Convergence to equilibrium distribution. The Klein-Gordon equation coupled to a particle

Abstract

We consider the Hamiltonian system consisting of a Klein-Gordon vector field and a particle in ${\mathbb{R}}^3$. The initial date of the system is a random function with a finite mean density of energy which also satisfies a Rosenblatt- or Ibragimov-type mixing condition. Moreover, initial correlation functions are translation-invariant. We study the distribution ${\mu }_t$ of the solution at time $t\in \mathbb{R}$. The main result is the convergence of ${\mu }_t$ to a Gaussian measure as $t\to \infty$, where ${\mu }_{\infty }$ is translation-invariant.

22 pages

References in corpus (4)

• On the convergence to statistical equilibrium for harmonic crystals
• On scattering of solitons for the Klein-Gordon equation coupled to a particle
• On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing
• On the Convergence to a Statistical Equilibrium in the Crystal Coupled to a Scalar Field

Cited by in corpus (1)

• On the convergence to a statistical equilibrium for the wave equations coupled to a particle