QUANTUM-THEORY OF DISSIPATIVE PROCESSES - THE MARKOV APPROXIMATION REVISITED

Adopting the standard mathematical framework for describing reduced dy namics, we derive two formal identities for the density operator of an open quantum system. Each of these is equivalent to the old Nakajima- Zwanzig equation. The first identity is local in time. It contains the inverse of the dynamical map which governs the evolution of the densi ty operator. We indicate a time interval on which this inverse exists. The second identity constitutes a suitable starting point for going b eyond the Markov approximation in a controlled way. On the basis of th e Bloch equations we argue once more that in studying quantum dissipat ion one has to pay attention to the von Neumann conditions. In the Nak ajima-Zwanzig equation we make the first Born approximation. The ensui ng master equation possesses the correct weak-coupling limit. While pr oving this rather obvious but at the same time important statement, we elucidate the mathematical methods which underlie the weak-coupling l imit. Moving to a two-dimensional Hilbert space, we find that both for short and for long times our approximate master equation respects the von Neumann conditions. Assuming exponential decay for correlation fu nctions, we propose a physical limit in which the solutions for the de nsity operator become Markovian in character. We confirm the well-know n statement that, as seen from a macroscopic standpoint, the system st arts from an effective initial condition. The approach to equilibrium is exponential. The accessory relaxation constants can differ from the usual Bloch parameters gamma(perpendicular to) and gamma(11) by more than 50%.