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arXiv · 1201.6221

On convergence to equilibrium distribution for Dirac equation

Alexander Komech·Elena Kopylova
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Abstract

We consider the Dirac equation in $\R^3$ with a potential, and study the distribution $μ_t$ of the random solution at time $t\in\R$. The initial measure $μ_0$ has zero mean, a translation-invariant covariance, and a finite mean charge density. We also assume that $μ_0$ satisfies a mixing condition of Rosenblatt- or Ibragimov-Linnik-type. The main result is the long time convergence of projection of $μ_t$ onto the continuous spectral space. The limiting measure is Gaussian.

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Alexander Komech, Elena Kopylova. 2011-12-05. On convergence to equilibrium distribution for Dirac equation. https://arxiv.org/abs/1201.6221

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