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Conductivity from Boltzmznn Equation for a metal

  1. Dec 10, 2014 #1
    I'm trying to show that conductivity of a metal in uniform Electric field is:

    $$
    \sigma=\int \frac{d\textbf{k}}{4\pi^3}\left (- \frac{\partial f}{\partial \epsilon} \right )\textbf{v(k)u(k)}
    $$
    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.
     
    Last edited: Dec 10, 2014
  2. jcsd
  3. Dec 15, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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