## 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 ± is raised through one. The scaling equations are derived by applying a perturbative renormalization group to the systems partition function. The dynamics is studied using Feynmans influence-functional theory. We compute directly the nonlinear mobility of the Brownian particle in the weak-corrugation limit, for arbitrary temperature. The linear mobility 1/4l is always larger than the corresponding classical mobility which follows from the Langevin equation. In the localized regime ±>1, 1/4l is an increasing function of temperature, consistent with transport via a thermally assisted hopping mechanism. For ±<1, 1/4l(T) shows a nonmonotonic dependence on T with a minimum at a temperature T*. This is due to a crossover between quantum tunneling below T* and thermally assisted hopping above T*. For low friction the crossover occurs when the particles thermal de Broglie wavelength is roughly equal to the distance between minima in the periodic potential. We suggest that the regime ±<1 describes the physics of the observed nonmonotonic temperature dependence of muon diffusion in metals.

Original language | English |
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Pages (from-to) | 6190-6206 |

Number of pages | 17 |

Journal | Physical Review B |

Volume | 32 |

Issue number | 10 |

DOIs | |

State | Published - 1985 |

Externally published | Yes |