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Repeated Quantum Interactions and Unitary Random Walks

Attal, Stéphane; Dhahri, Ameur (2010), Repeated Quantum Interactions and Unitary Random Walks, Journal of Theoretical Probability, 23, 2, p. 345-361. http://dx.doi.org/10.1007/s10959-010-0281-z

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00199955/en/
Date
2010
Journal name
Journal of Theoretical Probability
Volume
23
Number
2
Publisher
Springer
Pages
345-361
Publication identifier
Metadata
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Author(s)
Attal, Stéphane
Dhahri, Ameur
Abstract (EN)
Among the discrete evolution equations describing a quantum system $\rH_S$ undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by classical random variables in $\RR^N$. The characterization we obtain is entirely algebraical in terms of the unitary operator driving the elementary interaction. We show that the solutions of these equations are then random walks on the group $U(\rH_0)$ of unitary operators on $\rH_0$.
Subjects / Keywords
Obtuse random walks; Repeated quantum interactions; Classical and quantum noises