diff --git a/superconductivity_assignment2_kvkempen.tex b/superconductivity_assignment2_kvkempen.tex index 88290df..e1915fb 100755 --- a/superconductivity_assignment2_kvkempen.tex +++ b/superconductivity_assignment2_kvkempen.tex @@ -29,6 +29,8 @@ \usepackage{float} \usepackage{mathtools} +\newcommand{\pfrac}[2]{\frac{\partial #1}{\partial #2}} + \title{Superconductivity - Assignment 2} \author{ Kees van Kempen (s4853628)\\ @@ -41,8 +43,24 @@ \begin{document} -\section{Temperature dependence in Ginzburg-Landau model} +\section{Temperature dependence in Landau model} +In the Landau model, free energy is given as function of order parameter $\psi$ and temperature $T$ as +\[ + \mathcal{F} = a(T - T_c) \psi^2 + \frac{\beta}{2}\psi^4. +\] +To find the equilibrium value with respect to the order parameter $\psi_0(T)$, +we need to equate the derivatives with respect to both $T$ and $\psi(T)$ to zero. + +\[ + 0 = \frac{\delta\mathcal{F}}{\delta\psi} = \frac{\partial \mathcal{F}}{\partial \psi} - \nabla \cdot \frac{\partial \mathcal{F}}{\partial (\nabla \psi)} +\] + +Now we seek the Q = TdS, C = dQ/dT = T dS/dT +For the entropy, we know +\[ + S = -\pfrac{} +\] \section{Type-I superconducting foil} \section{Type II superconductors and the vortex lattice}