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Title: Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
Authors: Thingna, J.
Wang, J.-S. 
Hänggi, P. 
Issue Date: 21-May-2012
Citation: Thingna, J., Wang, J.-S., Hänggi, P. (2012-05-21). Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order. Journal of Chemical Physics 136 (19) : -. ScholarBank@NUS Repository.
Abstract: 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. Testing this modified method for a heat bath consisting of a collection of harmonic oscillators we assess that the system relaxes towards its correct coupling-dependent, generalized quantum Gibbs state in second order. We numerically compare our formulation for a damped quantum harmonic system with the nonequilibrium Greens function formalism: we find good agreement at low temperatures for coupling strengths that are even larger than expected from the very 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 large-sized system Hilbert spaces. © 2012 American Institute of Physics.
Source Title: Journal of Chemical Physics
ISSN: 00219606
DOI: 10.1063/1.4718706
Appears in Collections:Staff Publications

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