A perturbative method for nonequilibrium steady state of open quantum systems

Abstract

We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the remaining part $\mathcal{R}$. Regarding the steady state of the Lindblad QME as the unperturbed solution, we perform a perturbative calculation with respect to $\mathcal{R}$ to obtain the NESS of the Redfield QME. The NESS thus determined is exact up to the first order in the system-reservoir coupling strength (pump/loss rate), which is the same as the order of validity of the QME. An advantage of the proposed method in numerical computation is its applicability to systems larger than those in methods of directly solving the original Redfield QME. We apply the method to a noninteracting fermion system to obtain an analytical expression of the NESS density matrix. We also numerically demonstrate the method in a nonequilibrium quantum spin chain.

15 pages, 3 figures. To appear in J. Phys. Soc. Jpn

References in corpus (8)

• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Modeling heat transport through completely positive maps
• Transport in open spin chains: A Monte Carlo wave-function approach
• Geometrical Pumping in Quantum Transport: Quantum Master Equation Approach
• Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories
• Stochastic unraveling of Redfield master equations and its application to electron transfer problems
• Non-equilibrium BBGKY Hierarchy from the Redfield Equation

Cited by in corpus (1)

• Condition for emergence of the Floquet-Gibbs state in periodically driven open systems