On convergence to equilibrium distribution for Dirac equation

Details On convergence to equilibrium distribution for Dirac equation On convergence to equilibrium distribution for Dirac equation

2011-12-05

arxiv.org/abs/1201.6221v1

Physics

Mathematical Physics

15 pages, 0 figures

Scientific paper

We consider the Dirac equation in $\R^3$ with a potential, and study the distribution $\mu_t$ of the random solution at time $t\in\R$. 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.

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