On the Convergence to a Statistical Equilibrium in the Crystal Coupled to a Scalar Field

2005/08/26 by T. V. Dudnikova, A. I. Komech · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #math.PR

paper · pdf

published as Russ. J. Math. Physics, 12 (2005), no. 3, 301-325 · 33 pages

arxiv created 2005/08/26 · arxiv updated 2009/12/01

Abstract

We consider the dynamics of a field coupled to a harmonic crystal with n components in dimension d, d,n≥ 1. The crystal and the dynamics are translation-invariant with respect to the subgroup \Z^d of \R^d. The initial data is a random function with a finite mean density of energy which also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. Moreover, initial correlation functions are translation-invariant with respect to the discrete subgroup \Z^d. We study the distribution μ_t of the solution at time t∈\R. The main result is the convergence of μ_t to a Gaussian measure as t→∞, where μ_∞ is translation-invariant with respect to the subgroup \Z^d.

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