Nonequilibrium statistical mechanics of crystals

TL;DR

This paper applies a local equilibrium approach to crystalline solids, deriving their hydrodynamics, transport properties, and mode behaviors from microscopic dynamics, including Green-Kubo formulas and effects of crystal symmetry.

Contribution

It extends the local equilibrium framework to crystals, providing new derivations of hydrodynamics, transport coefficients, and mode analysis specific to crystalline symmetries.

Findings

Derivation of Green-Kubo formulas for crystal transport coefficients.

Analysis of eight hydrodynamic modes and their dispersion relations.

Identification of symmetry-dependent splitting of damping rates in certain crystallographic classes.

Abstract

The local equilibrium approach previously developed by the Authors [J. Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and their local thermodynamic and transport properties are deduced from the microscopic Hamiltonian dynamics. In particular, the Green-Kubo formulas are obtained for all the transport coefficients. The eight hydrodynamic modes and their dispersion relation are studied for general and cubic crystals. In the same twenty crystallographic classes as those compatible with piezoelectricity, cross effects coupling transport between linear momentum and heat or crystalline order are shown to split the degeneracy of damping rates for modes propagating in opposite generic directions.