Quantum diffusion of a light particle in the Meissner phase of a superconductor

The influence of a superconducting fermionic environment on quantum diffusion is investigated. Within the framework of a two-state model hopping rates are calculated both for the biased and unbiased case. As for the latter, the jump frequency shows towards lower temperatures an exponential increase caused by the dyingout of quasiparticle excitations. The calculated rates show a much stronger sensitivity on bias than in the normal state. For small bias (compared to the energy gap) they behave non-monotonically: below a certain temperature an exponential decrease is found which leads to a localization of the particle. For large bias the hopping rates are not substantially changed by the onset of superconductivity.