On the accuracy of the Pade-resummed master equation approach to dissipative quantum dynamics

TL;DR

This paper develops criteria to evaluate the accuracy of Padé-resummed quantum master equations, effectively identifying regimes where these approximations are reliable in modeling dissipative quantum dynamics.

Contribution

It introduces general criteria for assessing the accuracy of Padé-resummed master equations, validated through extensive comparison with exact results in the spin-boson model.

Findings

Criteria successfully identify reliable parameter regimes.

Padé-resummed equations match exact results in certain regimes.

Guidelines applicable to other resummation techniques.

Abstract

Well--defined criteria are proposed for assessing the accuracy of quantum master equations whose memory functions are approximated by Pad\'e resummation of the first two moments in the electronic coupling. These criteria partition the parameter space into distinct levels of expected accuracy, ranging from quantitatively accurate regimes to regions of parameter space where the approach is not expected to be applicable. Extensive comparison of Pad\'e--resummed master equations with numerically exact results in the context of the spin--boson model demonstrate that the proposed criteria correctly demarcate the regions of parameter space where the Pad\'e approximation is reliable. The applicability analysis we present is not confined to the specifics of the Hamiltonian under consideration and should provide guidelines for other classes of resummation techniques.