COULOMB QUANTUM KINETICS IN A DENSE ELECTRON-GAS

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 nonequilibrium 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.