Theory of Hot Electrons in Gases, Liquids, and Solids

Boltzmann's equation for electrons moving in a steady electric field is solved by the method due to Lorentz, Pidduck, and Davydov. Space-time correlations in the medium (gas, liquid, or solid) are included exactly through the use of sum rules of the Van Hove spectral function, $S(\mathbf{K},\omega )$. In liquids and solids the rates of momentum and energy transfer are different, the former being structure-dependent, the latter not. The error from neglect of this difference in previous treatments for solids is fortuitously canceled at low and intermediate fields by the error in the single-phonon scattering approximation also employed.