Quantum Brownian Motion in a Simple Model System

  • W. De Roeck
  • J. Fröhlich
  • A. Pizzo


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 O2).


Boltzmann Equation Irreducible Component Heat Bath Anderson Model Kinetic Limit 
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© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsK.U. LeuvenHeverleeBelgium
  2. 2.Institute for Theoretical PhysicsZürichSwitzerland
  3. 3.Department of MathematicsUniversity of California at DavisDavisUSA

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