deletions | additions       diff --git a/resistance.tex b/resistance.tex  index 43453b6..9a4ae90 100644  --- a/resistance.tex  +++ b/resistance.tex 
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The two key elements for conducting a current are mobile charged particles and an energy dissipation mechanism.\footnote{We're discussing here about non-superconducing metals. Superconductivity is a totally different beast.} Since a current is just the motion of charged particles, you need the former by definition. In order to prevent these particles accelerating indefinitely, you also need an energy dissipation mechanism -- without it, you have no steady state current for nonzero electric field.  We'll now derive Ohm's law starting only from these assumptions\cite{Drude_1900}. assumptions, following the argument set by \citet{Drude_1900}.  Assume that we have a uniform density $n$ of particles, carrying a charge $q$. These carriers are accelerated by an electric field $\mathbf{E}$ and scatter via a certain mechanism with a characteristic lifetime $\tau$. Assuming they have a well defined momentum $\mathbf{p}$, their equation of motion is:\footnote{As long as we only consider small changes in momentum, \mathbf{p} can also be crystal momentum} \begin{equation}  \frac{d\mathbf{p}}{dt} = - \frac{1}{\tau} \mathbf{p} + q \mathbf{E}  \label{eq:eom}