Space-time statistical solutions for the Hamiltonian field-crystal system

Abstract:

We consider the dynamics of a scalar field coupled to a harmonic crystal with n components in dimension d, d,n≥1. The dynamics of the system is translation-invariant with respect to the discrete subgroup Z^{d} of R^{d}. We study the Cauchy problem with random initial data. We assume that the initial measure has a finite mean energy density and the initial correlation functions are translation invariant with respect to the subgroup Z^{d}. We prove the convergence of space-time statistical solutions to a Gaussian measure.

Keywords:

the harmonic crystal coupled to a scalar field, Cauchy problem, random initial data, space-time statistical solutions, weak convergence of measures

Publication language:english, страниц:20

Research direction:

Mathematical problems and theory of numerical methods