On the convergence to statistical equilibrium for harmonic crystals

Details On the convergence to statistical equilibrium for harmonic crystals On the convergence to statistical equilibrium for harmonic crystals

2002-10-22

arxiv.org/abs/math-ph/0210039v2

Physics

Mathematical Physics

Scientific paper

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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