From Convolutionless Generalized Master to Pauli Master Equations

Abstract

Previously we have proved that time integrals of memory functions (i.e. markovian transfer rates from Pauli Master Equations — PME) in Time-Convolution Generalized Master Equations (TC-GME) for probabilities of finding a state of an asymmetric system interacting with a bath with a continuous spectrum are exactly zeroprovided that no approximation was involved. This is irrespective of the usual finite-pertubational-order correspondence with the Golden Rule transition rates. Here, attention is turned to an alternative way to derive the rigorous PME from the Time-Convolutionless Generalized Master Equations (TCL-GME). Arguments are given that the long-time limit of coefficients in TCL-GME for the above probabilities is, under the same assumption and presuming that this limit exists, equal to zero.