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Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052127. Epub 2013 Nov 20.

Reduced density matrix for nonequilibrium steady states: a modified Redfield solution approach.

Author information

1
Department of Physics and Center for Computational Science and Engineering, National University of Singapore, Singapore 117551, Republic of Singapore and Institut für Physik Universität Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany.
2
Department of Physics and Center for Computational Science and Engineering, National University of Singapore, Singapore 117551, Republic of Singapore.

Abstract

We describe a method to obtain the reduced density matrix (RDM) correct up to second order in system-bath coupling in nonequilibrium steady-state situations. The RDM is obtained via a scheme based on analytic continuation, using the time-local Redfield-like quantum master equation, which was earlier used by the same authors [J. Chem. Phys. 136, 194110 (2012)] to obtain the correct thermal equilibrium description. This nonequilibrium modified Redfield solution is then corroborated with the exact RDM obtained via the nonequilibrium Green's function technique for the quantum harmonic oscillator. Lastly, the scheme is compared to different quantum master equations (QMEs), namely the time-local Redfield-like and the Lindblad-like QMEs, in order to illustrate the differences between each of these approaches.

PMID:
24329234
DOI:
10.1103/PhysRevE.88.052127
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