Time evolution of open systems: I. Master equations

Abstract Exact equations of motion for a system interacting with a reservoir are derived from the exact evolution law of the composed system by means of projection-operator techniques. The following two cases are considered: a) an arbitrary system, b) a system consisting of weakly interacting particles. The equation of motion obtained in case b) is used as a starting point for the derivation of a Pauli master equation for a system consisting of weakly interacting particles weakly coupled to a reservoir and the range of validity of this markovian law is discussed extensively. The kernel of the master equation obtained in case a) is investigated in the thermodynamic limit of the reservoir. A diagonal singularity analogous to that of Van Hove is used. The problem of ergodicity and the derivation of a markovian master equation to general order in the system-reservoir interaction are discussed in brief.

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