Phonon hopping in disordered systems

Anharmonic interactions between localised vibrational states and extended l ow-energy phonons can lead to thermally activated hopping of the localized states. Such a mechanism has been proposed to explain the thermal conductiv ity behaviour of dielectric glasses and amorphous films above the so-called "plateau temperature". We derive rate equations for the occupation numbers of the localized states using the anharmonic coupling constant as an expansion parameter. The calc ulated localized state life times increase with the energy of the state, in accordance with recent experiments, as well as with the fracton hopping mo del (the functional form differs though). This is in contrast to another mo del, namely the model of diffusive transport by extended but non-propagatin g modes of Alien and Feldman. Our model, furthermore, predicts an increase of the conductivity with increasing frequency of an AC temperature gradient , again in contrast to the diffusive transport model. (C) 1999 Elsevier Sci ence B.V. All rights reserved.