A perturbative method for nonequilibrium steady state of open quantum systems

Tatsuro Yuge, Ayumu Sugita

Published 2014-09-01Version 1

We develop a method for calculating nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system by 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 larger systems than the methods of directly solving the original Redfield QME. We apply the method to a non-interacting fermion system to obtain an analytical expression of the NESS density matrix. We also numerically demonstrate the method in a nonequilibrium quantum spin chain.