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

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

2009-05-29

arxiv.org/abs/0905.4806v1

Physics

Mathematical Physics

35 pages

Scientific paper

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 $\varepsilon^{-\gamma}$, $0<\gamma<1$, 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 $\varepsilon^{-1}$, this covariance changes in time and is governed by a semiclassical transport equation.

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