Electric conduction
The Drude model
The Drude model is a classical model of electric conduction in which we have mostly free electrons, interacting occasionally with atoms via elastic collisions, and under the influence of electromagnetic fields.
Individual electrons, with position $\vec{x}_i(t)$, move most of the time under classical laws
\begin{equation} m \ddot{\vec{x}}_i(t) = q \vec{E}(\vec{x}_i(t), t) + q \dot{\vec{x}}_i(t) \wedge \vec{B}(\vec{x}_i(t), t) \end{equation}On average, each charge does on for a time interval $\tau$ without having a collision with an atom.