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Theses

Marches quantiques ouvertes

Abstract : This thesis is devoted to the study of stochastic models derived from open quantum systems. In particular, this work deals with open quantum walks that are the quantum analogues of classical random walks. The first part consists in giving a general presentation of open quantum walks. The mathematical tools necessary to study open quan- tum systems are presented, then the discrete and continuous time models of open quantum walks are exposed. These walks are respectively governed by quantum channels and Lindblad operators. The associated quantum trajectories are given by Markov chains and stochastic differential equations with jumps. The first part concludes with discussions over some of the research topics such as the Dirichlet problem for open quantum walks and the asymptotic theorems for quantum non demolition measurements. The second part collects the articles written within the framework of this thesis. These papers deal with the topics associated to the irreducibility, the recurrence-transience duality, the central limit theorem and the large deviations principle for continuous time open quantum walks.
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Hugo Bringuier. Marches quantiques ouvertes. Probabilités [math.PR]. Université Paul Sabatier - Toulouse III, 2018. Français. ⟨NNT : 2018TOU30064⟩. ⟨tel-02132906⟩

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