On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing

Details On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing

2005-08-22

arxiv.org/abs/math-ph/0508042v1

Comm. Math. Phys. 225 (2002), no.1, 1-32

Physics

Mathematical Physics

30 pages

Scientific paper

10.1007/s002201000581

Consider the Klein-Gordon equation (KGE) in $\R^n$, $n\ge 2$, with constant or variable coefficients. We study the distribution $\mu_t$ of the random solution at time $t\in\R$. We assume that the initial probability measure $\mu_0$ has zero mean, a translation-invariant covariance, and a finite mean energy density. We also asume that $\mu_0$ satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. The main result is the convergence of $\mu_t$ to a Gaussian probability measure as $t\to\infty$ which gives a Central Limit Theorem for the KGE. The proof for the case of constant coefficients is based on an analysis of long time asymptotics of the solution in the Fourier representation and Bernstein's `room-corridor' argument. The case of variable coefficients is treated by using an `averaged' version of the scattering theory for infinite energy solutions, based on Vainberg's results on local energy decay.

Affiliated with

Also associated with

No associations

Rating

On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-462599