Mean-field dynamical semigroups on C*-algebras

verfasst von

N. G. Duffield, R. F. Werner

Abstract

We study a notion of the mean-field limit of a sequence of dynamical semigroups on the n-fold tensor products of a C*-algebra A with itself. In analogy with the theory of semigroups on Banach spaces we give abstract conditions for the existence of these limits. These conditions are verified in the case of semigroups whose generators are determined by the successive resymmetrizations of a fixed operator, as well as generators which can be approximated by generators of this type. This includes the time evolutions of the mean-field versions of quantum lattice systems. In these cases the limiting dynamical semigroup is given by a continuous flow on the state space of A. For a class of such flows we show stability by constructing a Liapunov function. We also give examples where the limiting evolution is given by a diffusion, rather than a flow on the state space of A.

Organisationseinheit(en)

Institut für Theoretische Physik

Typ

Artikel

Journal

Rev. Math. Phys.

Band

4

Seiten

383-424

Anzahl der Seiten

42

Publikationsdatum

1992

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

Elektronische Version(en)

https://doi.org/10.1142/S0129055X92000108 (Zugang: Unbekannt)