Exact generator and its high order expansions in the time-convolutionless generalized master equation: Applications to the spin-boson model and exictation energy transfer

TL;DR

This paper introduces a new method to compute the exact time-convolutionless (TCL) generator and its high order expansions using hierarchical equations of motion, applied to the spin-boson model and excitation energy transfer, enhancing accuracy in quantum dynamics simulations.

Contribution

The paper presents a novel approach to calculate the exact TCL generator and its high order expansions using HEOM methods, improving upon approximate perturbative techniques.

Findings

High order expansions converge for certain parameters.

Exact TCL generator can become singular under specific conditions.

Application to Fenna-Matthews-Olson complex demonstrates practical relevance.

Abstract

The time-convolutionless (TCL) quantum master equation provides a powerful tool to simulate reduced dynamics of a quantum system coupled to a bath. The key quantity in the TCL master equation is the so-called kernel or generator, which describes effects of the bath degrees of freedom. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. By using the hierarchical equation of motion (HEOM) and extended HEOM methods, we present a new approach to calculate the exact TCL generator and its high order perturbative expansions. The new approach is applied to the spin-boson model with different sets of parameters, to investigate the convergence of the high order expansions of the TCL generator. We also discuss circumstances where the exact TCL generator becomes singular for the spin-boson model, and a model of excitation energy transfer in the Fenna-Matthews-Olson complex.