Dissipative quantum dynamics in terms of a reduced density matrix distributed over the environment energyM. Esposito and P. Gaspard
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles C. P. 231, Campus Plaine, B-1050 Brussels, Belgium
(Received 28 November 2003; accepted in final form 15 January 2004)
A new perturbative quantum master equation is presented for the dissipative dynamics of a subsystem inside a nanosystem with a constant and finite total energy. The degrees of freedom besides those of the subsystem play the role of the environment. Our equation rules the time evolution of the distribution functions of the subsystem populations and coherences over the energy of the environment. Thanks to these distribution functions, we can take into account the effects of the conservation of the total energy. This equation is more general than the standard perturbative equations used for describing a subsystem interacting with an environment (such as the Redfield or Cohen-Tannoudji equations) because these latter equations can be deduced from it in the limit of an infinitely large environment. We numerically apply this equation to the spin-GORM model for the interaction of a two-level subsystem with an environment described by random matrices. We compare our equation with the exact von Neumann equation of the total system and show its superiority compared to the Redfield equation (in the Markovian and non-Markovian cases).
03.65.Yz - Decoherence; open systems; quantum statistical methods.
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