The Time-Convolutionless Projection Operator Technique in the Quantum Theory of Dissipation and Decoherence

Abstract

The time-convolutionless projection operator method is used to investigate the non-Markovian dynamics of open quantum systems. On the basis of this method a systematic perturbation expansion for the reduced density matrix equation is obtained involving a time-dependent generator which is local in time. This formalism is generalized to enable the treatment of system-environment correlations in the initial state, which arise in the computation of equilibrium correlation functions or from the preparation of the system by a quantum measurement. The general method is illustrated by means of the damped harmonic oscillator and of the spin-boson model. The perturbation expansion of the equation of motion is applied to a study of relaxation and dephasing processes and to the determination of the stationary state and of equilibrium correlation functions. Special emphasis is laid on the construction of general, computable error estimates which allow the explicit validation of the obtained results. In particular, the parameter regime for which an expansion of the equation of motion to fourth order yields reliable results is determined. The results clearly reveal that a large range of physically relevant parameters, in particular those that might be interesting for experiments on macroscopic quantum coherence phenomena, can already be treated using the expansion to fourth order. It is thus demonstrated that the time-convolutionless projection operator technique provides a transparent and technically feasible method to go beyond the Markovian approximation in the study of open quantum systems.