On convergence to equilibrium distribution for Dirac equation

Abstract

We consider the Dirac equation in ${\mathbb{R}}^3$ with a potential, and study the distribution ${\mu }_t$ of the random solution at time $t\in \mathbb{R}$. The initial measure ${\mu }_0$ has zero mean, a translation-invariant covariance, and a finite mean charge density. We also assume that ${\mu }_0$ satisfies a mixing condition of Rosenblatt- or Ibragimov-Linnik-type. The main result is the long time convergence of projection of ${\mu }_t$ onto the continuous spectral space. The limiting measure is Gaussian.

15 pages, 0 figures

References in corpus (4)

• Stable directions for small nonlinear Dirac standing waves
• On the convergence to statistical equilibrium for harmonic crystals
• On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing
• On the Convergence to a Statistical Equilibrium for the Dirac Equation