On the theory of thermal conductivity of dielectrics with inclusion of the interaction with a thermostat (theory and numerical experiment)

This paper reports on the results of investigations into the internal microscopic dissipative phenomena occurring in crystalline dielectrics in which the interaction of all subsystems with a thermostat plays a dominant role. It is shown that, in realistic physical situations where allowance is made not only for the coupling between interacting phonon subsystems of a dielectric but also for the interaction with a thermostat, the umklapp processes proceeding in samples with a size smaller than the critical value L0 play an insignificant role. For these situations, it is proved that the phonon gas superflows through the volume without retardation and comes to rest only due to the interaction with immobile surface phonons of the thermostat. Numerical calculations demonstrate that the umklapp processes manifest themselves solely at high temperatures T (exceeding a temperature approximately equal to ThetaD /4, where ThetaD is the Debye temperature) and for samples with a size L > L0, which, according to authors' estimates, should be of the order of 10 cm.