On convergence to equilibrium distribution for Dirac equation

Publication date: 5 September 2012

Abstract: We consider the Dirac equation in

R^{3}

with a potential, and study the distribution

m u_{t}

of the random solution at time

t i n R

. The initial measure

m u_{0}

has zero mean, a translation-invariant covariance, and a finite mean charge density. We also assume that

m u_{0}

satisfies a mixing condition of Rosenblatt- or Ibragimov-Linnik-type. The main result is the long time convergence of projection of

m u_{t}

onto the continuous spectral space. The limiting measure is Gaussian.