Marek Miller

Ergodic properties of diffusion-type quantum dynamical semigroups

Quantum dynamical semigroups are recognized as a valuable tool to study the dynamics of open quantum systems, especially in the algebraic framework of quantum theory. Here we discuss the mathematical background and the physical motivation behind the definition of a quantum dynamical semigroup, as well as we investigate the ergodic properties of the semigroups of a special kind, namely the so-called diffusion-type semigroups.The diffusion-type quantum dynamical semigroups play an important role in the theory of open quantum systems subjected to the process of diffusion or quantum Brownian motion. Our effort has been concentrated on presenting the theory of such semigroups as representations of convolution semigroups of measures on locally compact topological groups. After formulating the results for compact topological groups, we discuss several examples of quantum dynamical semigroups originating from non-compact groups.