Izvestiya Mathematics

On expansion of quantum quadratic stochastic processes into fibrewise Markov processes defined on von Neumann algebras

Farrukh Maksutovich Mukhamedov

Published Oct 31, 2004• 16 citations

Abstract

We give an expansion of a quantum quadratic stochastic process (q. q. s. p.) into a so-called fibrewise Markov process and prove that, conversely, such an expansion uniquely determines the quantum quadratic stochastic process. As an application, we give a criterion (in terms of this expansion) for the q. q. s. p. to satisfy the ergodic principle. Using this result, we prove that a q. q. s. p. satisfies the ergodic principle if and only if the associated Markov process satisfies this prin- ciple. The expansion obtained is used to introduce a new notion of conjugacy of two q. q. s. p.'s and to study the relation between this notion and the ergodic principle.

DOI: 10.1070/im2004v068n05abeh000506

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