Kinetic description of an electron-LO-phonon system with finite phonon lifetime.

Abstract

We study the cooling of an electron plasma from a kinetic point of view. For this purpose, a quantum theory of fluctuations is applied to derive the kinetic equations for an electron--LO-phonon system from various model Hamiltonians. A polarization approximation is provided that goes beyond perturbation theory of the electron-phonon interaction. The description of electron-phonon energy exchange is shown to be impossible with the interacting Hamiltonian in Fr\ohlich's one-phonon form unless dissipation of the bare LO phonon is included. For a Hamiltonian including effects of the scattering of LO phonons by acoustic phonons, kinetic equations are derived. The equation for LO phonons is shown to describe the collective excitations with finite lifetime, in the limiting case of weak damping of the plasmon-phonon coupled modes. A reduction of the cooling rate similar to the ``hot-phonon'' effect is shown to occur for the case of weak coupling without assuming a steady state of the LO phonons. Finally, an electron-phonon interaction Hamiltonian in two-phonon form is considered and it is shown that electron-phonon energy exchange may be described in the polarization approximation without introducing a finite phonon lifetime.