Abstract:
The spin-boson model is a widely used model for understanding the properties of a two level open quantum system. Accurately describing its dynamics often requires going
beyond the weak system-environment coupling approximation. This work presents the
analytical derivation of the complete fourth-order time-convolutionless (TCL) generator
for a generic spin-boson model, accurate up to 4th order in the system-environment coupling parameter, for a very general class of environmental spectral densities. We use a higher-order quantum master equation (in system environment coupling strength) to analytically calculate all the deviations of the steady state of the quantum system up to second order in the coupling strength. We also show that this steady state is exactly identical to the corresponding generalized Gibbs state, the so-called quantum mean force Gibbs state, at arbitrary temperature. In the case of a semiconductor double-quantum-dot system, our results reveal corrections to the dynamics that may become physically significant in some parameter regimes. Furthermore, we report that the widely used second-order TCL master equation tends to overestimate the non Markovianity of a dynamics over a large parameter regime. The accuracy of the fourth order TCL generator is rigorously bench marked against specialized analytical calculations done for the Ohmic spectral density with Drude cutoff and against the numerically exact Hierarchical Equations of Motion technique.
