CONSISTENT APPROXIMATIONS IN GENERALIZED-MASTER-EQUATION THEORIES - APPLICATION TO THE ASYMPTOTIC-TIME SYMMETRY-BREAKING PROBLEM

The time-convolution as well as the time-convolutionless generalized master equations (GME) are rewritten in a simple form permitting an exact formal solution. Using this form, it is argued that possible approximations must be performed consistently on both sides of the GME in order to control deviations of the emerging approximate solution from the exact one. Arguments are given that after such consistent approximations, the initial-condition term can no longer in general be taken as proportional to (T-D0)/p0) (with D0 being the projector used in GME). These conclusions are illustrated for the asymptotic-time symmetry-breaking problem of the spin-boson model. Although standard approximate GME approaches do indicate a possible symmetry breaking, we argue that these results are strongly influenced by the inconsistency of the approximations used. To support this statement we prove the absence of any asymptotic-time symmetry breaking in the zero-bias spin-boson model with a partial site-occupation relaxation.