Coulomb quantum kinetics in a dense electron gas

Abstract

The semiclassical Boltzmann equation for a dense electron gas is generalized to a quantum kinetic equation beyond the approximation of isolated collisions. The resulting quantum kinetic equation for the Wigner function contains memory effects, which are determined by the retarded and advanced non- equilibrium Green’s functions of the scattered electrons and the screened Coulomb potential. A closed set of equations for the distribution and the spectral functions is given which is exact within the generalized Kadanoff-Baym ansatz and the random-phase approximation. Simplifying approximations are given which result in a quantum kinetic equation with memory kernels similar to those obtained for the electron-phonon scattering. In the limit of completed collisions, the quantum kinetic equation reduces to a Boltzmann equation in which the energy conservation is smeared out due to the finite time interval and due to collision broadening.