Generalized Peierls-Boltzmann Transport Equations for Phonons and Local Excitation Kinetics

Abstract

The Peierls-Boltzmann transport equation for phonons is re-formulated and modified by means of sequences of transport and statistical postulates. The transition probabilities within the collision term are expanded in a comprehensive way. The resulting nonlinear kinetic equations are applied to a simple model system, i.e. a local excitation coupled to a transport system. The steady state solutions reveal the possibility of a hysteresis-type of “transport phase transitions” from the “thermodynamic” branch to a “nonthermodynamic” one via a cumulative excitation. The stability of the solutions is checked and the approximations are discussed. © 1977, Walter de Gruyter. All rights reserved.