Exact Markovian kinetic equation for a quantum Brownian oscillator

B. A. Tay and G. Ordonez
Phys. Rev. E 73, 016120 – Published 18 January 2006

Abstract

We derive an exact Markovian kinetic equation for an oscillator linearly coupled to a heat bath, describing quantum Brownian motion. Our work is based on the subdynamics formulation developed by Prigogine and collaborators. The space of distribution functions is decomposed into independent subspaces that remain invariant under Liouville dynamics. For integrable systems in Poincaré’s sense the invariant subspaces follow the dynamics of uncoupled, renormalized particles. In contrast, for nonintegrable systems, the invariant subspaces follow a dynamics with broken time symmetry, involving generalized functions. This result indicates that irreversibility and stochasticity are exact properties of dynamics in generalized function spaces. We comment on the relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.

  • Received 13 July 2005

DOI:https://doi.org/10.1103/PhysRevE.73.016120

©2006 American Physical Society

Authors & Affiliations

B. A. Tay* and G. Ordonez

  • Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas at Austin, 1 University Station C1609, Austin, Texas 78712, USA

  • *Present address: 143, Jalan Green, 93150 Kuching, Sarawak, Malaysia.
  • Present address: Butler University, 4600 Sunset Ave., Indianapolis, IN 46208. Electronic address: gonzalo@ph.utexas.edu

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Issue

Vol. 73, Iss. 1 — January 2006

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