An algebraic construction of quantum flows with unbounded generators

Belton, Alexander C. R. and Wills, Stephen J. (2015) An algebraic construction of quantum flows with unbounded generators. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 51 (1). pp. 349-375. ISSN 0246-0203

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Abstract

It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of a classical Feller process and semigroup from a given generator. The construction is possible provided the generator satisfies an invariance property for some dense subalgebra A_0 of the C* algebra A and obeys the necessary structure relations; the iterates of the generator, when applied to a generating set for A_0, must satisfy a growth condition. Furthermore, it is assumed that either the subalgebra A_0 is generated by isometries and A is universal, or A_0 contains its square roots. These conditions are verified in four cases: classical random walks on discrete groups, Rebolledo's symmetric quantum exclusion processes and flows on the non-commutative torus and the universal rotation algebra.

Item Type: Journal Article
Journal or Publication Title: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Uncontrolled Keywords: /dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 65884
Deposited By: ep_importer_pure
Deposited On: 06 Aug 2013 09:22
Refereed?: Yes
Published?: Published
Last Modified: 01 Jan 2020 08:05
URI: https://eprints.lancs.ac.uk/id/eprint/65884

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