Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order

Details Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order

2012-03-28

arxiv.org/abs/1203.6207v1

Physics

Condensed Matter

Statistical Mechanics

11 pages, 2 figures

Scientific paper

A novel scheme for the steady state solution of the standard Redfield quantum master equation is developed which yields agreement with the exact result for the corresponding reduced density matrix up to second order in the system-bath coupling strength. We achieve this objective by use of an analytic continuation of the off-diagonal matrix elements of the Redfield solution towards its diagonal limit. Notably, our scheme does not require the provision of yet higher order relaxation tensors. Using this modified method we demonstrate that if the bath consists of a collection of harmonic oscillators the system relaxes towards its exact generalized Gibbs state up to second order in system-bath coupling. We numerically compare our formulation for a harmonic system that is coupled bi-linearly to a harmonic bath with the nonequilibrium Green's function formalism; we obtain good agreement for much stronger coupling strengths than expected from the regime of validity of the second-order Redfield quantum master equation. Yet another advantage of our method is that it markedly reduces the numerical complexity of the problem; thus allowing to study efficiently rather large-sized \emph{system} Hilbert spaces.

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