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

Abstract: We consider the lattice dynamics in the half-space. The initial data arerandom according to a probability measure which enforces slow spatial variationon the linear scale $\varepsilon^{-1}$. We establish two time regimes. Fortimes of order $\varepsilon^{-\gamma}$, $0<\gamma<1$, locally the measureconverges to a Gaussian measure which is time stationary with a covarianceinherited from the initial measure non-Gaussian, in general. For times oforder $\varepsilon^{-1}$, this covariance changes in time and is governed by asemiclassical transport equation.

Author: T.V. Dudnikova

Source: https://arxiv.org/