Non-Commutative Markov Chains and Multi-Analytic Operators

2009/02/19 by Rolf Gohm, Gohm, Rolf
Mathematics · Physics and Astronomy · #46L53 #47A13 #47A40 #47A48 #81R15 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Physics (quant-ph) #math-ph #math.MP #math.OA #msc:46L53 #msc:47A13 #msc:47A40 #msc:47A48 #msc:81R15 #quant-ph

paper · pdf · doi:10.48550/arxiv.0902.3445

19 pages

arxiv created 2009/02/19 · arxiv updated 2009/12/01

Abstract

We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input-output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.

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