Exact Markovian kinetic equation for a quantum Brownian oscillator

Details Exact Markovian kinetic equation for a quantum Brownian oscillator Exact Markovian kinetic equation for a quantum Brownian oscillator

2007-02-22

arxiv.org/abs/cond-mat/0702514v1

Phys. Rev. E, Vol. 73, 016120 (2006)

Physics

Condensed Matter

Statistical Mechanics

A few typos in the published version are corrected

Scientific paper

10.1103/PhysRevE.73.016120

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 Poincar\'e's sense the invariant subspaces follow the dynamics of uncoupled, renormalized particles. In contrast for non-integrable 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.

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