The rôle of one- and few-phonon processes in the quantum diffusion of light particles in superconductors

The hopping motion of charged light particles in superconducting metals is discussed within the framework of a two-state model. In addition to the coupling to the superconducting electrons, the influence of phonons is investigated. It is shown that sufficiently far below the critical temperature the hopping rate is dominated by one-phonon processes if the static energy shifts between the particle ground states (so-called energy asymmetries) are finite but smaller than twice the BCS energy gap. The rôle of special two-phonon processes (named diphonon processes) resulting from non-linear coupling to the lattice is investigated. In the limit of energy asymmetries larger than twice the BCS energy gap phonon coupling does not crucially influence the jump rates.This article was processed using Springer-Verlag T_EX Z. Physik B macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.