
\sect{Onsager}

%Baruch's  D52.

Consider the coefficients $\gamma_{ij}$ in Onsager's relations for heat and current transport (see lecture notes pages 70-71). Consider also Boltzmann's equation as in Ex. D07.
\begin{itemize}
\item[(a)] Show that $\gamma_{22}$ is related to the conductivity $\sigma=ne^2\tau/m$.
\item[(b)] Show that $\langle J_y\rangle=0$ and identify $\gamma_{21}$. [Note that $eV_i=\mu_i$ the local chemical potential.]

\item[(c)] Identify the thermal conductivity $\kappa$ in terms of $\gamma_{ij}$. Use 
$\kappa=\frac{5}{2m}k_B^2n\tau T$ (result of D07c) to find $\gamma_{11}$.
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
