Dynamical semigroup description of coherent and incoherent particle—Matter interaction

Abstract

The meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of nonrelativistic quantum field theory is proposed to describe both coherent and incoherent interaction of a single microsystem with matter. Compactly developing the calculations with superoperators, it is shown that the introduction of a time scale linked to irreversibility of the reduced dynamics directly leads to a dynamical semigroup expressed in terms of quantities typical of scattering theory. Its generator consists of two terms, the first linked to a coherent wavelike behavior, the second related to an interaction having a measuring character, possibly connected to events the microsystem produces propagating inside matter. In case these events breed a measurement, an explicit realization of some concepts of modern quantum mechanics (“effects” and “operations”) arises. The relevance of this description to a recent debate questioning the validity of ordinary quantum mechanics to account for such experimental situations as, e.g., neutron interferometry is briefly discussed.