Partial Abelian semigroups

Ivan Chajda, Jan Paseka, Qiang Lei

David J. Foulis, Richard J. Greechie

Franco Fagnola

Several quantum Markov semigroups admit an invariant abelian subalgebra which can be looked at as an algebra of bounded functions on some measurable space. The restriction to this subalgebra is a semigroup of positive and identity preserving operators i.e. a classical Markov semigroup (see Examples 3.3, 3.4).

André F. Verbeure

LEOPOLDO PANTALEÓN-MARTÍNEZ, Roberto B. Quezada

In this paper we study a class of quantum Markov semigroups whose restriction to an abelian sub-algebra coincides, on the configurations with finite support, with the exclusion type semigroups introduced in Liggett's book14 of exchange rates [Formula: see text] not symmetric in the index site r, s. We find a sufficient condition for the existence of infinitely many faithful diagonal (or classical) invariant states for the semigroup, that satisfy a quantum detailed balance condition. This class of semigroups arises naturally in the stochastic limit of quantum interacting particles in the sense of Accardi and Kozyrev.1 We call these semigroups asymmetric exclusion quantum Markov semigroups and the associated processes asymmetric exclusion quantum processes.

W. A. Majewski