On the Convergence to a Statistical Equilibrium for the Dirac Equation
Dudnikova, T. V. ; Komech, A. I. ; Mauser, N. J.
arXiv, 0508048 / Harvested from arXiv
Text on arXiv
We consider the Dirac equation in $\R^3$ with constant coefficients and study the distribution $\mu_t$ of the random solution at time $t\in\R$. It is assumed that the initial measure $\mu_0$ has zero mean, a translation-invariant covariance, and 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 convergence of $\mu_t$ 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.
Publié le : 2005-08-24
Classification:  Mathematical Physics 
@article{0508048,
     author = {Dudnikova, T. V. and Komech, A. I. and Mauser, N. J.},
     title = {On the Convergence to a Statistical Equilibrium for the Dirac Equation},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0508048}
}

Dudnikova, T. V.; Komech, A. I.; Mauser, N. J. On the Convergence to a Statistical Equilibrium for the Dirac Equation. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0508048/