ass2: Add first brainfarts on the Landau theory

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}