Abstract
We study the statics and dynamics of a quantum Brownian particle moving in a periodic potential and coupled to a dissipative environment in a way which reduces to a Langevin equation with linear friction in the classical limit. At zero temperature there is a transition from an extended to a localized ground state as the dimensionless friction α is raised through one. The scaling equations are derived by applying a perturbative renormalization group to the system’s partition function. The dynamics is studied using Feynman’s influence-functional theory. We compute directly the nonlinear mobility of the Brownian particle in the weak-corrugation limit, for arbitrary temperature. The linear mobility is always larger than the corresponding classical mobility which follows from the Langevin equation. In the localized regime α>1, is an increasing function of temperature, consistent with transport via a thermally assisted hopping mechanism. For α<1, (T) shows a nonmonotonic dependence on T with a minimum at a temperature . This is due to a crossover between quantum tunneling below and thermally assisted hopping above . For low friction the crossover occurs when the particle’s thermal de Broglie wavelength is roughly equal to the distance between minima in the periodic potential. We suggest that the regime α<1 describes the physics of the observed nonmonotonic temperature dependence of muon diffusion in metals.
- Received 9 May 1985
DOI:https://doi.org/10.1103/PhysRevB.32.6190
©1985 American Physical Society