On the Convergence to a Statistical Equilibrium for the Dirac Equation

2005/08/24 by T. V. Dudnikova, A. I. Komech, N. J. Mauser
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf

published as Russian J. Math. Physics, 10 (2003), no.4, 399-410 · 12 pages

arxiv created 2005/08/24 · arxiv updated 2009/12/01

Abstract

We consider the Dirac equation in \R³ with constant coefficients and study the distribution μ_t of the random solution at time t∈\R. It is assumed that the initial measure μ₀ has zero mean, a translation-invariant covariance, and finite mean charge density. We also assume that μ₀ 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→∞. The proof uses the study of long time asymptotics of the solution and S.N. Bernstein's ``room-corridor'' method.

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