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On the convergence to statistical equilibrium for harmonic crystals

T. V. Dudnikova·A. I. Komech·H. Spohn
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Abstract

We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$ components, $d,n$ arbitrary, $d,n\ge 1$, and study the distribution $\mu_t$ of the solution at time $t\in\R$. The initial measure $\mu_0$ has a translation-invariant correlation matrix, zero mean, and finite mean energy density. It also satisfies a Rosenblatt- resp. Ibragimov-Linnik type mixing condition. The main result is the convergence of $\mu_t$ to a Gaussian measure as $t\to\infty$. The proof is based on the long time asymptotics of the Green's function and on Bernstein's ``room-corridors'' method.

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T. V. Dudnikova, A. I. Komech, H. Spohn. 2002-10-22. On the convergence to statistical equilibrium for harmonic crystals. https://doi.org/10.1063/1.1571658

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