Dynamical aspects of phonon-phonon coupling in collective mode damping

Abstract

We present an extension of the Quantal Brownian Motion (QBM) model of vibration damping that incorporates phonon-phonon or phonon-(two-particle-two-hole) interactions as sources of dissipative evolution of the excited mode. Starting from the Schrödinger-on Neumann equation of motion, a reduction procedure combined with the proper approximations leads to coupled, nonlinear master equations for the density vectors of the separate oscillators. The fermionic heat bath remains equilibrated at temperature T. The evolution of the phonon system is numerically analyzed under different initial conditions that simulate excitation of one or more collective vibrations, for several strengths of mode-mode coupling. It is found that in the majority of cases the system reaches statistical equilibrium with relaxation times that can be extracted from the numerical treatment.