deletions | additions       diff --git a/magnetoresistance.tex b/magnetoresistance.tex  index 4f62ae7..788918e 100644  --- a/magnetoresistance.tex  +++ b/magnetoresistance.tex 
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Therefore, in a Fermi Liquid, there will be a population of decay timescales $\tau_k$ and conductivities $\sigma_0^{(k)}$. Without a magnetic field, these populations will just average out to result in an average timescale $\overline{\tau}$ and conductivity $\overline{\sigma_0}^{(k)}$. Thus, in the absence of a magnetic field, a distribution of decay timescales will not affect the conductivity. However, in the presence of a magnetic field, the picture changes. Let's assume we have $N$ different decay times. Let\footnote{With a slight abuse of notation, the way I see these equations is as a weighted average, with a weight of $\sigma_0 / (1 + (\omega_\textrm{c} \tau_k )^2)$}  \begin{equation}   \begin{split} \gamma(1) &:= :=  \frac{1}{N} \sum_{k=1}^{N} \frac{\sigma_0^{(k)}}{1 + (\omega_\textrm{c} \tau_k)^2} \\ \end{equation}   \begin{equation}  \gamma(\tau) &:= :=  \frac{1}{N} \sum_{k=1}^{N} \frac{\sigma_0^{(k)}}{1 + (\omega_\textrm{c} \tau_k)^2} \tau_k\end{split}  \end{equation}  Equations \eqref{eq:currentx-B}, \eqref{eq:currenty-B} will now read:  \begin{equation}