Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-02-24
Annals Phys.324:73-96,2009
Physics
High Energy Physics
High Energy Physics - Theory
Latex file, 28 pages, Published version
Scientific paper
10.1016/j.aop.2008.04.009
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.
Dias Nuno Costa
Prata Joao Nuno
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