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

Abstract

We describe a method to obtain the reduced density matrix (RDM) correct up to second order in system-bath coupling in \emph{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. \textbf{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.

9 pages, 3 figures. Notation has been modified and several arguments have been revised. This version is accepted in PRE

References in corpus (6)

• Heat Transport in low-dimensional systems
• Quantum thermal transport in nanostructures
• Dissipative Landau-Zener transitions of a qubit: bath-specific and universal behavior
• Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
• The Accuracy of Perturbative Master Equations
• Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation

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