Mesoscopic hydro-thermodynamics of phonons

Abstract

A generalized Hydrodynamics, referred to as Mesoscopic Hydro-Thermodynamics, of phonons in semiconductors is presented. It involves the descriptions of the motion of the quasi-particle density and of the energy density. The hydrodynamic equations, which couple both types of movement via thermo-elastic processes, are derived starting with a generalized Peierls-Boltzmann kinetic equation obtained in the framework of a Non-Equilibrium Statistical Ensemble Formalism, providing such Mesoscopic Hydro-Thermodynamics. The case of a contraction in first order is worked out in detail. The associated Maxwell times are derived and discussed. The densities of quasi-particles and of energy are found to satisfy coupled Maxwell-Cattaneo-like (hyperbolic) equations. The analysis of thermo-elastic effects is done and applied to investigate thermal distortion in silicon mirrors under incidence of high intensity X-ray pulses in FEL facilities. The derivation of a generalized Guyer-Krumhansl equation governing the flux of heat and the associated thermal conductivity coefficient is also presented.