On the convergence to statistical equilibrium for harmonic crystals

T. V. Dudnikova; A. I. Komech; H. Spohn

doi:10.1063/1.1571658

On the convergence to statistical equilibrium for harmonic crystals

数学物理 2015-06-26 v2 math.MP 概率论

作者: T. V. Dudnikova , A. I. Komech , H. Spohn

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摘要

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.

引用

@article{arxiv.math-ph/0210039,
  title  = {On the convergence to statistical equilibrium for harmonic crystals},
  author = {T. V. Dudnikova and A. I. Komech and H. Spohn},
  journal= {arXiv preprint arXiv:math-ph/0210039},
  year   = {2015}
}

On the convergence to statistical equilibrium for harmonic crystals

摘要

引用

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