Exact master equation for a noncommutative Brownian particle

Journal Article · Thu Jan 15 04:00:00 EST 2009 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2008.04.009· OSTI ID:21167699

Costa Dias, Nuno ^[1]; Nuno Prata, Joao ^[1]

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1. Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa (Portugal)

We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.

• OSTI ID: 21167699
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 324; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BROWNIAN MOVEMENT
COMMUTATION RELATIONS
EQUATIONS
EQUILIBRIUM
GEOMETRY
HARMONIC OSCILLATORS
QUANTUM MECHANICS
WIGNER DISTRIBUTION