ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 46, 47 Bulinskij, Andrej, Moscow Institute of Physics and Technology, Russia On dynamical semigroups compatible with states of von Neumann algebras Large time asymptotics is studied for semigroups τ of completely positive mappings (τ_{t})_{t≥0} ⊂ L(M) of a W^{∗}-algebra M which model evolution of open quantum systems in the Markovian approximation. We consider mainly the (classes of cocyclic conjugacy of) semigroups τ having a stationary faithful state ω ∈ M_{∗} and commuting with the modular automorphisms group σ^{ω}. The ergodic properties of the semigroups induced in spaces L^{p}(M, ω) are compared to those of the corresponding semigroups on M_{∗} and M′ in H = L^{2}(M, ω) and of their dilations and regular extension to B(H) to establish some scattering theory structures. The quasi-free evolutions τ related to non-Fock representations of the CAR-algebra are treated in detail, including the index and entropy.