Mesoscopic Hydro-Thermodynamics of Phonons

A. R. Vasconcellos; A. R. B. Castro; C. A. B. Silva; R. Luzzi

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arXiv · 1211.0342

Mesoscopic Hydro-Thermodynamics of Phonons

A. R. Vasconcellos·A. R. B. Castro·C. A. B. Silva·R. Luzzi

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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 a Mesoscopic Hydro-Thermodynamics. The case of a contraction in first order relevant variables 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 free electron laser (FEL) facilities. The derivation of a generalized Guyer-Krumhansl equation governing the flux of heat and the associated conductivity coefficient is also presented.

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A. R. Vasconcellos, A. R. B. Castro, C. A. B. Silva, R. Luzzi. 2012-11-02. Mesoscopic Hydro-Thermodynamics of Phonons. https://arxiv.org/abs/1211.0342

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