Condensed Matter Physics - Free Electron Theory of Metals : Boltzmann Transport Equation

The Boltzmann transport equation is an approach to transport phenomena in statistical system originally devised to study the transport properties of a molecular gas. This equation is governed by a parameter known as the distribution function. Electrons in metals get excited on the application of external fields such as heat,electric fields,magnetic fields or combinations of these. In the absence of these fields the electron gas in a metal has velocities distributed according to an equilibrium function f0. However,when an electric field is applied to the metal,there is a systematic electron drift. In this case the velocity distribution function f differs from f0. In Boltzmann transport equation,the rate of change of distribution function is measured.