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On the Convergence to a Statistical Equilibrium for the Dirac Equation

T. V. Dudnikova·A. I. Komech·N. J. Mauser
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Abstract

We consider the Dirac equation in $\R^3$ with constant coefficients and study the distribution $μ_t$ of the random solution at time $t\in\R$. It is assumed that the initial measure $μ_0$ has zero mean, a translation-invariant covariance, and 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 convergence of $μ_t$ to a Gaussian measure as $t\to\infty$. The proof uses the study of long time asymptotics of the solution and S.N. Bernstein's ``room-corridor'' method.

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T. V. Dudnikova, A. I. Komech, N. J. Mauser. 2005-08-24. On the Convergence to a Statistical Equilibrium for the Dirac Equation. https://arxiv.org/abs/math-ph/0508048

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