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The time-convolutionless (TCL) quantum master equation provides a powerfultool to simulate reduced dynamics of a quantum system coupled to a bath. Thekey 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 TCLgenerators are usually hard to calculate analytically, most applications of theTCL generalized master equation have relied on approximate generators usingsecond and fourth order perturbative expansions. By using the hierarchicalequation of motion (HEOM) and extended HEOM methods, we present a new approachto calculate the exact TCL generator and its high order perturbativeexpansions. The new approach is applied to the spin-boson model with differentsets of parameters, to investigate the convergence of the high order expansionsof the TCL generator. We also discuss circumstances where the exact TCLgenerator becomes singular for the spin-boson model, and a model of excitationenergy transfer in the Fenna-Matthews-Olson complex.

chinese journal of chemical physics/chinese journal of chemical physics

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