Operators versus functions: from quantum dynamical semigroups to tomographic semigroups

Quantum dynamical semigroups generated by noncommutative unbounded elliptic operators

We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola’s sufficient conditions for conservativity to show that the semigroups are conservative.

Quantum Dynamical Semigroups and Decoherence

Entropic fluctuations of quantum dynamical semigroups

We study a class of finite dimensional quantum dynamical semigroups {e}t≥0 whose generators L are sums of Lindbladians satisfying the detailed balance condition. Such semigroups arise in the weak coupling (van Hove) limit of Hamiltonian dynamical systems describing open quantum systems out of equilibrium. We prove a general entropic fluctuation theorem for this class of semigroups by relating t...

Covariant Quantum Dynamical Semigroups: Unbounded Generators

A survey of probabilistic approaches to quantum dynamical semigroups with unbounded generators is given. An emphasis is made upon recent advances in the structural theory of covariant Markovian master equations. As an example, a complete characterizations of the Galilean covariant irreversible quantum Markovian evolutions is given in terms of the corresponding quantum master and Langevin equati...

A resolution of quantum dynamical semigroups

We consider a class of quantum dissipative systems governed by a one parameter completely positive maps on a von-Neumann algebra. We introduce a notion of recurrent and metastable projections for the dynamics and prove that the unit operator can be decomposed into orthogonal projections where each projections are recurrent or metastable for the dynamics.