Energy transport in glasses due to phonon hopping:: Lifetime and ac behavior

Anharmonic interactions between localized vibrational states and extended low-energy phonons can lead to thermally activated hopping of the localized states. Such a mechanism has been proposed to explain the thermal conductivity behavior of dielectric glasses and amorphous films above the so-called "plateau temperature," i.e., in the high temperature regime. To investigate this transport scenario we derive rate equations for the occupation numbers of the localized states. Extending our previous model, we calculate the lifetimes of localized states and find them to increase with the energy of the state, in accordance with recent experiments as well as with the fracton hopping model (the functional form differs though). This is in contrast to another model for explaining the high temperature behavior of glasses, namely the model of diffusive transport by nonpropagating modes. Furthermore, the latter model predicts a decrease of the conductivity with increasing frequency of an ac temperature gradient. In our hopping model, on the other hand, the conductivity is frequency independent or might even increase. This could provide an additional approach in order to experimentally distinguish between these two models. Moreover, essential differences to electron hopping are discussed, including particle number and energy nonconservation, which would correspond to charge nonconservation in the electron case. These lead to some intricacies which have to be considered in deriving the current theory. [S0163-1829(99)01213-8].