Quantum diffusion of a heavy particle moving in a periodic potential and interacting with an electron gas

Abstract

We study the diffusion of a heavy particle moving in a strongly corrugated periodic potential and interacting with an electronic bath. Using a path-integral approach we are able to integrate out the electrons and to derive an effective action for the particle in two different limiting cases: (i) arbitrary large coupling between heavy particles and electrons and linear dissipation, and (ii) weak coupling and nonlinear dissipation. In the first case we obtain an effective action for the particle of the Caldeira-Leggett ohmic form, with a friction coefficient equal to that of a classical Brownian particle in a fermionic bath. In the second case we obtain a nonlinear, but still ohmic, dissipative term. Using an instanton approach we evaluate the mobility (and the diffusion coefficient) of the particle, whose temperature dependence shows a cross-over from diffusive to localized behaviour at a critical value of the friction, which is different in the two considered cases. Finally we discuss whether the friction can reach such a critical value, and we arrive at the conclusion that this might happen only for a rather high spin degeneracy.