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arXiv · hep-th/0602261

Exact master equation for a noncommutative Brownian particle

Nuno Costa Dias·Joao Nuno Prata
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Abstract

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.

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Nuno Costa Dias, Joao Nuno Prata. 2009-07-12. Exact master equation for a noncommutative Brownian particle. https://doi.org/10.1016/j.aop.2008.04.009

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