One-particle densities, thermal propagation, and second sound in dielectric crystals

Abstract

A description of propagation of heat and other thermal quantities in terms of lattice dynamics and of ensemble techniques is developed. First a general method for the construction of the microscopic energy, energy flux and momentum densities is presented. Then the density matrices describing local thermal equilibrium, local phonon drift and their perturbation by dissipation are discussed. For this purpose an effective Liouville equation is derived. In this formalism the Boltzmann equation does not occur explicitely so that the hydrodynamical balance laws are additional assumptions. The ensuing dispersion laws already given earlier are derived. In particular two types of second sound called “driftless” and “drifting” are found, and it is concluded that the recent discovery of this phenomenon is of the “drifting” type, while the realizability of the “driftless” type is uncertain.