deletions | additions       diff --git a/magnetoresistance.tex b/magnetoresistance.tex  index b847b1f..6b20a44 100644  --- a/magnetoresistance.tex  +++ b/magnetoresistance.tex 
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However, this derivation hinges on a crucial assumption: \emph{all} charge carriers have the same decay time and thus lead to the same contribution to the conductivity. We've seen that not to be true in the case of the Landau quasiparticles -- their decay time depends on how far away their energy is to the Fermi energy.  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 $\overline{\sigma_0^{(k)}}$. $\overline{\sigma_0}^{(k)}$.  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} \\