = 0.25 in a 1D\n",
|
|
" chain of n atoms at distance a = 1 from eachother.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" i: origin site index.\n",
|
|
" j: destination site index.\n",
|
|
" n: number of atoms in the chain.\n",
|
|
" sigma: standard deviation to the Gaussian wave functions.\n",
|
|
" a: the lattice constant of the 1D chain of atoms.\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" Hopping parameter t_ij.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" positions = atomic_positions(n, a)\n",
|
|
" \n",
|
|
" # This 'infinity' is large enough, as the Gaussians decay quite quickly\n",
|
|
" # away from the atomic positions, which we already saw in the overlap\n",
|
|
" # above. In fact, 99.7% of all probability mass is under the integral\n",
|
|
" # for x radius of 3*sigma from the centers x_i.\n",
|
|
" h = 1e-5\n",
|
|
" x = np.arange(positions[0] - 10*sigma, positions[-1] - 10*sigma, h)\n",
|
|
" \n",
|
|
" def V(x):\n",
|
|
" ret = np.zeros(x.shape)\n",
|
|
" for x_i in positions:\n",
|
|
" ret += -1./(np.abs(x - x_i) + 0.001)\n",
|
|
" return ret\n",
|
|
" # Instead of using a loop, one could vectorize the problem further by calculating all sum\n",
|
|
" # terms as elements of a len(x) by len(positions) matrix and then summing along the rows.\n",
|
|
" # In testing I found that this was slower than using the loop, so I commented it out.\n",
|
|
" # This might be due to the large memory overhead O(len(x)*len(positions)), and the fact that\n",
|
|
" # the len(positions) iterations already do vectorized calculations on len(x) >> len(positions)\n",
|
|
" # numbers, making the theoretical speed gain only plausible at larger len(positions). \n",
|
|
" #V = lambda x: np.sum( -1/( np.abs(np.subtract.outer(x, positions)) + 0.001 ), axis=1 )\n",
|
|
" \n",
|
|
" integrand = lambda x: atomic_basis(x, positions[i], sigma)*V(x)*atomic_basis(x, positions[j], sigma)\n",
|
|
" return integrate(integrand, x)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "b1a56ecde33e723ff450defcf5dc2e74",
|
|
"grade": true,
|
|
"grade_id": "cell-ea36ee5a2b35154c",
|
|
"locked": false,
|
|
"points": 0,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"For i = 0 ...\n",
|
|
"\tt_{i,i+1} = -0.13849173441658025\n",
|
|
"\tt_{i,i+2} = -3.088088057066831e-06\n",
|
|
"\tt_{i,i+3} = -1.8833562200578063e-15\n",
|
|
"\n",
|
|
"For i = 1 ...\n",
|
|
"\tt_{i,i-1} = -0.13849173441658025\n",
|
|
"\tt_{i,i+1} = -0.14871538221422848\n",
|
|
"\tt_{i,i+2} = -3.1306987950404085e-06\n",
|
|
"\tt_{i,i+3} = -1.945630457066332e-15\n",
|
|
"\n",
|
|
"For i = 2 ...\n",
|
|
"\tt_{i,i-1} = -0.14871538221422848\n",
|
|
"\tt_{i,i+1} = -0.15363274031153992\n",
|
|
"\tt_{i,i-2} = -3.088088057066831e-06\n",
|
|
"\tt_{i,i+2} = -3.152251440766849e-06\n",
|
|
"\tt_{i,i+3} = -1.9763481552880358e-15\n",
|
|
"\n",
|
|
"For i = 3 ...\n",
|
|
"\tt_{i,i-1} = -0.15363274031153992\n",
|
|
"\tt_{i,i+1} = -0.1560583006931239\n",
|
|
"\tt_{i,i-2} = -3.1306987950404085e-06\n",
|
|
"\tt_{i,i+2} = -3.1616643825949025e-06\n",
|
|
"\tt_{i,i-3} = -1.8833562200578063e-15\n",
|
|
"\tt_{i,i+3} = -1.9857521228152284e-15\n",
|
|
"\n",
|
|
"For i = 4 ...\n",
|
|
"\tt_{i,i-1} = -0.1560583006931239\n",
|
|
"\tt_{i,i+1} = -0.15680086580653224\n",
|
|
"\tt_{i,i-2} = -3.1522514407668485e-06\n",
|
|
"\tt_{i,i+2} = -3.1616580341274714e-06\n",
|
|
"\tt_{i,i-3} = -1.945630457066332e-15\n",
|
|
"\tt_{i,i+3} = -1.9763479030784917e-15\n",
|
|
"\n",
|
|
"For i = 5 ...\n",
|
|
"\tt_{i,i-1} = -0.15680086580653224\n",
|
|
"\tt_{i,i+1} = -0.1560582807779115\n",
|
|
"\tt_{i,i-2} = -3.1616643825949025e-06\n",
|
|
"\tt_{i,i+2} = -3.1503943708763577e-06\n",
|
|
"\tt_{i,i-3} = -1.9763481552880358e-15\n",
|
|
"\tt_{i,i+3} = -9.75855063584149e-16\n",
|
|
"\n",
|
|
"For i = 6 ...\n",
|
|
"\tt_{i,i-1} = -0.15605828077791148\n",
|
|
"\tt_{i,i+1} = -0.07705640452986241\n",
|
|
"\tt_{i,i-2} = -3.1616580341274714e-06\n",
|
|
"\tt_{i,i+2} = -1.8615080260773555e-09\n",
|
|
"\tt_{i,i-3} = -1.985752122815229e-15\n",
|
|
"\tt_{i,i+3} = -1.2516261372405081e-23\n",
|
|
"\n",
|
|
"For i = 7 ...\n",
|
|
"\tt_{i,i-1} = -0.07705640452986241\n",
|
|
"\tt_{i,i+1} = -9.883210483852472e-10\n",
|
|
"\tt_{i,i-2} = -3.1503943708763577e-06\n",
|
|
"\tt_{i,i+2} = -8.453472394803474e-24\n",
|
|
"\tt_{i,i-3} = -1.9763479030784917e-15\n",
|
|
"\n",
|
|
"For i = 8 ...\n",
|
|
"\tt_{i,i-1} = -9.88321048385247e-10\n",
|
|
"\tt_{i,i+1} = -7.16787287550824e-31\n",
|
|
"\tt_{i,i-2} = -1.8615080260773555e-09\n",
|
|
"\tt_{i,i-3} = -9.75855063584149e-16\n",
|
|
"\n",
|
|
"For i = 9 ...\n",
|
|
"\tt_{i,i-1} = -7.16787287550824e-31\n",
|
|
"\tt_{i,i-2} = -8.453472394803472e-24\n",
|
|
"\tt_{i,i-3} = -1.2516261372405081e-23\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"n = 10\n",
|
|
"\n",
|
|
"for i in range(n):\n",
|
|
" print(\"For i =\", i, \"...\")\n",
|
|
" for r in range(1, 4):\n",
|
|
" if i - r >= 0:\n",
|
|
" print(\"\\tt_{{i,i-{}}} = {}\".format(r, hopping(i, i - r, n)))\n",
|
|
" if i + r < n:\n",
|
|
" print(\"\\tt_{{i,i+{}}} = {}\".format(r, hopping(i, i + r, n)))\n",
|
|
" print()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "7d2c8f74993fe38c2c979376961f869a",
|
|
"grade": false,
|
|
"grade_id": "cell-8a0f18c44306ae00",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 3.2 [3 points]\n",
|
|
"Implement a diagonalization routine for tri-diagonal matrices which returns all eigenvalues, for example using the $QR$ decomposition (it is fine to use Numpy's $\\text{qr()}$). \n",
|
|
"\n",
|
|
"Hint: For tri-diagonal matrices with vanishing diagonal elements, the $QR$-decomposition-based diagonalization algorithm gets trapped. To get around this you could, for example, add a diagonal $1$ to your matrix, and later subtract $1$ from each eigenvalue."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "c20cbcce0a7df50b6ae7b90c7aa35721",
|
|
"grade": true,
|
|
"grade_id": "cell-9d4942b717eadeb2",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def QREig(T, eps=1e-6, k_max=10000):\n",
|
|
" \"\"\"\n",
|
|
" Follows the method of the QR decomposition based diagonalization routine\n",
|
|
" for tridiagonal matrices. The matrix T is diagonalized, resulting in\n",
|
|
" all diagonal elements being an eigenvalue.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" T: a tridiagonaliz matrix.\n",
|
|
" eps: the desired accuracy.\n",
|
|
" k_max: maximum number of iterations after which to cut off.\n",
|
|
" \n",
|
|
" Returns:\n",
|
|
" A one dimensional array with the eigenvalues of the matrix T.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" # A square matrix is assumed.\n",
|
|
" assert T.shape[0] == T.shape[1]\n",
|
|
" \n",
|
|
" # Add identity matrix to prevent trapping.\n",
|
|
" T += np.eye(len(T), dtype=T.dtype)\n",
|
|
" \n",
|
|
" e = eps + 1\n",
|
|
" k = 0\n",
|
|
" while e > eps and k < k_max:\n",
|
|
" k += 1\n",
|
|
" Q, R = np.linalg.qr(T)\n",
|
|
" T = np.matmul(R,Q)\n",
|
|
" e = np.sum(np.abs(np.diag(T, k=1)))\n",
|
|
" \n",
|
|
" # Subtract 1 before returning to compensate the addition\n",
|
|
" # of the identity matrix.\n",
|
|
" return np.diag(T) - 1"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "19976946c5746804cb08c34f0bda50fc",
|
|
"grade": false,
|
|
"grade_id": "cell-2d8fb5c080951dd5",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 3.3 [3 points]\n",
|
|
"Implement a unit test for your diagonalization routine."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "d95777361c07514a97ff1458f26f4f44",
|
|
"grade": true,
|
|
"grade_id": "cell-001cb3c043c4e371",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def test_QREig():\n",
|
|
" \"\"\"\n",
|
|
" Test the implementation of function QREig using two test\n",
|
|
" cases.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" # Test case one\n",
|
|
" T = np.array([\n",
|
|
" [1,4,0,0],\n",
|
|
" [3,4,1,0],\n",
|
|
" [0,2,3,4],\n",
|
|
" [0,0,1,3]\n",
|
|
" ])\n",
|
|
" # Eigenvalues are roots of λ^4 - 11*λ^3 + 25*λ^2 + 31*λ - 46.\n",
|
|
" eigenvalues_of_T = np.array([-1.45350244, 1., 4.65531023, 6.79819221])\n",
|
|
" assert np.allclose(np.sort(QREig(T)), eigenvalues_of_T)\n",
|
|
" \n",
|
|
" # Test case two\n",
|
|
" T = np.array([\n",
|
|
" [1,4,0,0],\n",
|
|
" [3,0,1,0],\n",
|
|
" [0,2,0,4],\n",
|
|
" [0,0,0,3]\n",
|
|
" ])\n",
|
|
" eigenvalues_of_T = np.sort(np.linalg.eig(T)[0])\n",
|
|
" assert np.allclose(np.sort(QREig(T)), eigenvalues_of_T)\n",
|
|
"\n",
|
|
"test_QREig()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "83df149b46d779a846f9de925342b681",
|
|
"grade": false,
|
|
"grade_id": "cell-85c89b0eb0930f2b",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 3.4 [4 points]\n",
|
|
"First, write a function that generates your tight-binding Hamiltonian $\\mathbf{H}_{tb}$, for a given chain length $n$. Use $t = t_{i,i\\pm1}$, as calculated in task 3.1. You can choose any $i$ near the center of the chain for the calculation of $t$, as the chain is (approximately) periodic.\n",
|
|
"\n",
|
|
"Second, use your diagonalization routine to calculate all the eigenvalues $E_m$, for a variety of $n=10,20,40,80,100$. Sort the resulting $E_m$ and plot them vs. $m$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "a0779b496fd41a4664bb0cdd857c70fc",
|
|
"grade": true,
|
|
"grade_id": "cell-764cb41c37700042",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def TBHamiltonian(n, sigma=.25, a=1):\n",
|
|
" \"\"\"\n",
|
|
" Generates the tight-binding hamiltonian H_tb for given chain length n,\n",
|
|
" using the approximation of constant hopping parameter in a periodic\n",
|
|
" chain of atoms.\n",
|
|
" \n",
|
|
" By taking the hopping parameter in the center of the chain, the\n",
|
|
" periodic boundary is approximated the best.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" n: number of atoms in the chain.\n",
|
|
" sigma: standard deviation to the Gaussian wave functions.\n",
|
|
" a: the lattice constant of the 1D chain of atoms.\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" Tight-binding hamiltonian H_tb.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" i = n//2\n",
|
|
" t = hopping(i, i + 1, n, sigma, a)\n",
|
|
" H_tb = (np.eye(n, n, -1) + np.eye(n, n, 1))*t\n",
|
|
" \n",
|
|
" return H_tb"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
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|
|
"grade": true,
|
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"grade_id": "cell-39ada0528e69d2e5",
|
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|
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"points": 1,
|
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"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
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},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.figure()\n",
|
|
"\n",
|
|
"for n in [10, 20, 40, 80, 100]:\n",
|
|
" H_tb = TBHamiltonian(n)\n",
|
|
" E_m = QREig(H_tb)\n",
|
|
" plt.plot(np.arange(len(E_m)) + 1, np.sort(E_m), label=\"n = {}\".format(n))\n",
|
|
"\n",
|
|
"plt.legend()\n",
|
|
"plt.title(\"Energy eigenvalues of $H_{{tb}}$ for different chain lengths $n$\")\n",
|
|
"plt.xlabel(\"$m$\")\n",
|
|
"plt.ylabel(\"$E_m$\")\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "c2b46d2fef4b0c243103a5a6f1111e2d",
|
|
"grade": false,
|
|
"grade_id": "cell-b7c84b8c4ed4c1be",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 3.5 [3 points]\n",
|
|
"Implement a function to calculate the so-called density-of-states \n",
|
|
"\n",
|
|
"\\begin{align*}\n",
|
|
" \\rho(\\omega) = \\frac{1}{N} \\sum_i \\delta(\\omega - E_i),\n",
|
|
"\\end{align*}\n",
|
|
"\n",
|
|
"for a variable energy grid $\\omega$. Do this by approximating the $\\delta$-distribution with a Gaussian. In detail, you can use your atomic orbital function $\\delta(\\omega - E_i) \\approx \\phi(\\omega, E_i, \\sigma_\\rho)$. Calculate the normalization factor $N$ such that $\\int \\rho(\\omega) dw = 1$ is fulfilled.\n",
|
|
"\n",
|
|
"Your function should take as input the energy grid $\\omega$, the eigenenergies $E_i$ and the broadening $\\sigma_\\rho$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "ca46cf0b09305fafb522fc0395d1e495",
|
|
"grade": true,
|
|
"grade_id": "cell-d7c225b7687b5a9c",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getDOS_ED(w, Ei, sigma):\n",
|
|
" \"\"\"\n",
|
|
" Calculates the density-of-states (DOS) for energy states Ei\n",
|
|
" over energy grid w by counting the occupation using a Gaussian\n",
|
|
" approximation to the delta function.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" w: grid of energies to calculate the DOS over.\n",
|
|
" Ei: array of n eigenenergies for the system.\n",
|
|
" sigma: standard deviation to the Gaussian.\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" Tight-binding hamiltonian H_tb.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" # Luckily, the function is built in such a way it can also\n",
|
|
" # handle an array input as its first argument.\n",
|
|
" delta = atomic_basis(w, Ei, sigma)\n",
|
|
" \n",
|
|
" rho = np.sum(delta, axis=1)\n",
|
|
" \n",
|
|
" # Now normalize rho.\n",
|
|
" N = integrate(rho, w)\n",
|
|
" rho /= N\n",
|
|
" \n",
|
|
" return rho"
|
|
]
|
|
},
|
|
{
|
|
"attachments": {
|
|
"dosN010.png": {
|
|
"image/png": 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j5EsI7r2UJRYF/gcwD6ghQHUQq9gNNY4c95U3UapkoMO4gv+KybYxm+dH38JCIScG3z3g21PK9FIW0XIr5U6c00JdldpHqdILpVPqaqU640Lmj9ArA10riCMEwFhg2gdEMChNKZ3C690Q6VX63KWvAzlczoQcSi2j0QkNKcgGZLFTGfsUvHrVVugQirBYxIvMKLIrhvIsVlGoQXspKoNew4quW8BW0dAyCxtR6GXycs5V5gqInd8s/FAOLpnsYnhqG+ieQ2PSy6qrLEKzVKGjW4BGKouAYnjZbZeNm5sNN5bss8pjICBQfPCtuzjxcffiBPhAWocqPvoozBIdSyuHzW6RcrHuEpNrvVwAda+VIBvRbgnhN89jR4m76odKiT2FV4F5AnWQBmRHqiDAidMcv4im38qqWqvWOkatk58raj0HzVkV3qpwVW3Wa/OaaovHllF7P3QSjsbt2s961VUHk4cwkPrhjEDJ61NzxtTXvFW5k/xikXarqlQZG+hx1O3U2YLmD9gsDDm92hNbNiXwiO6psAnFg4G0MYuDFumHjgMSqXU3gZatbiaCiPqozZtVl1udDf0onOn1EJejUg8HnwsuAc3tniqWweFaqZmKg3D5qmGlBq5EwFxtwF4U36J6z6YOgHInfYSobL6jNmxLrUpr1Ta83xszW4Ocm0Zre7ZGyjq20iO1brf1M+lkWhvw85j0Z17biENxaGqiBH/dJtcQi970iYZ506Ntlt5oQNqc3qbP16x8kmQcZBvHA7pjm6U9NVxFWaLhcdsCLNdq+04yqo22rzku+W3t1NqolgZOGwzTLop0OfSiSDBJIj+lBRNollrcijI2arY/inzkQ2hBoVDRy0HpxR6UCtPrHgRUiQcn6aGrRaI6cthpR/tcnQp/pIGU0VBDyuNcuvTaX08oa3cJpI0oqW5gh8QhWBPJ7hRyn9CjUTkmxHRZp5MhL9qXno4hfQP/Tbw3G2+spv46Se2+VwdSnVmpHyMZx/ulCbhyO1D40kpaZWLZ4zyhh7CVi9h+VA9VIIXQwaAwByAYlUsNqNMBrQ3yiLCuQcBG7+xKY9nPpsrmGIqjTrXAq4K0yrJBlzwIxlAqCRVPYwLBqWdM38NgGROD8JC8rGOxbC1GjLGJ2jbGZc/GgMT8yDhYe3SmcdwG1DSu+Lj7DCgfBS8DAaDVwggurAgbxjj8y5sFjWJYJaLVuOSg4I+zBXRJQ1v6S7p16ddAD0cZRX5VhN+UoFDlgqyLGhhmDoUtqLPM6/IuNWK2xOIhZeJ60COobE7ei+8I7FTxxbUVcT/0GGebUKtyZct10EDEA9ck4HTaMYSevuWSGwBfbCg9AgmmmheG0EE2IkH9gdD+dbd0sgTZ0LkrsUnPLxWYXYLrJ02Q7obAIBRc1yeTrS61SdtwYS0uliSWJqcr/K6bOoJX1Scb+VMV7jfUkL7+9UKBlwmwAx1M17h0WZ3L7pqvpZho1Cx+IJEM00HA0aEETZMqRT/PBOuzX4qdRWNtuqMX3UpguGU9nywmO84pBhncaZC2GbbGnZRlmsvXROonMZw7fLrAGDw7UNdhzYmY95OcO6Mhm0bfTO9Gu0a3gbTQfJY1kyEfkPYytPwVi8ElUA491aToqJMxwobbpwxJr9FBGcE04mCzu82NYbUnrMtm4YBg2jqAGq7fKwwZNGeOh9oBYaiQoXt21wUtB0e3RdDiCe3tmYkOQZFWgd4ZJguCpvAZKGWnqihzCnCusTiLVoUALDADyu7CqjURkkl7vCBYphjNjK+F6KMoa1Nm+xqS7svpBE+nF0HLL9pxkf2HXyza725HSdJ1rbRpQ3Y5CFZH8R2mb8R+XTykTo1KLm2PuejPsFttQ2yAbm6sobQp78NtBj7axmJYeq892Ony4+GsbLf9Gp59aG3xABqH0wLlR0kjaCppJfOloxClcWgJlglUD0mASNrhMkDbD9366BvPQEPn6u/cOPprSMBHOz63O/rBWUaDMp1YJIctfHOLZSfHEUexHD5DOMTvu9029cABbjMnb9q25jhDG9ricFs6sP1BbhJxNOyAiPo94xCtMY4cWJz9iMOZgixesCk0xOSddJ0Vm9jT/HIL8blov3I6zEDC/dDynKA9iMXNBrnMm8ed647T3wxk7GyMbBfuusjI7eFUITSfzxWTdOGLCwCQRNqA7fRYYP+QUEh1XUgTctnEG2q99L33mNMlzEteb6B84fTRYya67xGFfqFE0MsQkmIBJUVHQNAd2BruPTdETshLGo3mZM4EdLQ6lIAGzJJi0cpv1SCfFMokghaHGrl9xz0OR1K2Eek/7ZEEyHOGWosAAEzqSURBVHja7d19g+O2gd9xRs2k7cpeaeNmtoZEURD0lPjhsru5h8YXJ83d+mqv1+6lTZr2etfntO//FXQkjTR6IECAACWQ+P7+sGdGSwqEiI8A8CnLCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYSQFuQHPUJIh/MDlANAQgCQXOaf9Xo/vIsgP/rRP79rW/75j/5F68r8L3/0o3/ZukL/i1buHD+KoRg/7PX+GcoZ8qzXexZDOfr9D1pXdx/0P2xdmZ/3+89bV+gPW7lz9GnfAAiAAAiAtG8ABEAABEAABEAABEAABEAABEAABEAApIIAEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAABEAAJAAIgAAJgWhkMtwFAAARAAEwuw/2zUYYACIAACIBpZWffUCsgAAIgAAJgl/t/g/0PAAiAAAiAiQE4PHQFhwAIgAAIgGmNgIfnFAIgAAIgAAIgAAIgAAJgMkPgAQACIAACYIJdwMH5FOCLZ7v8oNf78fMI0u9/9Lxt+aj/r1pX5p/0+z9pXaH/VSt3jn4Mxfhx8ucB9srPA7w//L33sk8I6WReJg/goPw8aAAkBABTmATsDUtOhGYI3LUh8L/++F+HGwLbrYwhMEPgFvh3+IGDIBEeBBGj0ThEYUSe5yLUQRDLlVVnPBoFWA8HQTgIUn8GcHB+PBgAIwJwUuT5NERhRg9mjUIBaLmy6kzzvJgAIADecALwvC8IgDEBuOlrBelsyYf1yFAAWq7sWlsHgADoOQLedQYBEAABEADpAQIgAAIgAHY/PW6GAIAACIApj4GHj11BjgIDIAACYHJdQOMtoQEQAAEQALvdB+zp+n8ACIAACIDdzuapSINB5BWUKoCz7gM4A0AAjDYAeFsAVfcBVABI+wZAAGwWwOnDeopQABZ2KwNAAARAAIwCwM168lAAWq4MAAEQAAEQAAEQAAEQAAEQAAEQAAHQEUAVoDBRAqgAkPYNgAAIgAAIgAAIgAAIgAAIgAAIgAAIgFQQAAIgAAIgFdReAGdyDoBNbd1MzgAQAAEwXgBnfk0cAE2Z7y4lBkAABMBIAfS8bFZ2H0DP2pEACIAACIAACIAACIAAaDCr+gnDVgCOARAAAbCbAC4WHQaw+po6KwBFhwEM+PkDIAC2DkBVwY2Sy4n9Pg6AsQE4WUrl8/kDIAB2GcDt4M7QB1g9vLxsI4CT8ABO/Et1fQCXD0usDP0/u4kCAATAbgJY9ZAK5dL12QJYxAGgCA9ggHvUhACwcAKwojqDPYIFAAEQADcA5gDYLIA5AAIgAAIgAAIgAAKgX+YVDUDeBMCl/4bFCeDyJgDKii2bX2NPA0AAjBBAFSWAAR7AFieAMkoAr3IYGAABMBkAi9sR0W0ACwAEQACMHkCPU+bW3QdwWn/5HAABEAC7DGDefQB9awcAARAAYwVQAGDTAAoABEAAvA6A03YDWH180wrAebsBnAIgAAKgvkWKyjFXWwGsbtpWAKp2A5hXVJO8xp4GgAAIgAAIgLRvAARAAARAAARAAARAAARAAARAAARAAKSC2g7gCgCbBnAFgAAIgGGyvfBipn157AygigTAeXgAA9wzIAiAyhlA/R1PNw8xzdcASBIFsIIJ0VoAVXgAA5wudyMARcWWASABQAAEQAAEQAC8AFBY7+PeAI5TAHDs+3HZAygAEAABsD0A7t4wQIuME8Dc82gKAAIgAAIgAAIgAAIgAFaZVT2WtgJQAiAAAmAHAZxUtGzlDOASAJsGcOkMYNUHvABAkiSAIjiA0q9FAaApi8eNCg3gNR4LB4AAmA6Awq9AAGiqHQAEQAAEQAAEQAAEQAAEQAAEQAAEQAAEQAAEQAAEQAAEQACszqyifUgA7AKAsqKa5lfY1QAQAOMDUAUHsPBr4qsUAFz5AVgEB/Aaj4UDQABMAUDPPo5KAcDaK9r3jwEQAAEQAKvNCgpggHvUACDtGwABEAABEAABEACbBrB6RVYA5gAIgADYWQD17WN6IwD9r86PEsDFjQCcVlQTAJI0ARxVtOz8RgD6n5gWJYDiRgDmFdU0AkCSJIDSCsAZALYVwJkVgNd4LiYAAmBbAVTW+/iHAgCbB1DYA6gAEAABEAABEAABEAABEAABEOUAEAABEAAJABr3/3FdAGtf7QqApqzqAjgGQADcZnAcAKxo2aIugLWb+DIFAJe+Xw/OAArfagLAjqR3nCEAxgagTAHA2isCQAAMCeAAAEMDuALA5gFcASAA+g6Bhw8AMgQODqCKDMBJCAAnkQGoABAAA3QFhwDYeQArV2QDoABAAOxaT1AzAgbAjgCYhwfQnwkABMBIohsBpwVg1dhOAWA3AFS+MwUAmMgIOC0ABQAC4JUeCweAsY2A464gAARAAATA5kbAZx3Au/tdftrr/ezDCNLvf9L8m3y62/0/073++e71zy1X90n/zxyXuMhnnssf8mjWp1X/7uf9/s8tqyn3LtTnFfVtufznf2a9c1R9Hp9ZVpN/Pun3Y2hXPwPAxxHw2SGQ+6fTA1/2U8mr3e7/Wvf6m93rb+zX+AvnJU7z2nP5Qx7NehWwmnLvFb2pqG/L5X/hvMSbivp+lcwu/xIAyw+BpNwD/PNwPcDP6AE23wP8LFwP8C/oAXIIJPk5wDzcHKAMMwfo/5CKKOcAVZg5QBluDjBnDpBDIOkCOKto2fLqAOYpAJh7Lu8OoKyoplnz+xoAxnwIJFEAlR2AI+t9HAAjA3BkB+AVHgsHgDEfAgFAE4DSeh8HwMgAlAAIgCUdwF70FQSAQQCsvDOrDYArAATAbnUAhwCYBoCVK7IBUAEgAHYnA9MIGAD9ACwAsHkACwAEwIZGwAB4nMIZwNzzRA8AtOAsdwawAEAAtBoBpwXgqKJB5gDYDQCrPuFR8/saAEYzBB4MWlBBVwFQdhbARRMALjoL4BUeCweA7QgAdgJA0QSA3tdLACDtGwABEAABEAABEAABEAABEAABcJ/He/TXf3R43AA+Pva99h3oARAAAfB6AApnAD/1bFAiVIOME0DpuaL98p86AygAEAABULP7A2DqAF7hsXAACIAACIAASPsGQAAEQAAEQAAEwIYBrFyRDYASAAEQADsM4BgA0wRwDIAEAHXNYwWAXQFwZa4mACQJAjipAHA/97W23sf/EgCvAeBfWe8ca/Nc6AHASeM7GwACYGwACksAc+t9/HMAvAaAn1vvHLklgM0/Fg4AARAAARAAad8ACIAACIAACIAACIAACIAA2DEAi5olmocCUDUBoPc9avYrmtdcvgBAAATAqwG4rA1g3dMqVBoA1l1RXhvAJQACIACeZVax+0sA7AqAsgLAGQCS5ABUwQH8N4EAXIfatLgAXAcC8N8EB7D5x8IBIAB2H8DPAgGYh9q0aQgAp6GUyAMB+BkAAiAAAmCAFdkAmAMgAAIgAAIgAAIgAHYKwDUApg7gGgBJsgBKA4AFAHYFwMIAoARAkiSAowoA960DAFsNoOEjPAA4AkCSHIASAAFw93rzj4UDQADsPoA5AF4DwBwAARAAwwG4AsA0AVwBIAFAXYPcvuQM4NoDMJkGgNJj+bUzgIaPUAEgSRtAFRxACYBNAiiDA6gAkADgZcSh9YwBsJ0ALg4foQBAAATA0xS2AArbfXx756UYAFw2AaD3uSIhAFy6AChsASwa39kAEABjAzBvBEAVA4CHFS38AVzkoW7SFQJA1QiAzT8XEwABsPMA/jI+AKuKbgGgiA/AXwIgAALgNQCcuwD46rDGRb0SAWBlV3Rbva9cAJwDIAACYE0ART0Aa95i/eDW2HPTogTQdywt6gEoABAAAVADoNADuLoNgNMQz6iIEsDtiqa3AXClB1AAIAFAU+u4KoCy2wDK2wBY9REDIEkNQAGAAOj4EQMgAAKgGcAVADYJ4AoAARAAIwbQpz1N0wBw6vuBASAAAmAYAKWxdUydAPzCtz3lIQFchwRwHRLA3OcD2/znCycAp8aPWAIgSRfAsQzXOj54ExWAy5AALqMC8I0TgBUf8RgASbIAZvrWsW3zi/YCqEICqNoL4GL7baAHMANAkiKAqwoApWvrAMAoAcz0x12eAFwBIEkMQJUCgHN/AGcpANj4Y+EAEAAB0AbAZVAAqxq2BYAqKIBLAKR9A2BcAC4DAug0a1gGoAoB4LoJANchAFSeAG5n9EIBuARAAoCa1rHrGzoDmMUAYN4EgL7XiwUBMHMHUBk/YgAk6QI4DQrgX4cAUHQbQBECwL8OCuAUAEmiAEoDgMUBQMvW8cFrALwOgK8/sP+IdwAWBgAlAJIEAVxWAJjfEEDfszKiBHB1QwDzCgCXAEgSA1BGDKBvhyRKAFXEADb+WDgABMCEAKzXgxunAmC9G16vABAAATByAEceBxVFWABlOABlWABF/eWzEQACIABeCUDhDKACwGYBVM4ACgAEQAAs3ftHAAiAIwAkiQKoggKYA+B1AMyDAqgAkABgNwEc+QM4AkAABEAAbBuAwmZuywJAebgxLAACIAB2DEDtBNACALsE4EK3aSMAJAkDqN37xY0AHHcbwPGNABQ1dgEA7GYGw00GANgEgDNfALNuA5j5AjgDQAD04q+3T+IAFlYArh0BFN4Ayi4DKL0BFI4Arq0ALAAwkQy39g0B8BGqKgAdOPpVNACOmwFw7FeqgAD+yuUdbQDMm97bADCe/t9u9DscAmBYAL/0BXAVCkDRDICeN+nyfQTREYBfAiAA1srGvzZUUIsBLGoDplIBsH71FAAIgJ4dwFZU0FUBzIMCKGMBUIUDUMUCoAwKYA6AiWVY0QEEwDgAHPltWpwAjgAQAG8/Ah5sT4MZAKA9gJa3Cw4IoOdZGXECKAEQACMA8PEkmFMCXzzb5Qe93o+fR5B+/6Om32Kz23/8/OPN/8pe/vXmhV8//83Df39jt8J/+7TEx7VKtCuLwzvqsiv7xxYr+km//5OKf7Ldnsfa8Mpuw3Kv6vnNbtv+rcs76stesQuEzEcP3zQR5MdpA/h0DuD5wZD7p7+/7KeR7RO2+9uHmZe9/Grzwqv+5hZXr+1WeLTEm1ol2pXF4R3NJdms7rf+9fTbzfY8bptXdhuWe1XP675LSV5XLFGxC3QwL9MGcLjv+w3OzwMEwG4CmAeqJwAEwK4AONgPhocMgZsaAv8mliFw7j8EzmMZAv+GITBDYP8h8PDJQg6CVB0Embgckvhyt6r6BzF2V24FPQhSNblvcRAkD3sQZF37IMhjxTgcBNktMeEgCAdBng6CDJ9+BMAqALOrAyiDAbgICeAiGIDy6gBmAAiAAJgcgFlIADMABEAA7ByAAgABUABgMhkyBxgxgMtUABx5LA+AAOjXBSw9CgyAEQC4W3LZZQCX3tUDgADo1wUsPQ8wWQBXur1/5czZ34QBMMANilcVDwNyBlB43MXqZPNUGAD/1nmJlW7TVgCYWhew9Fq4VAHU7v3KmbO30QComgHQ8x41AQF867yEqrELAGBX+4Ba/wDwHMARALYbwBEAAuBpuBvMJhM7ABUAthtAZQfgBABJUgCKmAFcBwNQ+AIoggG4jhlA0fDuBoAACIDWAHqOyOIEMAdA2jcAxgjgJCSACgCbA1CFBHACgAQANXv/jQBUXQdQxQOgAEACgAAIgABIAFALYAGA7QSwAEAABEBvAC05AsDYAMwBEAABsDUA5iEBLMICWIQEsN7mASAAAmA7ACxuIsRJ2WU2DgfgOMTj2n03rwBAAATAVgCY30SIMwCzcABmMQCYAyAAAuA1AZw6AygBsGkApTOAUwAEQACsAaAEwC4AKAEQAAGwLQCKLgMoAJD2DYDRALjoJoBV98FzAVD5XuEcPYALACSJApgBIABmAEgAMBIAZ10HcAaAtG8AjAbALDIARdcBFJEBmAEgAcDLjJw5+yoggOPuATgOCOBXzkuMABAAAdBh739s8bPbAOjXHqMEUNwGwJm+7ABIALACQHE9ACfpALi4HoACAAEQALUNOyIARToA1tq8RgFUDe9uAAiAiQC4igbAIhSARTQArgAQAAEwNIDzkACKaACUoQCU0QAoQgI4B0ACgJq9HwA7D6ACQAKAFgDaPTU7LgBVWABVCwGcACAAAmAAAO3aKwBGBqAAQAAEwLQBlL4ASgAEQAAEQDcAF7cQotsALgAQAAGwJQCKukI8zVx1EsBJ/dOOBQACIAB2H8AAFyZMmwFw6g9gBoC0bwDsLoAqCgDzZgD0u0dNKAAVAAIgAF4FQAWAXQBQASAAAmD0AM7TAXAOgAAIgDcHsIgKwOP2uOoegCtPbpoDsABAkiSAMloA/drj4xqWoQAchQBQRQugBECSLIDT7gKoQgGougvgFABJ0gDKYAD+HQBeC8C/CwagBEACgCWvT505ywHwWgDmzktMARAAAdBh79+305YDuPYFcN1yADP9EgBIALDjAOa+AOYACIAA2D0Al00BuPABsAgG4DwsgPNgABY+AC6aAnAEgCQpAGVTAGY+AMpgAIqwAIpgAEofALOmAJQN724ACIDxAigBMEUAJQASAARAAARAAoB6zmZXBbDoLoDFVQGcASAAAmAAAJU1Oz4AymAHJaMF0IcbdwAVAAIgAN4EwJVnibwAFE0B6HWPGl8AVwAIgADYEgCVZ4mCADgLBeAsBgAVAAIgAAKgPYAiFIACAAEQAAEQAAEQAAEQAE2DxSAAerXHOAGUgQCcASAAAuBVAFw5AyiiA3DiB+AkOgCFM4ArAARAAKwBoBtncQIo/AAUHQBQACAAAiAAAiAAAiAAPu39KjoAVfcBVNEBqACQJAugAsCUAVQASAAQAAEQAAkAHrI/+ml/awIRF4BZWACzuAAUtksUmf5oOAASANTs/YdmJgGwzQBKwxIASAAwPIAFADYFYAGAAAiAQbJuDMC6l7Ll6QBY58ZaVZz5AbgGQJIUgPnR3j+NCkDVXQBVVABOPUsEgO3L4CkAaNr72wzg4WrZUADu1zXvFoA5ACaX3lMAsKsAqqYA9LpHDQACIAC2E0ArjgAwNgAlAALgBYBDhsAACIAAmCyAraigtgMoPUs07R6Aa09uJAACIAAmAqBXe4wTwBwAARAAAfDKACo/ABUAAmC3ABwMh8MBAAIgAAJgggA+ZgCATQC4AMCmAVwAIAD6A3g2FL673+Wnvd7PPowg/f4nDb/DZqf//OH/n29+uHz5082f/93DD589/P8zmxV+ul+R9RJuJbLPYQX7Nerz837/56HW1fDmHap1s/ynLkv8O80SwSrcIp/0+zG0q58lD+Bm9DsYXPQB759kfNlPIpud/s3D/99sfrh8+dX+z68f/v/aZoXuS5SU6At9iexzWMF+G6NY134FX9TcvEO1bpZ/FWKJil2gi3nJtcBPPUF6gFU9wA+v3gP8NFQP8M9D9wD/PFQP8NOr9wA/pAdID/AsA800YFpzgJun+M4Nc4CZ8xyg0xIlJRKh5gBl6DlAGWoOUHjOAWbOc4CZYQ5wc3nzjDnAJLuAw+QBFPr2CIBpACg8SgSALc4QAAEQAAGQHiAAGgG0vjJXhQJw3l0A56EAVLZLKAAEwJIwB1ix98+vDuAiWHuMF8DD5i2uDuAcAAEwGxx1AHsxV9DNAVT1Aax5NxcRrD3KpgCUwSpc1NsqVR9ABYAAuL0SrvQ8QADsIoDTMABOARAAuwKg5kqQ5AAUFe2xEwDKMADKbgIofEsEgK3LkGuBARAAATDdDIw3gwHAUs6snpkYFkCf9hglgOL6AK4BEABbWkFxAWjVHwPA2ADMARAAAfAmABYAGHrzpgAIgADYEgDzGwhRDuDID8BlNADmAAiAAAiAjgBKPwAlAAIgAAIgAAIgAAIgAAIgAAIgAAJg2RJFNACq0ACqaAAsABAAATBKAKUvgFn3Acx8AZQACIAAeAUA3TgDwGgBlAAIgAAIgAAIgAAIgIe9f/zwwyQ6ACfdBXASHYCbEo0BkCQJYKZvjzcEMPNtj0VTABYNVviNAAxS4QAIgAAYD4B5UwDmDVY4AAIgFRQhgNY3pxp5UqFSAlB5btXIdgkBgAAIgO4ALp0BPFCxAsCmAFzZbVUZgEsABEAAtN77ZX0ARQgAZyEAVGEAVCEAnIUAUNQHUAIgAAKgZu9fRQegzwPYogRQRQfgCgBJsgBWdUgAsPMAnpZoDoAkIQAVAAJgqAoHQADsNoBjAGwfgAsABEAADAKgzQTR6RKLWABc+wG4jgXAiTOAAgABEABvBKC4uhAaAHM/APNYABQACIAACICWAM5CAzgDQAAEQABsCYAiNIACAAEQAAEQAAEQAAEQAJsAsEgBwCkAAiAAdhLAkSeAu1ZadBXA4lBRPgCOABAAATBKAFUQAKVfe5w0B+DEr8J9Nk+cbBUAAiAANg2gG2fRACiaA1D4VfitAFQACIAACIAACIAACICne78EwHQBlABIkgVQAiAABqhwAATA7gK4uBaA8qREHg9gixNA382rCeACAAEQAD0AtL5b5tSZzMYBXIUBcBUNgAfOprZLZAAIgADoDuDaGcDceYnGARRhABTRAJjZ9WvLllgDIAACoPXenwNgtwDMARAAAVCz948AMD0ARwBIAFDTHgGw8wBKACTJAig7DuA4NIDjjgMom93fABAAWwygTffgdInVjQE8o7AugEfs3RjAlTOACgABEABvBKC6uhA6AIUPgCIaABUAAiAAAiAAAiAAAiAAAiAAAiAAdhBA1VUAFQDSvgEQACuE8ARQNQeg8qtwn80DQAAEQAAEQAAEwPIMdwFAAARAAEwLwMGw95ThAABvA6APFQDoslUACIBH/PXOM2h5BUUB4OyGAE67BuD0hgDOALDLAO75exwC738DQDsAl1oA3Rp+WAA9nkAZJ4D5DQEUWgCXANj6XI56H8fDAGgFoIoEwCIlAItIAPQ5MQcAowHwsrc3BMBqAJdRAZiHB3AcBsBxeABzj60KD+ASANsM4FAzMAZA6wGnCcC1M4BFLABmYQDMYgGwcAZwbQWgAkACgBrOLG8WN3FeAgBdt0o+lWnhvAQAAiAANgegAMBrAiiclwBAAARA271/3HIA1+EBXLccwDEAdhvArwd3d988+xoAawCY+3MWF4AyPICy5QAKc4kAsN25358C/e7brztQQQAYDMCVD4ArAATAVuToKpD3dwDo2x7POFu2GEDlA6BKBsC82f0NABsH8P39Q97teoHPATAogBbdg7MlRh4lmnUVwJkHNyNnACUAJgTgfrOef3Nf+zo4AAwHoPQokfBrj8vmAFz6Vbjw4EYCIABabuQ7boaQMoCyOQClX4UDIABeIy/e974z/4vBYACAEQI4TwHAOQACYLP5rndvfF1/txgAvCmAIgUABQACYLO5NwM4BEAABEAA7GDX7/7uId/3jEPgQQ8A4wew/gPYogRQACAAXqPr93gq4NfmAfAQAAEQAAGwa7l7v+Hv+2+fmwfAAwBsBsAJADYP4AQAAVCbF5sB8LsXxgHwMAPAZgD0oGKSFoATz60CQADUEve+9/65aQCcAWDVWXfunPkCKNICUHhulfBfwvfMRACMKe+OtuvF+963pgEwAKYC4DoEgGsABMDo0+vdPx34uNOeBjPYyXcB4Itnu/yg1/vx8wjS73/U7Btsdvl/v/3p15sfz18++uPfP/z0m+oVHi3xG7slSpb/9fmPdbJ5+79/+vFj07/9Sb//E9PrHz9tyt/X2apwm3dUqZbLH9VD6RJPf/z3ZbtA2Hz08E0TQX7c6bvBfLe/vOOdFsDHZyVdAHj/dDOZl/0UstnlX21/erX58fzloz++efjpdfUK3ZcoWf7V+Y918vph6TcXP9bL0abU2qpwm3e0KZbLVy1RsQt0Mi87C+Dg++3pL9/dDZ59e6+9G8Lw8SphAAwO4O8A8JoA/g4AAfA0u1NgHvONbgDcyzKGwCfjn6oh8Md2Q7+PnZdocgj8cfgh8Me3HwJ//PTZfey8xK8ddwGGwG3L87vv9/59px0ADwebDLc/pH4Q5GhO/vwhY0e35LO8XbByXqLJgyDq4sf6B0Gkx1aFPQiiLI9tly4xO3t5EezaQw6CRJMXd5u7ot59Y5goPMoQAHXtUd0SwCwogCMfAEdBAcxuCaCqIBkAux8ATAHA/BRA6QOgPAWwvhIACIARHCnZJ/kh8MINwMIZwKKWEACozdQZwMINwEWjOxwARpXkT4QWbgBaNHz3JQCw5lZZApi7ASga3eEAsDnMym/uPBgCIAACIAB2HcBe2RNANoNcAGwdgJOn9jrvFoBHh9UnAAiAYQE852x7y2cAbB+AmVMLbxOA6mzzABAAg42BH4/p7tMz3PH50ENM/KFIAAiAANg1As1nuLSqggAQAAEQAGsSOGx9BQEgAAIgADoZOHwcCHehggAQAAEQAJOtoHYC+BceVMzSAnDusVV/AYAACIChAByHA/AzDypUUABXux+XIQB8vJh4FRRAVWerHhf6LByAYwDskl7Pnj0HQFcAMx2A6xYDKJ5W6g2guhyjtw3AtQ7ADAC7khfD3SMx774GwDAAug39ADBiACUAdh3AF0+3Qx0+b38FRQTgzBnAFQA2A+DKGcAZACYC4OZeqO/u77e3tn8/AEAbADMrAIUzgMIXwGk3AZz6AiicARRWAGYA2PoO4MPgd/s09OffbCh8AYBtBlD6ALhoEsDa94w6LgkAAmCTG/btQ18QAK8NoIwFQHEG4NQHwPUZgLWVCA2gdFoCABMA8OmXb3UPRQJA3d6vugtg7gNg3l0AFQB2C8CjHfl73VORANASQAmAXQNQAmCHAfz6pNN3p30wOgDWA3DiDOCkhhAAqM3EGcAJACYEYHbf+/45AFpn5Qhgdes4B1DUECLP9O215QBKTwCFM4DCEcAVALa6C/i+9+6wae8YAjtwEw+ARRoAFlECqBrd4QCw6XyzeR769gTA59/V30oAvCWAMg0AJQACYDMCbk6Gfvfw37u2VxAAAiAAAqBTXtzvL4b7/rtva94WAQABEAABsK0E3t0/3Rb6++Hd89ZWEAACIAACYB0Ev3lS8FlrKwgA/QBchAdwAYAA2CYF3wNgugBm4QHMABAAW5WvB1+3toLSA1CmBaCss1UACICJVFA7AfwPsQEoQgAoYgPwPwAgAAJgMADXwQD8HACvAeDnwQBcAyBJHkCpAXB5MwCVD4CrJgGsfb3YcSVfH8ClBkCv2zMAIAB2GkC30z+OAMxuCqBqEsDaSgQBMKsLoAJAAATAegBmANheADMABEAALFdiCoAAuMsUAElyAMpEABT1ARSJACgBkACgF4D5GYAzTwCLbgFYeAI4OwOw+o7bAAiAAGgLoAwOoGt7Ogcw99m0+ADMPQFUwQGUAEgAUNMeCwDsGoAFAAIgAFoCeH4J2MyqhQNgRADOKi4JBEACgLYAKqsW7gvgMg0Al1cBUAEgAAKgRX8rHgBVGgCqKAGUje5wAAiAAAiAAEj7BkAAbBpA2QSAEgABEAABEAABEAABEAABEAABEAAB8BzAOlRM0wJw6rFVAAiAABgOwGUUAB6/yywUgIsQAC5CATjz8L0ZAJcASJIHUEUHoPABcHS8OSEAPK6zkQ+AIjoAfU7NBkAATAPAqTWAfxUDgLJJAGsrERLAv7IGsABAAARATwClNYCfloyuADAIgMfzFJ9aAygBEAAB8CYAyhpCAKDVVgEgAAJgWABzQ3u9EYCTLgE4uS2AQvMRAyABwEgBFAE2rfJONhUAzkIBKAAQAAEwLgBHDgBWt454AVT1AVQtBlA6ADgCQJIcgAoAAfCytwiAAAiAzgAKALwugMJlCQAEQAAEQAAEQAAEwGoAFwDYPQAXAAiAAGgFoPADcFQTQBEKwGUTAC5DAShqAjjyA1AAIAAC4DUAVLcGUDUBoLo1gAoAARAAg2Rqvu4CANMA8HhQPgVAkgyAOQACoN+sJAACYBoAKgBsK4AKAAEQAG8CYOEBYOYD4LpJANc+AGYeABYACIAA2ByA49AA5jWECAJg3iSAdZW4BFDU36ogAI4BkACgpnV0BkDpD6DsJoACAAkA2raOwqqFA2BEABYACIAAGAjA3KqFA2BEAOYACICXGQy3GQBgAwD+x5AAzrsE4DwkgP8RAAGwXoa9QwYAGBzAD0MCqAJsWjQAqpAAfgiAAOgB4KOCAAiAAAiAiQ2Adx2/gU5AAHz606QjAMr6AMqOADgBQAA8lRAAKwF0avgnAM4BsAkA57UBzAAQAE8DgJXdg/oACgBsAkARHMBJgE0DQABsJ4CritbRYgDnTQA47x6A+19WAJhYhgBoOuvOvXXMowJQNAGgiArAuc0Stt9xAgCTymCoOw8GAGu2DhUCwEUaAC5CAKiu/hEDYGf6fpfnAd7d7/LTXu9nH0aQfv+TRte/vW7j+Je/PHn5L7ecPebT4190+Xzzj/7seIlPnQp0+iabXz4PsWmfPfzymeEf/7zf/7nh5ZPFrerBVD3lRbSvnv0if2ZVPcE/Yq980u/H0K5+BoCPAJ5dC3L/dIb0y34C2ezwr45/eXPy8pvNn/a/vDr+RZfLJV45Fej0TS5LVHPTXj/88rp+NZ0sblUPNtXTr1k9r5yqJ/hH3IW8BMDttXAXXcBv7nb5Ya/3+w8iSL//otH1b3b4L49/eXvy8tvNn/a/fLn55VcVK9wu8cnxEl86FejL43f84A8XJaq5aV89/PKV4R9/1O9/ZHj5ZPHTIrplUz1/KC+iffXsF/kkt6ieXzl/xI3ucC/6/Rja1e8BkIMg2fmZL5dTSu5z9pdzgG6TXKezULL+HOC42TnAcf05QJnpZ+ScjhFZzQEK5494whxgQtmMgtMFUHQXQNEsgDXvUdMGAEWTexwAxtcFBMCIAFylBuAMAAEQAAGw7B3DAaj8AVTNAKjqbxUAAiBDYAAEQAAEQLcMjjqApWdCA2A0AMoQmxYLgBIAATCKft/2/L/tlSDDmCvoqgAWoQFcAGATAC5CA1gAYHoD30OirqCrAihDA5gBYBMAZqEBDHJ8BwBblKdb4g/jrqCYABzbAvhbALwOgL+1BXAMgAB4msHmSpDBIPYKignAzBbA13ECWNQHsIgTwNe2AGYACICtrCAADAdgXh/AHAABEABTAFBetI6pJ4BuLTwsgJMmAJzcEEDlCeD0YgkJgAQADQC6XbkVF4BZEwBmLQZQAiAAAqAHgMqihQJgRAAqAARAADQpsQBAANxlAYAkOQCzkAAuAwD49I6jLgI4MnDkDuAyJIAZABIA9AFQBgVQ1Qdw1iyAs3qlOgUoBIDSZQkABEAATANA1SyANW/RAIAACIDtAXAEgN0DcASAAAiAVgBKAOwegFUfMQCSNAFUwQFcA2B4ANfBAQxyfAcAAbB1AKqGAXRv4aMLAIsQmzb3B3AeAsDiAsBR/e+HhgBUTe5xAAiArQVQXgFAeQFgHmLThD+AIoQS+QWA0nmr3AGUAAiAAAiAAAiAAAiAJgCnAJgWgFMAJACo4SYEgG4tHADtqycIgDkAEgC0BnBp0UIBMCIAlwAIgAAYDEBp0UKjAbA4BXBSF8CzOwAWbQJQAiAAAmCaAMpTAEVdAM+WlgAIgAAIgLr29gYArwPgGwAEQAAEQAAEQAAEQAAEQAAEQAAMCqBbew0L4KqLAK5uCKACQAAEQA15s0gAHJ3KU2/TZLMA1rxFw+mKRpEAOANAkiyAhYEbXwBVrRauUgHQs3qCARjkDB8ABMBWAiitAVxatLcpAF4XwKnFEktrACUAEgDUtAeb9poD4HUBzJ0qFAABEACNAE6iA3DRHQAn0QE4AUACgDolpgEAXPsCWO8OxVECKHwBXAcAcFqxaQBIAPCJs9PWU8XZJYB5/RaeAoBu3w+5M4Dri48wB0AABMCaAOYWLdQHwLwZACf+AE6aAdCjeqwAzAEQAAFQk2UqAGb+AGapALhsco8DQACMCEAJgAAY6AA3AAIgAAIgAAIgAAJgFACqZgBUAAiAAAiAAAiAAAiAANgSAOd1AZwDIAACYOcBzDoOoKoLoOo4gBkAEgCsBHDuDKDwBHDcRQDHngAKZwDnAAiAAOgNoLBsb78LBmBWH8BpswBO6wOYBQPwd5YfiABAAATAqwH4KgYA82YBrHePmsAAvgJAAATAsADOATAlAOcASABQp8TpIyxqArhwbeGrVAB0fuTJwhfAi3dUAEgA0ASgOG2+Y2cAnQA7W6DbADp3kIUzgOOSjxAAARAA6wIorg5gvbuTRAmgujqAAgABEABNAKqQAE4A8NoATkICqACQAGB9AAUAXhtA4bAEAAIgAAIgAAIgAAJgJYCTqwM4bgrAqS+ARVMAjq8O4AQAARAALQAUVwdQNAWg9AVQNgVg/eqpC6AAQAAEwBIW1h0DcNYMgLOOAbgGQJImgGtzN6ntAIpmABQdA1BqPQRAAOw0gLkTgBNnADMADA9g5gzgxAnAvMk9DgABsLUAZgDYTgAzAARAAEwewCUAAiAAAqARQBkVgOu6AE5KAJR1AZQlAE7qAriOCkAJgAQAHQCcOQM49wBQ1gVQNA1grVs0KM8VzZwBnAEgAAJgQACVM4AugAGgwxDaBkAFgAAIgAAIgAAIgAB4FQB/CYDXAfCXAAiAABgdgH1PAMenJVp2B8Dl6YrGngD2ARAAAbBzAGbWbrUNwPNSACAA3iiD4TYAWAngAgC7A+ACAAHwIcPePkMAfPp1VAZgBoDdATArA3AEgKml16sQME0AFQCmCKACwPQAHA72PcFB4gDO7AGcVnK2OgOwAMDQABZnAK4clqgEcAaAaQyBj7qCw8QBFPYAVp+Uos4AdD2NZZUegCtHAOUZgMphiUoABQAmJuGDgAAYD4AqKIAGCJwBVB4dNyOArtUDgAAYdDAMgFp+ALDzAOYASA8QADX8zAGwiwDOARAAnzqAQwDU8ePOURmAIwAMBeDIGcCqdwRAOoDH+eZulx/2er//IIL0+y+aXP1md//y6de3m98/0P/+1cOvXxlXuF2i/4nDEiXLH/3+nxyXP+TLkk0xrOijfv8j/aubrXirrzb7bFb0n85W9NZx+aet+KRfvfz5B5CXbMpbfbUFz4uHr/QI8nsA3GRwcRbM/dMJgi/7nc8ft/duefr9zZYv/e+vH359bVyj+xLm5d84Ln/Ifw61ov1WvDn6fbPu/xxqRW8cl3/ttHzVEme/b+8v88fu7/kvAfDRv7MBcFoAvuougFWb4pTc062WAfgKAFP1L7E5QHGVOUCXOTzlNnXntqK87hxgxcSZ2xygz4rkVeYARYO7HHOArfAPAAEQAAEwWf8AEAABEACT9S9RAFdRAljrtIw4AcyjBHAFgPgHgFn5yXMA2HkABQDiHwBaAKisAPzDEYDLGgCu0wFwXQPA0RGAf7ACUAEgAJ5meyPAfQAwLIBfHQGoagAo0wFQ1gBQHQH4FQACYF0ADwHAk98XAJgOgAsABEAA1P0OgF0HUABgkhkcBwBNAJ5zVLQHwGlTAE7bA2BhfkcAJFFXUHwA5s4AugAWFECHFbkBKG8FYO4MYA6AAAiAJgDHMQG4bArAmS+As6YAHNVevgEAxwBIEgMwCwmg9ARQNgWg8AVQNAWgrL38DkAZEsAMAAkAAiAAAiAAJg+gvDmAq+4BuLo5gBIAARAAs8tnfsQHYO1btMumAax1iwbfFV0HwDkAAmASAJ7ztADAFAFcGP49AAJgOgBmHQdwUQ/ARccBzACQAKAFgKuWAyjqAShaDuAKAAEQAGsCqJw4OgdwFgLARVcAXIQAcOYMoDj7yAEQAAFw3xoKQ3/BH0ARAsA6RyWjBFCEAFCEBPCiTz8FQJIUgNLw/T8FwC4CODWMASQAEgDUjIe2DXgCgO0BcFIGYA6AAAiAZe3PBkBRtca3AHgtAN9WLS/qACgb3OUAEACTA1C4lcjtHVsNoOPdwgQAAiAAxgxgEROAo6YAHMUEYAGAAAiAkQCYxwSgw4rcAFQxAZgDIAACYGMACgDsEoACAAEQADVKAGDyACoAJAC4yxgAuwngGAABEABLTvs/ZUPUA/BvPQA8n3UchwIw8wUwhBLnjyBwvVT6AsC/rQeg0G/J+cOkABAAuwtg7gjg2ArALwMCWPsGnUXTABZ1AcwCAvilFYBjRwDzBnc5AATA9gJYydEiGgDzpgGso0QzAC5c3hEAARAAGwNQnAM4AcDQAE7OARQu7wiAAAiARgBHp41l4QVgBoChAcy8ADy7I9cIAEnaAM7PAZT61gOArQfwrB4uTvubAyBJCkChB3BV2nrU1QFUNTfNYUVGAFUoANXVAVSlH+FKD6AAQAKAptZTCeB/OQdwBYBhVrQ6B/C/1ANQASAAAmDJQY4gAH5wDqADYADosPyH/Q+aAbDBBwMDIAB2GMAVAF4fwBUAAiAARgGgAsDrA6hc3hEAARAAARAAARDlALAaQHl9AGehAFw1BeAqFICz6wMoARAAAfBpZ1+ct5ebAyhCAeiwIjcARSgARQwAniy/AECSFICZHsBlLQALALwegEUtAEd6ADMAJKkAuKoA8PLuwNKivUkAvB6AVh9Ipp/lKAdw1dw+B4AAGA2ACgABsAzABh8MDIAAGDmAaw8A5QWAa08Aaz6oe9I8gIt6Fe5z3cXpx7MHUHoAuAZAAoCav4QA0A2wRSgALw9mrv0AXJvX7gPgou7yAQDMAZAAoAHA0UXrWTYIoGgOQOkHYJBzRXxX5A7g5XGsEQACIABaA6gM3QcAjB7Ay9cVAAIgAGrGRwCYPIASAAkAGlpHVXtTFwDaP0Ct3K1lVwBceq5IXgCoagFY9REDIACmAOCoJQDWeAJlnADKlgA4AkAATABAGRzAIm4AR/UAXMYNYHHVjxgAARAAdcnjBlDWA1DGDWAOgAAIgEEAnANgegDOAZAA4FODPGkdKwDsFoCri49YACBJFsBlBYCnrWPZKgDHTQE4bhWAYT9iAATALgGo9K3j8nraTFkAuIoGQIeejRuAWTQAriwALPmIF/oNUQBIEgFwbQZQ1ANQAOD1ABT1ABRmANcACIAJAJibW4c7gItLAJU7gA5utR3AzB1AdQngojaAmo+4wQcDAyAAthzAdVUHDgCvDKBw7uQDIAACYE0A8wYBvFz/smsALis+grAA5gAIgADYYgBrzslfrmjkB+DIwy3DgBQAARAAYwYwc2kdGgCnMQCo/AAMcs8o3xVNAwCYASAAAuChKayCA7i4ANC+PV1e2hoUwKIegEVzABZOK8ovAFwEB3AFgCQhAIUewHk9ADNPAGVzAOb1AMybA1B6ApjVA3CuB1AAIEkDwEUFgMoZwJUvgOU36KpxWlqcAK49bz6lAXDlDKCqAHDR2E4HgAAYC4AiOIDKF8Cqa/dbDqDvvVc0AKrgADb3ZHQABMCIAcy6C6DwA1B0F8DqvQIAARAAN5m3HMBFHQAXLQdwDoAACID1AJxmDt2oMACqBgEUdQAUDQKorgDg2UZPARAAtxk8JHkAx2YApTOAhQ+A6xQBXNddfgNg4QygNAM4BsAUMhz2tkkewJIGM/MCUPoAmKcIYO3q2QAovQCcaXYBAOx6ej0A1AGojlqKN4DidgCe9qwmfgBOKnqqVwNQhABQGt4eABMBcNsJTBlAVRPAsXaNMioA5eW6V3UALLk2QkYFoH4ScVwTwOYeDAyAcWQz+QeA9QAUzQI4axBAVQdA1SCAs2YBFAAIgNoAYJQABrk2vy0ACgAEQADsOoBjyxKJNAG0nXFbACAAAuBVAVRBALRt4eGuzS+5j+rUB8Dp5YYu6wHoceGZCAKgAkAABMCs/Bw0fwBVFACWuCB9AJSVq78RgCo4gGsATBjA+94hL/sdz5uHPf312d82DeLN48//cPTzY15tXn+lXeNr5yVK/vEfL//kvm2vL7et5E/XXtdlXfzRuXpeVX+I1Uv8w9HPefWH2L28BEAALGs7x+jlzpzlIQDspwRgPwSAee0ljjE83rZfAGCiAH5zt8sPe73ffxBB+v0Xja37q4c9/auSv719/Dk/+vkxX27+9qV2jbslXvQ/sV7iNP91849L3jHItpVt7iEf9fsfhVrXB8b6+fLyT//VcvHzuvzkYed4a6yfsto/XuKtZhf4qrGd7kW/H0O7+j0AMgdYNpF1PFFWMhtuvpzicYn6c4BKc23+OMS2GZ+KZJoDLLlpab05wIXm7hO2M266OcDcvMREX8lKswvIxnY65gABsMUAZrcBUITYNuUDoAqBhLgNgBkAAiAA1gNw3i0AizoAFt0CcA6AAAiABgClAbtqAFenAI5dAVw3CWBeB8C8SQDXrgCOTwFcOQN4/DcJgACYNICqBoAzI4DiFMDMFUC3a09aD6B0BTA7BdB8nuSsBoAKAAEQADX0GEdsY18AZZoASpflywAcO8wpnJQCAJPFb5PtPbGGw0GiABahARRxATiqHg5aA3hWglFcAIrQABYA2PH0jjJMFMC8wwBONZfxLdwBXGguJ5t2GMDmnowOgACYHoBzBwCXQQDMHa9jNgCou57WHYmyNS0dAJwDIAAGyuAoMVdQNwC0neWXzqdetw/AktOSbQFUAAiAiVXQrQFcOAO48ABQd+q1qrVts+YAnNVCQlWcllwHwIUzgAsABEAALEfiAsDMhaPHJSIAsIyFiQ+Ak1LqIwAwcwYwqwBwBoAkGQBFph2RrZwBnEUDoHb4vnIHcFUxjIwAwJkzgCvtnEPdOzACIAC2C8BJBYCljcd4W2XVBIAyKIDKHUAVFECfAacWQOMnUhhqWQvgBAABsOMAijoAysYBFPpBueO2ucxfOgK4qAVg2aaIxgGUdQBs7MHAAAiAAKjJIhiAM9fhuyOAFZcEugJoOZsIgAAIgM0DWNwKwNIS1brownn4XgHg1AVTI4AjD27CA1gAIAHA8jZWD8DiHMCpJ4Blj26qB6CsD6AMAuDak5vzGb0tgIUPgDkAEgDUAyhtRnHnze0UQBkAQOeDkqVqmspuALB0sVqPTssDACjPATTWr9R9hgAIgABYIsvtAZyEAHDkWnZXAMtGs7UAnEQHYAaABABrILJ/sTaApWce1jovV14DQOeZydIjJ6azE20BlM71MAJAAEwcwFkFgPLqAJZ29mpddFFazFF9AEchACw/dyZ3q59AAMoKAOdN7XUACICRAKiuB6D0KFGtKalSdVV9AJ3WZexy+wAorwegamqvA0AABMDGASx0aBXuADqvCwABEABTBXDkCeDUbuBYkVyHVu4OoPO6jABeDOanngCOABAAATAUgKtTAN3mvh4Hi14AylKAXKekogRwXrqM9ARQOQO4PAVwBYAkVQCL0l6KoWU2CqDUAujaHksbdkgAVzUAVFoAa9ZPTQDVKYDCaswPgADYQQClAcC18+R/HguA5bNtoj6Awu4dbgVgXvGVdFmOtWHbJAASANQP/a4M4DoogAtXABdBAVxHAmAOgACYOIBSC+AkKgBrXHQhnNHSAyiCATjSbt6tAJxoAWzswcAACIDRAyhuCKDKArTH8sFuSADrXC5RviHqhgAKACQA6Apg4QSgw3Mfp6EAVNcBUAWocJdHDJ8/NbQawAIAARAAAwOYmwAU5wA6nDJcjooKBeCkPoCTUACqzKlGzZxtARRVnwgAAiAA1gTQ6VQSPYCWDTz3FaJiEcN9B/QArvTrcgTQe/PyMACuABAAAbC8Q3IGoHBpruNSAGc3AlA6oaUHUPP28kYAzkoBHLu8pagAUAEgAcCFM4CiFECH46XlPbS5O4DyOgA6KlF+SYv9KdUXNfkEoHAGcAGAKJc2gOWHHA69jPLGMWsQQM0cXY3HNEYJoPfm1QRwpl9P+afpcFgGAAGwtQDmWgCVHi5TcysHcGJ9x09hEMLtjBPNqYPTugCWcOD+rCbvzVudU1kJYNVnqLQANvZkdAAEwKgBnIYG0P5wQTgANRePyLoAyvI/uz2ryXvzLmAKAuAUAAkAXg7tDOe/zQ3NbXIBYOEJ4NgdwFwPoHQFUOoBdFNCc7TCDcDiAkDTyT3zivMh9WcmAiAAAmBZezX05/ZHF88AtL6UTXc80/0h5FECqJk+tff9YtS9BdB0TUp5IccACIAAqOnLHboZmvPLDPNoMz2AVrNlujPa3E+503RTQwLofmxaGTbPCkCpB3Cmf8up4R3LO+dzACSJACj0zVQ4H/1U5QBaXws3DwWgblQ4qgvgSD/eDwOg1Q1fz6+EOwJQOeF9qJ7yRQUAkmQBPBxqVKEAtB5R6f7h1BVA3bSaqgugsn8P8+ZNfXy/+Ic+AKpMe4AeAEkCAI4rDkpqODJc2tsUgBc9Hx8AC1cAi1AA6nrCDQKoKft+CdNx6TEAAmCnAaw65moAMHcC0PrBviYApfOmjZ3KrgdQ44v7sWnpCeDlpTmVAOYWAPoclwZAAOwagIcpKY0WK/3c136MVwagTXvSjVCdAdRdrhISQPdj09KwearWB7YDUD9DoDsHfb9JmklXACSJA6j0Whhaxx6wMwCt+0q6MaLztanqWgA6zUzqoLMd4V/213YA6gEN/xEDIAB2HcD1Y3vUzNmPnQG0PswpDQA6PYRcB52oC6AIAWBhANDG98v+mhWAJVMB+z7jsvxqFgAkqQC40LdHZZiymhsBKwPQhgoTgE5HJXXHWw2zkVoAtc9ldz42nXsCqAwASksyT/uimiUXAEgSAbDk7yMLAJUTgNNrA6gbSxu6NloAtcs4H5sOAeDUCUBlAeDIodMLgADYHQBXFRNluna1dgbQtoXrxnLO56XJawHoNDOpW5FyqB7pDODasCbT9Oaqod0OAAEwDgBVTQD17c0XwLUJQJceSZQAChOA61pbVQVg1UcY7PgOAAJgZwDcT5TpWs/I2N5GJQDa3mAzDwlg2eh0UhfAicM4uxaANh3cy5mEHYDVH4gGwEWw4zsACIDdAlDUmZHbD2HLALRp4cEA1E466s/d0wKovWO9632TvQHMNQDqh9AVs44CAAkAnmdRG8C1BsC5J4DOc1LGFSk3AJUJQJeZyZXvii4Pvz8BuK4N4AIACQCW7P66QxIr7bkkuQZA22tLtSfYuDbIKAHU/nvL74eSEzCfACxdfqH74njsM1btAQAIgB0HUNYAUD8gNQJoMYStXLELgKumAVyFAtDyILdwBlBUHHfWLigBEADTBfBx6lx34cLYGUDLxyLpV1y4NUj9iqb1AJxqeRm71XfhsaKSi7BtABzrizIy7QEACIDdBtC4+8s640gdgJY9OH1H0bFB1lmREUDp9i5ZIysqca4CwKoXZMVXIAACYIcB1O7+j1eIRgagwxkndVakBVCGAlBGB+Bady2LbPDJ6AAIgJED+Ng8tGpprwHbN+QLAO2uGgsL4KRpACdXBrDkvMMdgNo5xKXPJwyAAJgogPO6zcMIYHWD0h8McDzneG48UzEUgPbP8qj6FrADUDoDaPMVNwdAAoCXEI31zaPyVgMXANoBNtO65XjOsf4ElVE9AEeZ01RAefQHYOxurVoC6BGATrdr2H1DjEP1uAEQAFsK4MgwJNM2j6pLSC4BtDtlThkBdDjjxLyiGgCqEADmnisq+VcVAGrXu+sz6ofeIwAEwCQALG0e28mt2aTdAK4dV6QFUK/Tut0ATmbaqVIFgADYdQAnFQ1yrgVQdwWVHsCV1TN09To5nnPsfoO8WgA6DhT1J0NaAVh2MqUZwIX5E5xXfOFMmtnvABAAowBwpW+Q2/OO19r70Osa3EwLoN1xTv1Mn+M5x1ECaHiUgNUNY8vq8AjAmf3n9PgJr/VPGlg1eENAAATAKABc6r/lNy170yg1By11l5iO9rp4ACidyG0TgIZtkH4Abos40jC20H/4U235J7nr3a4BEABbBqB+9982yNzQCTA8bXZUCqDdGSMyJICGpwS5Aygcwa4BYOWKys7teQRw5PwE59X+EzbsAVMABMDuAjg2mKQeW4fuSWzlAK4OI7FyACv7ONLcI7EHMHd+TJoewIqH4NnPTApzj7sSQKUHcFb+ZWUqX/H4ESuDtuNGdjwABMAYADTt4nsAlwapRoYx9SWAUz8AHc84yZ0flKsHUIQC0PCvrQGclgOoGbGaTmZZmgEcO57kDYBtzGD4kEGiAJoGOTPzCFjTYIvDXy8BtGrihkvwuw3gyLZ2ZDmA29cKJ1f3Y+CZ+wQJAHaEv94uwyQBNE5zi13j0E4ClT5PWzx1GuoBuDAo5w6g0G+ZcgFQVawsBIBKf7TCDsDyU5bWpiMZ091nLEw9xEZOhAHAiPwbbglMEUDjiQ7CODzStOWjVnwJoM2Dz5aGHonT/bBMh0y2U5sTewAnhd4tt0MzhkMmM5uDrmWnXe8BLP/uqP4M9cVv7kQYAIwjj32/ga4P2HEAzd/wu8ahnQQvvdnA9Mm4cgBziw7g1GnQXQPApU4FDYDKYJMbgKZNmFp0AXMDgFsdp2VLaOfxxrvPuNYIAQC70QE8/SEtAM1zPOYRcOmx1PFRA70E0OKxF6YO4G7G0nZEpgx6b3t0ZV3AcgC1//x8k6vnHEw1btMFLOPsAKDSfSIiM4+BjV5PAbCzGR46fg8ADpIDsOIo39TctMu6PsdHlS8BrL6Uw9gB3J3pZtkhmRlbttJsWjmAylgRud1tXJ58H2W1u4ClnB0ALPs8Kzqoyvwl19iJMAAYywh4cE5hQgBW7N7S/PKkpLkdD8I0AKraHcDHWUmr3ta4MGKp69OVAmjsAD6WubBSQhln3Cy6gMoI4PEExMlnPDGLKut+RQJg+wF86gv2kgOwYoAzqhj/bFvzaHHegVtqAVzsLjtY1OwA7s9bs+ht7Y5arCdmSZZ2AC7N7E7WuRHI817p0jwlYegCLnYX5yy0AC7PX16M8opph6n5wR9NnQgDgDFkEBZA1VzevHkbfJ1LWdEcRQU2u/mj4mmNo/XxUcNLALcdxJMlziKrfNu15+pt25m0qBJSni/38Zs3Hx+XZ5sq3xY7batLlecVjxnaCjkd6ZbfXbhxcRz9CcDtUdv16HyJacVbioqvHLkMvvO9ffOmweYCgNZTgL3LzuAm39zt8sNe7/cf2CZvY/7GsEH/+PZL0/Z+WbrCf9q//KL/ycUK/6m6QH8wveWv/s5h0/7RtKa3btX01rSuf3RY0d/9yrSmP1Sv4J8uNuuT/ov9j+X1a/4UjR/y37Ryp7Zusr8HwHIA73uHvOzbppX7yi/79fPfXpes8BemJX7515UF+sL4lr/8rfWWVazoH1xq6R/M1fSF9Yp+67uivzau4BclS7z+bx4f8S9buVNbb95LAEwcwDd9r3xx6dEfzUv8rkKw/17xjn+0FfAXVUV3qaYvKlb2C1v/Kmqn/98rlv9dRe1cLvGF3yf8BgCTAHAQYA6wZXvJVCrlfYbDRBVPa5QPa1wczXN/WLrEstCXSC4rjyWMR7Jqywr5UJLqY+DbCb6ifPHTVB8HVaVrOs1ajirre7I8TDuWFKy8dj48OkK22ExcHi2hvC9kGz+scdqyXZs5wJscBGndUeBmowEw6mjvBxhzPmzlzsFR4AgCgAAIgACYMoDDA4BDAARAAATAhJL4pXAACIAAmDKAg717wzRvhgCAAAiAiY+BNwIONR1AAARAAATAjgtouCU0AAIgAAJghzNM+Zb4AAiAAJh6BvpnIgEgAAIgAKYbAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAARAAKR9AyAAAiAAAiAAAiAAAiAAAiAAAiAAAiAVBIAACIAASAUBIAACIAACIAACIAACIAACIAACIAACIAACIAACIAACIAACIAACIAACIAACYJD8j17vp/cR5N27/3nftvzPd/+rdWX+3+/e/e/WFfp/tXLneBdDMX7a6/0PlDPkBz1CSIfzA5Qz5P/86U//N4Zvql7v/7XuS/7/9f7UujL/NJIev1P+1MqdoxdDMf7vn/70f1CuBen17lpX5rvePXO+18h9K3eOHq2aACAAAiAhAAiAAEgIAAIgABICgAAIgIQAIAACIAFAAARAACQACIAACIAkpTx79nXryvz1sxetK/PzZ8/ady3wi1buHFyDSwghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIaSrGQwfMtC++pAWlXn7wnDQhsqNq6A2JdtV7rBVZT7sxTR0UrprPD68RbNbDzevtaXMg+HhWTSD2Ct3GFVBbUr2VLnD1pT5MXEWmsTSRHe7j74Ft6XMu78No4HFULnDw0uDGC0pK9nRo86GbSnz8cs0dlL63Th8bKpDzVdndABqyzx8bACDSAqtr9zBY1sdRle7+pI9bMRgz8mgJWU++hYHQFK+b5z+cCFKlE20vMyHiZ5BFG3UULmHBhldy9SXbHjxT+Iv8+GvAEg0g4PhYS8ZlOw6wyw6ACvKHE8bNRT0UKnRdQEtStayMm++xQGQ6HadwXlrPRtSRgegucxVr0RR0KOGGln1WpWsVWUebOoeAEnFrlzy5bnddaIEsLIr0osEQE1Bj9pjZBNqNiUbxgegoczbwgIgKcvAiMnuL7EBOLAAMIqJy4EtgMNoMRnG++1iW+bdgTEAJFXf5WUnlQwiBNBY5piaqKGgR+WLrGlalCzGKUBtmXejGAAkzpg87jptBDCOs2A6CuAgurNgTGV+rHgATD33vfNUYbL//XaYPLso8zMrACM5Ua2bAA7iO6XOUOb9maEACIAVAA4up6kGsQOoPXkxii6KoaDtBTBC/wxlPtQ7AKaeb+7Oc9Ywz2Z2tgOdbXY/3KLMX1+U+eus+iBINBcqdPEgSIz+Gcq8+XW7Ew+3P8AAufzyLG+jw5L+Yuxljsu/Lp4GM4j1TgiaMp/txHQCiXb0cDZIiBvAoXaQFtOFqvqCPoE4iPak4kHpiaExIqIvMwAS2y/PczgG+9xuCOxc5sgu1Le8FC6uZmko2SBWQ7RlPuzEDIFJaQ7nNBy+RS9ueBnt/UqeyjzYFzquG5UYKncY7c0QLkp2qNxo/SupzfO9mIMgRPvl+XimvO6gb5S3wzot8/DooHZv+JhBzJW7x6QX5dfLScmGR+dDHSp3GHeZL3ZaACSGRno8QdICAC/KfAJgTBM++sqN7d7Vp7MIxyU7ATDGOeGy2gRA4rjzDLP2AHhe5mgBNFTuIEpJSkrWBgAvahMAicPeczxevDjgEefzZE7KfCjj4CjRV+4g1ucLnZWsrHIHLSnz0R9o54QQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQjqSb3u97w6/3PV6d1QJISSRPH/fe//14bdnvd49dUIISSTfnfT5XvR631MnhJA08iDe++dHv/d6vefUCiEkwQ7gFsBn1AohJIU8fwDvawAkhKSYb3q9d9sf7u/vAJAQklTue71vN///ej8SPu8REkJIV/P+scP30BP8ZvP/Z73ee2qFEJJE9h2+7x4hvDs+K5oQQjoO4OMIeAfg973egFohhKQC4Itdx28L4DeMgAkhyeTd9uDH5mzozdD3xXs6gISQZPLdQ9fv7u59737Ye7/5P1cCE0KSyfOHLuBDvn/+bPv/3ndcB0cISUfAu+977+4e2Bvc994PGf8SQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEELIdfP/AR2es/ErXdicAAAAJXRFWHRkYXRlOmNyZWF0ZQAyMDIxLTAzLTAzVDE2OjM0OjU0KzAwOjAwgGbizgAAACV0RVh0ZGF0ZTptb2RpZnkAMjAyMS0wMy0wM1QxNjozNDo1NCswMDowMPE7WnIAAAAtdEVYdGljYzpjb3B5cmlnaHQAQ29weXJpZ2h0IEFydGlmZXggU29mdHdhcmUgMjAxMQi6xbQAAAAxdEVYdGljYzpkZXNjcmlwdGlvbgBBcnRpZmV4IFNvZnR3YXJlIHNSR0IgSUNDIFByb2ZpbGUTDAGGAAAAJHRFWHRwZGY6SGlSZXNCb3VuZGluZ0JveAA0NjAuOHgzNDUuNiswKzAvndwyAAAAE3RFWHRwZGY6VmVyc2lvbgBQREYtMS40JDFqVwAAAABJRU5ErkJggg=="
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},
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"dosN100.png": {
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"image/png": 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"
|
|
}
|
|
},
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "b2049bb4d5fb56c59e7d0e742a91d3c8",
|
|
"grade": false,
|
|
"grade_id": "cell-7560c4658b1da5d3",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 3.6 [3 points]\n",
|
|
"Use your density-of-states routine to calculate $\\rho(\\omega)$ for $n=10,20,40,80,100$ for $\\sigma_\\rho \\approx 0.005$. See below for two examples with $t \\approx -0.195$ and $n=10$ and $n=100$.\n",
|
|
"\n",
|
|
"Hint: if your plots look like they are smoothed out, try decreasing $\\sigma_\\rho$. If they look like there is a lot of noise, try increasing $\\sigma_\\rho$.\n",
|
|
"\n",
|
|
"$n = 10$ | $n = 100$\n",
|
|
":-: | :-:\n",
|
|
" | "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 14,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "10cb847540f9e1998c9c1b40c5e43a7b",
|
|
"grade": true,
|
|
"grade_id": "cell-c3083a03553a2aa9",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 1152x1152 with 5 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"\"\"\"\n",
|
|
"The resulting graphs look similar to the examples,\n",
|
|
"but there are some notable differences.\n",
|
|
"* The maximum values seem to coincide.\n",
|
|
"* The height of the peaks seems to decrease in the example\n",
|
|
" for n = 10 whereas that is not observed in my results.\n",
|
|
"* The oscillations in -0.2 < omega < 0.2 are more\n",
|
|
" pronounced in my results. Tuning sigma did not seem\n",
|
|
" to help.\n",
|
|
"\"\"\"\n",
|
|
"\n",
|
|
"sigma = .005\n",
|
|
"w = np.linspace(-.5, .5, 1000)\n",
|
|
"\n",
|
|
"fig = plt.figure(figsize=(16,16))\n",
|
|
"\n",
|
|
"for i, n in enumerate([10, 20, 40, 80, 100]):\n",
|
|
" H_tb = TBHamiltonian(n)\n",
|
|
" # TODO: Decide whether to implement this + 1 - 1 trick here or in QREig above.\n",
|
|
" E_m = QREig(H_tb + np.eye(n)) - 1\n",
|
|
" DOS = getDOS_ED(w, E_m, sigma)\n",
|
|
" \n",
|
|
" ax = fig.add_subplot(3, 2, i + 1)\n",
|
|
" ax.plot(w, DOS, label=\"n = {}\".format(n))\n",
|
|
" ax.set_xlabel(\"$\\\\omega$\")\n",
|
|
" ax.set_ylabel(\"$\\\\rho(\\\\omega)$\")\n",
|
|
" ax.grid()\n",
|
|
" ax.set_title(\"n = {}\".format(n))\n",
|
|
"\n",
|
|
"fig.suptitle(\"Density of states $\\\\rho(\\\\omega)$ for different chain lengths $n$\")\n",
|
|
"fig.tight_layout()\n",
|
|
"fig.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "69c457b9ef8fbd13ad935fe12c37c81c",
|
|
"grade": false,
|
|
"grade_id": "cell-362439917c95705f",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"## Step 4: Tight-Binding Propagation Method\n",
|
|
"\n",
|
|
"Now we turn to the time-dependent Schrödinger equation\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" i\\hbar\\frac{\\partial}{\\partial t} \\psi(x,t) = H \\psi(x,t),\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"which has the formal solution\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" \\psi(x,t) = U(t) \\psi(x,t=0),\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"with \n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" U(t) = e^{-i \\hbar H t}\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"being the time-propagation operator. Within the propagation method we can calculate the so-called local density-of-states\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" \\rho_{loc}(\\omega) = \\frac{1}{2\\pi} \\int_{-\\infty}^{+\\infty} \\, e^{i\\omega t} \\, f(t) \\ dt,\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"with respect to an (arbitrary) initial state $\\psi(x,t=0)$, where\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" f(t) &= \\int_{-\\infty}^{+\\infty} \\, \\psi^*(x,t) \\, \\psi(x,t=0) \\, dx \\\\\n",
|
|
" &\\approx \\int_{-\\infty}^{+\\infty} \\sum_i c_i^*(t) \\phi(x,x_i,\\sigma) \\, \\sum_j c_j(0) \\phi(x,x_j,\\sigma) \\, dx \\notag \\\\\n",
|
|
" &\\approx \\sum_i c_i^*(t) c_i(0). \\notag\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"Thus, the time propagation of an initial state towards positive *and* negative times followed by a Fourier transform of $f(t)$ yields the local density-of-states. To obtain the full density-of-states we need to average $\\rho_{loc}(\\omega)$ as follows\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" \\rho(\\omega) = \\lim_{S \\to \\infty} \\frac{1}{S} \\sum_p^S \\rho^{(p)}_{loc}(\\omega)\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"over a variety of *random* initial states $p$.\n",
|
|
"\n",
|
|
"### Task 4.1 [3 points]\n",
|
|
"Implement a function which calculates the exact time-propagation matrix $U(\\tau)$ for a small time-step $\\tau$ given the Hamiltonian $H$. For simplicity, set $\\hbar = 1$ in the following. \n",
|
|
"\n",
|
|
"Hint: Use Scipy's $\\text{expm()}$ function."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "6cb01e4b3c6c192a0df3c4111b91c8fa",
|
|
"grade": true,
|
|
"grade_id": "cell-42a7aac3f0fa4d1b",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getU_exact(tau, H):\n",
|
|
" \"\"\"\n",
|
|
" Calculates the time propagation matrix for time-step tau.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" tau: Time-step numeric to calculate the time-propagation matrix at.\n",
|
|
" H: n by n array representing the hamiltonian matrix.\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" The n by n time propagation matrix U(tau).\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" hbar = 1\n",
|
|
" return scipy.linalg.expm(-1j*hbar*H*tau)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "79f8101b73fbb28ff9138437e9767178",
|
|
"grade": false,
|
|
"grade_id": "cell-9b02ad5515424242",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.2 [3 points]\n",
|
|
"Implement a function which performs the step-by-step time propagation given an initial state $\\vec{c}(0)$, the matrix $U(\\tau)$ and the discretized time grid $t_j$. In other words, your function should calculate \n",
|
|
"\n",
|
|
"$$\\vec{c}(j+1) = U(\\tau) \\cdot \\vec{c}(j)$$ \n",
|
|
"\n",
|
|
"for all $j$ of a given discretized time grid $t_j = j \\tau$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 16,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "dc040cc32e832b097bfb8c367f4203a1",
|
|
"grade": true,
|
|
"grade_id": "cell-4e444f44bf3bc9c1",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def timePropagate(U, c0, t):\n",
|
|
" \"\"\"\n",
|
|
" Calculates the time propagation of c over the equidistant time grid t from\n",
|
|
" initial state c0 using constant propagation matrix U\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" U: Time propagation matrix for constant time interval tau.\n",
|
|
" c0: Array of length n representing the initial state.\n",
|
|
" t: Array of equidistant time steps such that t[j] = j*tau for constant\n",
|
|
" tau.\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" The time propagation array c over time grid t of dimension len(t) by n.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" # The function assumes that t[j] = j*tau, so we assert that the\n",
|
|
" # values are equidistant.\n",
|
|
" assert np.allclose(t[1:] - t[:-1], t[1] - t[0])\n",
|
|
" # And that indeed t[0] = 0*tau = 0.\n",
|
|
" assert np.allclose(t[0], 0)\n",
|
|
" \n",
|
|
" c = np.zeros(t.shape + c0.shape, dtype=c0.dtype)\n",
|
|
" c[0] = c0\n",
|
|
" \n",
|
|
" for j in range(1, len(t)):\n",
|
|
" c[j] = U@c[j - 1]\n",
|
|
" \n",
|
|
" return c"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "61362905e7a2d19219ae21f10a417823",
|
|
"grade": false,
|
|
"grade_id": "cell-62bfe608c358ff6d",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.3 [4 points]\n",
|
|
"Use both of the above functions to calculate and animate the time propagation of an initial state\n",
|
|
"\n",
|
|
"$$\\psi(x,t=0) = \\phi(x, x_{i=n/2}, \\sigma) \\leftrightarrow \\vec{c}(0) = [c_{i=n/2}(0) = 1, c_{i\\neq n/2}(0) = 0]$$\n",
|
|
"\n",
|
|
"for a $n=100$ chain. Discretize your time grid as $t_j=j\\tau$ with $j=0 \\dots 200$, and $\\tau=1.5$. Use again $a = 1$ and $\\sigma=0.25$. \n",
|
|
"\n",
|
|
"To plot / animate the time propagation you should plot the real-space wave function $\\psi(x,t) \\approx \\sum_i c_i(t) \\phi(x, x_i, \\sigma)$.\n",
|
|
"\n",
|
|
"Hint: use your function from task 3.4 to get the Hamiltonian $H$.\n",
|
|
"\n",
|
|
"For the animation you can use the following draft:\n",
|
|
"```python\n",
|
|
"# use matplotlib's animation package\n",
|
|
"import matplotlib.pylab as plt\n",
|
|
"import matplotlib\n",
|
|
"import matplotlib.animation as animation\n",
|
|
"# set the animation style to \"jshtml\" (for the use in Jupyter)\n",
|
|
"matplotlib.rcParams['animation.html'] = 'jshtml'\n",
|
|
"\n",
|
|
"# create a figure for the animation\n",
|
|
"fig = plt.figure()\n",
|
|
"plt.grid(True)\n",
|
|
"plt.xlim( ... ) # fix x limits\n",
|
|
"plt.ylim( ... ) # fix y limits\n",
|
|
"\n",
|
|
"# Create an empty plot object and prevent its showing (we will fill it each frame)\n",
|
|
"myPlot, = plt.plot([0], [0])\n",
|
|
"plt.close()\n",
|
|
"\n",
|
|
"# This function is called each frame to generate the animation (f is the frame number)\n",
|
|
"def animate(f): \n",
|
|
" myPlot.set_data( ... ) # update plot\n",
|
|
"\n",
|
|
"# Show the animation\n",
|
|
"frames = np.arange(1, np.size(t)) # t is the time grid here\n",
|
|
"myAnimation = animation.FuncAnimation(fig, animate, frames, interval = 20)\n",
|
|
"myAnimation\n",
|
|
"```"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 17,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "dac0e917be4cfe57c7d30715f3f61912",
|
|
"grade": true,
|
|
"grade_id": "cell-dd676b90f6a61df6",
|
|
"locked": false,
|
|
"points": 4,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"n = 100\n",
|
|
"a = 1\n",
|
|
"sigma = .25\n",
|
|
"tau = 1.5\n",
|
|
"t = np.arange(201)*tau\n",
|
|
"\n",
|
|
"H = TBHamiltonian(n, sigma)\n",
|
|
"U = getU_exact(tau, H)\n",
|
|
"# In general, c0 is complex.\n",
|
|
"c0 = np.zeros(n, dtype=np.complex128)\n",
|
|
"c0[n//2] = 1\n",
|
|
"\n",
|
|
"c = timePropagate(U, c0, t)\n",
|
|
"xi = atomic_positions(n, a)\n",
|
|
"x = np.linspace(-1, 101, 150)\n",
|
|
"# In general, psi is thus also complex.\n",
|
|
"psi = c@atomic_basis(x, xi, sigma).T\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "6786036a70e4fffbda4c92e340ff90de",
|
|
"grade": true,
|
|
"grade_id": "cell-70e223783d806888",
|
|
"locked": false,
|
|
"points": 0,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# use matplotlib's animation package\n",
|
|
"import matplotlib.pylab as plt\n",
|
|
"import matplotlib\n",
|
|
"import matplotlib.animation as animation\n",
|
|
"# set the animation style to \"jshtml\" (for the use in Jupyter)\n",
|
|
"matplotlib.rcParams['animation.html'] = 'jshtml'\n",
|
|
"\n",
|
|
"# create a figure for the animation\n",
|
|
"fig = plt.figure()\n",
|
|
"plt.grid(True)\n",
|
|
"plt.xlim(-1, 101) # fix x limits\n",
|
|
"plt.ylim(-.5, .6) # fix y limits\n",
|
|
"plt.xlabel('$x$')\n",
|
|
"plt.ylabel('$\\\\psi(t, x)$')\n",
|
|
"\n",
|
|
"# Create an empty plot object and prevent its showing (we will fill it each frame)\n",
|
|
"myPlot, = plt.plot([0], [0])\n",
|
|
"plt.close()\n",
|
|
"\n",
|
|
"# This function is called each frame to generate the animation (f is the frame number)\n",
|
|
"def animate(f): \n",
|
|
" myPlot.set_data(x, np.real(psi[f])) # update plot\n",
|
|
"\n",
|
|
"# Show the animation\n",
|
|
"frames = np.arange(1, np.size(t)) # t is the time grid here\n",
|
|
"myAnimation = animation.FuncAnimation(fig, animate, frames, interval = 20)\n",
|
|
"myAnimation"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "74ab18f8b5e98bc5456ef221449f9299",
|
|
"grade": false,
|
|
"grade_id": "cell-0395602360fd9e4c",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.4 [3 points]\n",
|
|
"Implement a function which calculates the Crank-Nicolson time-propagation matrix \n",
|
|
"\n",
|
|
"\\begin{align*}\n",
|
|
" U_{CN}(\\tau) = (I - i \\tau H / 2)\\cdot(I + i \\tau H / 2)^{-1}.\n",
|
|
"\\end{align*}\n",
|
|
"\n",
|
|
"Here, $I$ is the diagonal identity matrix. Use Numpy's $\\text{inv()}$ function to invert the needed expression."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 19,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "1b2677753953d9a528f0dbb71d4077bb",
|
|
"grade": true,
|
|
"grade_id": "cell-d74914e5d0a13365",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getU_CN(tau, H):\n",
|
|
" \"\"\"\n",
|
|
" Calculates the time-propagation matrix for time-step tau using\n",
|
|
" the Crank-Nicolson algorithm.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" tau: time-step numeric to calculate the time-propagation matrix at\n",
|
|
" H: n by n array representing the hamiltonian matrix\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" The time-propagation matrix U(tau).\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" n = len(H)\n",
|
|
" \n",
|
|
" return (np.eye(n) - 1j*tau*H/2)@np.linalg.inv(np.eye(n) + 1j*tau*H/2)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "3746f3298575d0e0c37d35c01039e60e",
|
|
"grade": false,
|
|
"grade_id": "cell-1daec83575502040",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.5 [5 points]\n",
|
|
"Implement a function which calculates the time-propagation matrix using the Trotter-Suzuki decomposition \n",
|
|
"\n",
|
|
"\\begin{align*}\n",
|
|
" U_{TZ}(\\tau) = e^{-i\\tau H_1} \\cdot e^{-i \\tau H_2}.\n",
|
|
"\\end{align*}\n",
|
|
"\n",
|
|
"In this approach you choose a decomposition of the tight-binding Hamiltonian $H = H_1 + H_2$, which allows you to analytically diagonalize $H_1$ and $H_2$ (see last lecture). From this analytic diagonalization you will be able to calculate the matrix exponentials $e^{-i\\tau H_1}$ and $e^{-i \\tau H_2}$.\n",
|
|
"\n",
|
|
"Write your definition of the 2x2 blocks in $e^{-i\\tau H_1}$ and $e^{-i \\tau H_2}$ in the Markdown cell below. (Double click on \"YOUR ANSWER HERE\" to open the cell, and ctrl+enter to compile.) "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "566fe9a7f8031baea9812438b155671c",
|
|
"grade": true,
|
|
"grade_id": "cell-bef909a443eb2a68",
|
|
"locked": false,
|
|
"points": 2,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"In the Trotter-Suzuki decomposition, we seek diagonal block matrix forms for $\\mathbf{H_1}$ and $\\mathbf{H_2}$ such that their sum equals the original matrix $\\mathbf{H}$. The exponential is than done for each block instead of the whole matrix, which is a lot less complicated. Afterwards the result is combined such that\n",
|
|
"$$\n",
|
|
"e^{-i\\tau\\mathbf{H}} = e^{-i \\tau\\left( \\mathbf{H_1} + \\mathbf{H_2} \\right)} \\approx e^{-i\\tau\\mathbf{H_1}} \\cdot e^{-i\\tau\\mathbf{H_2}}.\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Here are the forms for the matrices. For $\\mathbf{H}$ an $n \\times n$ matrix, the form for $n$ odd is written down below. For $n$ even, the last row and column for both matrices can be omitted to see the shape.\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbf{H_1} =\n",
|
|
"\\begin{pmatrix}\n",
|
|
"0 & t & & & & & & \\\\\n",
|
|
"t & 0 & & & & & & \\\\\n",
|
|
" & & 0 & t & & & & \\\\\n",
|
|
" & & t & 0 & & & & \\\\\n",
|
|
" & & & & \\ddots & & & \\\\\n",
|
|
" & & & & & 0 & t & \\\\\n",
|
|
" & & & & & t & 0 & \\\\\n",
|
|
" & & & & & & & 0\n",
|
|
"\\end{pmatrix}\n",
|
|
"\\qquad\n",
|
|
"\\mathbf{H_2} =\n",
|
|
"\\begin{pmatrix}\n",
|
|
"0 & & & & & & & \\\\\n",
|
|
" & 0 & t & & & & & \\\\\n",
|
|
" & t & 0 & & & & & \\\\\n",
|
|
" & & & 0 & t & & & \\\\\n",
|
|
" & & & t & 0 & & & \\\\\n",
|
|
" & & & & & \\ddots & & \\\\\n",
|
|
" & & & & & & 0 & t\\\\\n",
|
|
" & & & & & & t & 0\n",
|
|
"\\end{pmatrix}\n",
|
|
"$$\n",
|
|
"\n",
|
|
"For the exponents, we find the following for $n$ odd, again with the remark that the result for $n$ even can be reached by omitting the last row and column for both matrices and calculating the exponents for them.\n",
|
|
"\\begin{align}\n",
|
|
"\\exp{(-i\\tau\\mathbf{H_1})} &=\n",
|
|
"\\begin{pmatrix}\n",
|
|
"\\exp{\\begin{pmatrix}0 & -i\\tau{}t \\\\ -i\\tau{}t & 0\\end{pmatrix}} & & & &\\\\\n",
|
|
" & \\exp{\\begin{pmatrix}0 & -i\\tau{}t \\\\ -i\\tau{}t & 0\\end{pmatrix}} & & &\\\\\n",
|
|
" & & \\ddots & &\\\\\n",
|
|
" & & & \\exp{\\begin{pmatrix}0 & -i\\tau{}t \\\\ -i\\tau{}t & 0\\end{pmatrix}} &\\\\\n",
|
|
" & & & & \\exp{0}\n",
|
|
"\\end{pmatrix}\n",
|
|
"\\\\\n",
|
|
"\\exp{(-i\\tau\\mathbf{H_2})} &=\n",
|
|
"\\begin{pmatrix}\n",
|
|
"\\exp{0} & & & &\\\\\n",
|
|
" & \\exp{\\begin{pmatrix}0 & -i\\tau{}t \\\\ -i\\tau{}t & 0\\end{pmatrix}} & & &\\\\\n",
|
|
" & & \\exp{\\begin{pmatrix}0 & -i\\tau{}t \\\\ -i\\tau{}t & 0\\end{pmatrix}} & &\\\\\n",
|
|
" & & & \\ddots &\\\\\n",
|
|
" & & & & \\exp{\\begin{pmatrix}0 & -i\\tau{}t \\\\ -i\\tau{}t & 0\\end{pmatrix}}\\\\\n",
|
|
" & & & &\n",
|
|
"\\end{pmatrix}\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"As $\\exp{0} = 1$, we just calculate\n",
|
|
"$$\n",
|
|
"\\exp{\\begin{pmatrix}0 & -i\\tau{}t \\\\ -i\\tau{}t & 0\\end{pmatrix}}\n",
|
|
"= \\begin{pmatrix}\\cos{\\tau{}t} & -i\\sin{\\tau{}t} \\\\ -i\\sin{\\tau{}t} & \\cos{\\tau{}t}\\end{pmatrix}.\n",
|
|
"$$\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 20,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "f9f25759b1a81bbac8c1834c2f4565b8",
|
|
"grade": true,
|
|
"grade_id": "cell-1425de6027596dea",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getU_TZ(tau, H):\n",
|
|
" \"\"\"\n",
|
|
" Calculates the time-propagation matrix for time-step tau using\n",
|
|
" the Trotter-Suzuki algorithm for a known shape of the hamiltonian\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" tau: time-step numeric to calculate the time-propagation matrix at\n",
|
|
" H: n by n array representing the hamiltonian matrix\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" The time-propagation matrix U(tau).\n",
|
|
" \n",
|
|
" Note:\n",
|
|
" Only the size of H is taken into account, as the decomposition is\n",
|
|
" pre-defined.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" # We assume that H is n by n in the form with constant hopping parameter\n",
|
|
" # t on the upper and lower diagonal, and the rest zero.\n",
|
|
" n = len(H)\n",
|
|
" assert len(H[0] == n)\n",
|
|
" \n",
|
|
" t = H[0][1]\n",
|
|
" H_tb = (np.eye(n, n, -1) + np.eye(n, n, 1))*t\n",
|
|
" assert np.allclose(H, H_tb)\n",
|
|
" \n",
|
|
" \n",
|
|
" # First we calculate the exponent of the block.\n",
|
|
" exp_block = np.array([\n",
|
|
" [ np.cos(tau*t), -1j*np.sin(tau*t)],\n",
|
|
" [-1j*np.sin(tau*t), np.cos(tau*t)]\n",
|
|
" ])\n",
|
|
" \n",
|
|
" # Now we use the block to calculate the exponent of matrices\n",
|
|
" # H_1 and H_2.\n",
|
|
" \n",
|
|
" # If n is even.\n",
|
|
" if n % 2 == 0:\n",
|
|
" num = n//2\n",
|
|
" exp_H_1 = np.kron(np.eye(num, dtype=int), exp_block)\n",
|
|
" \n",
|
|
" num = n//2 - 1\n",
|
|
" exp_H_2 = np.block([\n",
|
|
" [1, np.zeros((1, num*2)), 0 ],\n",
|
|
" [np.zeros((num*2, 1)), np.kron(np.eye(num, dtype=int), exp_block), np.zeros((num*2, 1))],\n",
|
|
" [0, np.zeros((1, num*2)), 1 ]\n",
|
|
" ])\n",
|
|
" \n",
|
|
" # If n is odd.\n",
|
|
" else:\n",
|
|
" num = n//2\n",
|
|
" exp_H_1 = np.block([\n",
|
|
" [np.kron(np.eye(num, dtype=int), exp_block), np.zeros((num*2, 1))],\n",
|
|
" [np.zeros((1, num*2)), 1 ]\n",
|
|
" ])\n",
|
|
"\n",
|
|
" num = n//2\n",
|
|
" exp_H_2 = np.block([\n",
|
|
" [1, np.zeros((1, num*2)) ],\n",
|
|
" [np.zeros((num*2, 1)), np.kron(np.eye(num, dtype=int), exp_block)]\n",
|
|
" ])\n",
|
|
"\n",
|
|
" U_TZ = exp_H_1@exp_H_2\n",
|
|
" return U_TZ"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"158 µs ± 268 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n",
|
|
"256 µs ± 2.04 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
|
|
"45.2 µs ± 84.3 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"(2, 2, 201)"
|
|
]
|
|
},
|
|
"execution_count": 21,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# TODO: Delete this cell!\n",
|
|
"n = 10\n",
|
|
"sigma = .25\n",
|
|
"tau = 1.5\n",
|
|
"H = TBHamiltonian(n, sigma)\n",
|
|
"%timeit U = getU_TZ(tau, H)\n",
|
|
"%timeit U = getU_exact(tau, H)\n",
|
|
"%timeit U = getU_CN(tau, H)\n",
|
|
"\n",
|
|
"exp_block = np.array([\n",
|
|
" [ np.cos(tau*t), -1j*np.sin(tau*t)],\n",
|
|
" [-1j*np.sin(tau*t), np.cos(tau*t)]\n",
|
|
" ])\n",
|
|
"exp_block.shape"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "1747285f36e24921cb5c2811632f33c3",
|
|
"grade": false,
|
|
"grade_id": "cell-f53dc443bd1858b1",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.6 [3 points]\n",
|
|
"In your implementation of $U_{TZ}(\\tau)$ you analytically evaluate the matrix exponentials $e^{-i\\tau H_1}$ and $e^{-i \\tau H_2}$. Test your implementation by comparing your results for these matrix exponentials to those obtained using Scipy's $\\text{expm()}$ function."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "684e4173792cb10809386ef097c561e4",
|
|
"grade": true,
|
|
"grade_id": "cell-5aa3ffce9359fa7e",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann printed\n",
|
|
"#Biggest differences of U1 with Scipy:\n",
|
|
"#Real: 1e-16 \n",
|
|
"#Imag: 2.77e-17\n",
|
|
"# \n",
|
|
"# and difference with U_exact in the order of 1e-1 or 1e-2."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "94ca5bdd479043f3c73214a3c4916923",
|
|
"grade": false,
|
|
"grade_id": "cell-c255a2bf5eac4e2b",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.7 [6 points]\n",
|
|
"In the next task you will need a Fourier transform to calculate the local density-of-states. Therefore you will need to implement a function that returns the Fourier transform $f(\\omega)$ of a given function $f(t)$ defined on a time grid $t$, for a given energy grid $\\omega$. I.e. it should calculate:\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" f(\\omega) = \\frac{1}{2\\pi} \\int_{-\\infty}^{+\\infty} \\, e^{i\\omega t} \\, f(t) \\ dt.\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"Hint: use your integration function from task 2.2.\n",
|
|
"\n",
|
|
"Then implement a unit test for your function."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "37055009cb70e69bc9b1dbc761859c51",
|
|
"grade": true,
|
|
"grade_id": "cell-87ece8e50b1f8de5",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "49aa23055a91a51494bcb9d64924cc75",
|
|
"grade": true,
|
|
"grade_id": "cell-46e1530333341bc6",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Implement your unit test here ...\n",
|
|
"\n",
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "028bf13b6bf982c70fd1057c9d6f23f6",
|
|
"grade": false,
|
|
"grade_id": "cell-dc5656a6bdea875a",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.8 [3 points]\n",
|
|
"Calculate the local density-of-states $\\rho_{loc}(\\omega)$ from the Fourier transform of $f(t)$ using all three time propagation methods: $U(\\tau)$, $U_{CN}(\\tau)$ and $U_{TZ}(\\tau)$.\n",
|
|
"\n",
|
|
"Start from $\\psi(x,t=0) = \\phi(x, x_{i=0}, \\sigma)$ and $\\psi(x,t=0) = \\phi(x, x_{i=n/2}, \\sigma)$, using a $n=100$ chain. Discretize your integration time grid as $t_j=j\\tau$, with $j=-150 \\dots 150$ and $\\tau=1.5$. Use again $a = 1$ and $\\sigma=0.25$.\n",
|
|
"\n",
|
|
"Be careful: for the Fourier transform you will need positive *and* negative time steps! Thus you will need to do two time propagations: one using $U(\\tau)$ towards positive times and one using $U(-\\tau)$ towards negative times, both starting from $\\psi(x,t=0)$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "29ff620823bca3839839fbc35ba9b236",
|
|
"grade": true,
|
|
"grade_id": "cell-316f9c26031f89df",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "1c27de03eb5f84673d52e1e621c316ee",
|
|
"grade": true,
|
|
"grade_id": "cell-d7a678fdeef64ea2",
|
|
"locked": false,
|
|
"points": 0,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Do your own testing here ...\n",
|
|
"\n",
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann had a plot for Tau = 1.5\n",
|
|
"# DOS: looking like a hill (\"like a dome with a peak around zero energy 0\")\n",
|
|
"# for CN, TS and the exact one\n",
|
|
"# a plot of f(t)\n",
|
|
"# a plot of local DOS\n",
|
|
"# in the title he mentiones the inital values."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "c3e0ecb1b67f93590abf1a796bd507b8",
|
|
"grade": false,
|
|
"grade_id": "cell-ffbf1e8460ac69d8",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.9 [6 points]\n",
|
|
"Use the Trotter-Suzuki decomposition to calculate the full density-of-states by averaging over about $100$ local density-of-states you obtained from the time propagation of $100$ random initial states $\\vec{c}(0)$. To this end, you will need to make sure that each $\\vec{c}(0)$ is (a) normalized and (b) can have positive *and* negative elements. \n",
|
|
"\n",
|
|
"Compare this approximation to the total density-of-states to the exact one from task 3.6, which you obtained directly from the eigenvalues.\n",
|
|
"\n",
|
|
"Hint: don't expect the results to be the exact same. Check for the location of the peaks, and whether they have a similar order of magnitude.\n",
|
|
"\n",
|
|
"Hint: if you did not get the Trotter-Suzuki decomposition to work, you can instead use the exact or the Crank-Nicolson time-propagation matrix."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "81edbb8d07068d29021696fd87a961ba",
|
|
"grade": true,
|
|
"grade_id": "cell-2493a46a63277eda",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann says the initial states do need to be negative, too."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "5438067dfec55e69ee224e67178d9e36",
|
|
"grade": true,
|
|
"grade_id": "cell-a40dfcd993da467c",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Do your plotting here ...\n",
|
|
"\n",
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann plotted the exact diagonalisation and the TS propagation results\n",
|
|
"# he had two plots, one peaky, one with peaks on the edges (looking a little\n",
|
|
"# like my 1f/2f results in my bachelor internship hmmpfff)"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.8.10"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 4
|
|
}
|