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.

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

Mathematical problems and theory of numerical methods

Dudnikova Tatiana Vladimirovna,  ,  orcid.org/0000-0001-9274-3212,  KIAM RAS