Repeated Quantum Interactions and Unitary Random Walks

2007/12/20 by Stéphane Attal, Attal, Stéphane, Ameur Dhahri +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · doi:10.48550/arxiv.0712.3417

openalex publication_date 2007/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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(\rH₀) of unitary operators on \rH₀.

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