Nonunitary effects in the time evolution of one-body observables

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Abstract
We present a formal derivation of the exact dynamics of the one-body density matrix. Its essential ingredients are shown to be the following: (a) a mean field unitary time evolution; (b) irreducible nonunitary corrections to the unitary evolution (collision effects); and (c) effects due to the time evolution of initial state correlation [which contribute to both (a) and (b)]. In the weak coupling limit the collision effects give rise to a term of Boltzmann form. A qualitative discussion of the importance of collision effects for the expectation values of one-body operators and a quantitative illustration in the framework of an exactly soluble model are given. In this case one finds large nonunitary contributions.