Nonrecurrence of the stochastic process for the hydrogen atom problem in stochastic electrodynamics

Abstract

It is shown, following a criterion borrowed from Khas’minskii, that the stochastic process associated with the (approximate) Fokker–Planck equation of the hydrogen atom problem in stochastic electrodynamics (SED) is nonrecurrent and therefore also nonergodic. The demonstration of this nonrecurrence property does not use any explicit solution. The property implies, among other things, that all the invariant measures of the process will be nonfinite. Some remarks concerning the consequences for SED are made.