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Conductivity from Boltzmznn Equation for a metal
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[QUOTE="Abolfazl, post: 4940554, member: 534902"] [B]I'm trying to show that conductivity of a metal in uniform Electric field is: [/B] $$ \sigma=\int \frac{d\textbf{k}}{4\pi^3}\left (- \frac{\partial f}{\partial \epsilon} \right )\textbf{v(k)u(k)} $$ where u(k) is a solution to the integral equation $$ \textbf{v(k)}=\int \frac{d\textbf{k'}}{(2\pi)^3}W_{kk'}\textbf{[u(k)-u(k')]} $$ $$ g(\textbf{k})=f(\textbf{k})+\delta g(\textbf{k}) $$ \delta g(k) is of order of E. I also want to derive to linear order in E an integral equation obeyed by \delta g. I wrote: $$ -\frac{e}{\hbar}\frac{\partial f}{\partial E} \textbf{v.E}=\int \frac{d\textbf{k'}}{(2\pi)^3}W_{kk'}[\delta\textbf{g(k)}-\delta\textbf{g(k')}] $$ so what is the next step? this is problem 4 of chapter 16 Ashcroft and Mermin. I don't have any idea for part b of the problem too. Any help is appreciated. [/QUOTE]
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Conductivity from Boltzmznn Equation for a metal
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