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

Simple item page
dc.creatorDudnikova, T. V.
dc.creatorKomech, A. I.
dc.date2005-08-26
dc.date.accessioned2026-07-07T04:32:18Z
dc.date.available2026-07-07T04:32:18Z
dc.descriptionWe consider the dynamics of a field coupled to a harmonic crystal with $n$ components in dimension $d$, $d,n\ge 1$. 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 $t\in\R$. The main result is the convergence of $μ_t$ to a Gaussian measure as $t\to\infty$, where $μ_\infty$ is translation-invariant with respect to the subgroup $\Z^d$.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0508053
dc.identifierhttp://arxiv.org/abs/math-ph/0508053
dc.identifierRuss. J. Math. Physics, 12 (2005), no. 3, 301-325
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58139
dc.subjectMathematical Physics
dc.subjectProbability
dc.titleOn the Convergence to a Statistical Equilibrium in the Crystal Coupled to a Scalar Field
dc.typetext

Files

Collections

arXiv