**Definition 0.0.1 **  The **Drude model** is a simple model of electron motion and scattering in a material with a differential equation describing of the momentum $\vec{p}$ of electrons experiencing the Lorentz force from an external electric field $\vec{E}$, magnetic field $\vec{B}$ and scattering with a mean scattering time of $\tau$.
\[\frac{\partial \vec{p}}{\partial t} = -e\left( \vec{E} + \frac{1}{m}\vec{p}\times\vec{B} \right) + \frac{\vec{p}}{\tau}\]