We introduce the notion of Markov states and chains on the Canonical Anticommutation Relations algebra over ℤ, emphasizing some remarkable differences with the infinite tensor product case. We describe the structure of the Markov states on this algebra and show that, contrarily to the infinite tensor product case, not all these states are diagonalizable. A general method to construct nontrivial quantum Markov chains on the CAR algebra is also proposed and illustrated by some pivotal examples. This analysis provides a further step for a satisfactory theory of quantum Markov processes.

Accardi, L., Fidaleo, F., Mukhamedov, F. (2007). Markov states and chains on the car algebra. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 10(2), 165-183 [10.1142/S0219025707002683].

Markov states and chains on the car algebra

ACCARDI, LUIGI;FIDALEO, FRANCESCO;
2007-06-01

Abstract

We introduce the notion of Markov states and chains on the Canonical Anticommutation Relations algebra over ℤ, emphasizing some remarkable differences with the infinite tensor product case. We describe the structure of the Markov states on this algebra and show that, contrarily to the infinite tensor product case, not all these states are diagonalizable. A general method to construct nontrivial quantum Markov chains on the CAR algebra is also proposed and illustrated by some pivotal examples. This analysis provides a further step for a satisfactory theory of quantum Markov processes.
giu-2007
Pubblicato
Rilevanza internazionale
Articolo
Nessuno
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
integration and probability; mathematical quantum statistical mechanics; noncommutative measure; quantum Markov processes
Accardi, L., Fidaleo, F., Mukhamedov, F. (2007). Markov states and chains on the car algebra. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 10(2), 165-183 [10.1142/S0219025707002683].
Accardi, L; Fidaleo, F; Mukhamedov, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/44142
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