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Pré-Publication, Document De Travail Année : 2024

Quantum Trajectories. Spectral Gap, Quasi-compactness & Limit Theorems

Résumé

Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit a unique invariant measure under a purification and an irreducibility assumptions. This paper is devoted to the spectral study of the underlying Markov operator. Using Quasi-compactness, it is shown that this operator admits a spectral gap and the peripheral spectrum is described in a precise manner. Next two perturbations of this operator are studied. This allows to derive limit theorems (Central Limit Theorem, Berry-Esseen bounds and Large Deviation Principle) for the empirical mean of functions of the Markov chain as well as the Lyapounov exponent of the underlying random dynamical system.
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Dates et versions

hal-04530764 , version 1 (03-04-2024)

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Tristan Benoist, Arnaud Hautecoeur, Clément Pellegrini. Quantum Trajectories. Spectral Gap, Quasi-compactness & Limit Theorems. 2024. ⟨hal-04530764⟩
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