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

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

2007-11-07

arxiv.org/abs/0711.1091v1

Physics

Mathematical Physics

22 pages

Scientific paper

We consider the Hamiltonian system consisting of a Klein-Gordon vector field and a particle in $\R^3$. 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 $t\in\R$. The main result is the convergence of $\mu_t$ to a Gaussian measure as $t\to\infty$, where $\mu_\infty$ is translation-invariant.

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