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arXiv · 0905.4806

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

T. V. Dudnikova
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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 $\varepsilon^{-1}$. We establish two time regimes. For times of order $\varepsilon^{-γ}$, $0<γ<1$, 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 $\varepsilon^{-1}$, this covariance changes in time and is governed by a semiclassical transport equation.

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T. V. Dudnikova. 2009-05-29. Lattice Dynamics in the Half-Space, II. Energy Transport Equation. https://doi.org/10.1063/1.3451109

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