Stationary states of quantum dynamical semigroups

Hiroshi Hasegawa, Teruaki Nakagomi

Francesco Ticozzi, S. G. Schirmer, Xiaoting Wang

Wawrzyniec Guz

Franco Fagnola, Rolando Rebolledo

We provide two criteria on the existence of stationary states for quantum dynamical semigroups. The first one is based on the semigroup itself, while the second criterion is based on the generator which is in general unbounded and interpreted as a sesquilinear form. These results are illustrated by physical examples drawn from quantum optics.

Herbert E. Spohn

In analogy to the phenomenological theory of irreversible thermodynamics we define the entropy production for an arbitrary quantum dynamical semigroup with a stationary state. We prove that the entropy production is convex and positive and that the entropy production is a measure of dissipativity of the semigroup. The entropy production is used to prove the approach to equilibrium and to classify the stationary states of semigroups arising in the weak coupling limit.

Dharmendra Kumar, Kalyan B. Sinha, Sachi Srivastava