On dynamical semigroups and open systems

Robert Alicki, Joachim A. Messer

Andrzej Posiewnik

Paolo Aniello

Semigroups of operators are known to play an important role in theoretical physics. In particular, quantum dynamical semigroups are fundamental in the theory of open quantum systems. We will describe a class of semigroups of operators which has interesting applications, for instance, in quantum information science. Each of these semigroups of operators is generated, in a suitable way, by a representation (or an antirepresentation) of a group in a Banach space and by a convolution semigroup of probability measures on that group. Some significant examples—including a remarkable type of quantum dynamical semigroups introduced by Kossakowski in the pioneering times of the theory of open quantum systems—and their mutual relations will be discussed.

E. B. Davies

Hiroshi Tamura, Valentin Anatol'evich Zagrebnov

We consider a dynamical semigroup for unbounded Kossakowski-Lindblad-Davies generator corresponding to evolution of an open system for a tuned repeated harmonic perturbation. For this evolution, we prove the existence of uniquely determined minimal trace-preserving strongly continuous dynamical semigroups on the space of states. The corresponding dual W∗-dynamical system is shown to be unital quasi-free and completely positive automorphisms of the canonical commutation relation-algebra.

Wawrzyniec Guz