Fulltext

Quantum Brownian Motion in a Simple Model System

De Roeck, W. ; Fröhlich, J. ; Pizzo, A.

In: Communications in Mathematical Physics, 2010, vol. 293, no. 2, p. 361-398

Ajouter à la liste personnelle
    Titre
    • Quantum Brownian Motion in a Simple Model System
    Auteur
    • De Roeck, W.. Institute for Theoretical Physics, K.U. Leuven, B3001, Heverlee, Belgium
    • Fröhlich, J.. Institute for Theoretical Physics, ETH Zürich, CH-8093, Zürich, Switzerland
    • Pizzo, A.. Department of Mathematics, University of California at Davis, 95616, Davis, CA, USA
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Communications in Mathematical Physics, 2010, vol. 293, no. 2, p. 361-398. Springer-Verlag
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:315199
    Summary
    We consider a quantum particle coupled (with strength λ) to a spatial array of independent non-interacting reservoirs in thermal states (heat baths). Under the assumption that the reservoir correlations decay exponentially in time, we prove that the motion of the particle is diffusive at large times for small, but finite λ. Our proof relies on an expansion around the kinetic scaling limit ( $${\lambda \searrow 0}$$ , while time and space scale as λ−2) in which the particle satisfies a Boltzmann equation. We also show an equipartition theorem: the distribution of the kinetic energy of the particle tends to a Maxwell-Boltzmann distribution, up to a correction of O(λ2)