HOPPING THEORY OF HEAT-TRANSPORT IN DISORDERED-SYSTEMS

Heat transport is studied in a simple model system of Anderson localized optical (carrier) phonons which perform thermally activated hopping due to anharmonic interaction with delocalized acoustic phonons. The corresponding kinetic equations (rate equations) are derived by using the density-matrix formalism. The calculated hopping contribution to the heat conductivity exhibits a linear increase with temperature at lower temperatures and (depending on the choice of parameters) eventually reaches a "saturated" value at higher temperatures. Thus, unlike other authors, we do not need a special mechanism, such as lifetime broadening of the optical phonon states, to explain the transition to the saturation region. Furthermore, we show that particle (carrier) number nonconservation leads to a quenching of the hopping mechanism. © 1994 The American Physical Society.