Exact master equation for a noncommutative Brownian particle
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.
Cite
@article{arxiv.hep-th/0602261,
title = {Exact master equation for a noncommutative Brownian particle},
author = {Nuno Costa Dias and Joao Nuno Prata},
journal= {arXiv preprint arXiv:hep-th/0602261},
year = {2009}
}
Comments
Latex file, 28 pages, Published version