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Title: Quantum diffusion with drift and the Einstein relation. I

We study the dynamics of a quantum particle hopping on a simple cubic lattice and driven by a constant external force. It is coupled to an array of identical, independent thermal reservoirs consisting of free, massless Bose fields, one at each site of the lattice. When the particle visits a site x of the lattice it can emit or absorb field quanta of the reservoir at x. Under the assumption that the coupling between the particle and the reservoirs and the driving force are sufficiently small, we establish the following results: The ergodic average over time of the state of the particle approaches a non-equilibrium steady state describing a non-zero mean drift of the particle. Its motion around the mean drift is diffusive, and the diffusion constant and the drift velocity are related to one another by the Einstein relation.
Authors:
 [1] ;  [2] ;  [3]
  1. Institute for Theoretical Physics, K.U. Leuven, 3001 Leuven (Belgium)
  2. Institute for Theoretical Physics, ETH Zürich, 8093 Zürich (Switzerland)
  3. Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138 (United States)
Publication Date:
OSTI Identifier:
22306194
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 7; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSONS; CUBIC LATTICES; DIFFUSION; EQUILIBRIUM; QUANTUM MECHANICS; RESERVOIR TEMPERATURE; STEADY-STATE CONDITIONS