The time-convolution less projection operator technique in the quantum of theory of dissipation and decoherence

The time-convolutionless projection operator method is used to investigate the non-Markovian dynamics of open quantum systems. On the basis of this me thod a systematic perturbation expansion for the reduced density matrix equ ation is obtained involving a time-dependent generator which is local in ti me. This formalism is generalized to enable the treatment of system-environ ment correlations in the initial state, which arise in the computation of e quilibrium correlation functions or from the preparation of the system by a quantum measurement. The general method is illustrated by means of the dam ped harmonic oscillator and of the spin-boson model. The perturbation expan sion of the equation of motion is applied to a study of relaxation and deph asing processes and to the determination of the stationary state and of equ ilibrium correlation functions. Special emphasis is laid on the constructio n of general, computable error estimates which allow the explicit validatio n of the obtained results. In particular, the parameter regime for which an expansion of the equation of motion to fourth order yields reliable result s is determined. The results clearly reveal that a large range of physicall y relevant parameters, in particular those that might be interesting for ex periments on macroscopic quantum coherence phenomena, can already be treate d using the expansion to fourth order, It is thus demonstrated that the tim e-convolutionless projection operator technique provides a transparent and technically feasible method to go beyond the Markovian approximation in the study of open quantum systems. (C) 2001 Academic Press.