Lattice Dynamics in the Half-Space, II. Energy Transport Equation

Abstract

We consider the lattice dynamics in the half-space. The initial data are random according to a probability measure which enforces slow spatial variation on the linear scale ${\epsilon }^{-1}$. We establish two time regimes. For times of order ${\epsilon }^{-\gamma }$, $0<\gamma <1$, locally the measure converges to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian, in general). For times of order ${\epsilon }^{-1}$, this covariance changes in time and is governed by a semiclassical transport equation.

35 pages

References in corpus (3)

• Local stationarity for lattice dynamics in the harmonic approximation
• On a Two-Temperature Problem for Wave Equation
• Harmonic Crystals in the Half-Space, I. Convergence to Equilibrium

Cited by in corpus (2)

• Derivation of the Boltzmann equation and entropy production in functional mechanics
• Hierarchy of space-time structures, Boltzmann equation, and functional mechanics