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Systèmes quantiques d'interactions répétées: l'approche perturbative

Abstract : Repeated interaction quantum systems are both simple and flexible models which arise naturally in several domains including, particularly, quantum optics and the theory of quantum noises. In this thesis, I became interested in their perturbative study. I generalized a theorem by Attal and Joye [Weak Coupling and Continuous Limits for Repeated Quantum Interactions, J. Stat. Phys., 126, (2007)] on the existence of van Hove limit for those systems to the framework of general von Neumann algebras. Then, I proved that, when the reference system is finite dimensional, the existence of a unique asymptotic state for its van Hove limit implies the convergence of the reference system's state towards a unique periodic asymptotic state, provided that the perturbation parameter is sufficiently small. Moreover, the zero-th order term in a power series expansion on the perturbation parameter of this periodic asymptotic state coincides with the asymptotic state of the van Hove limit, except for their difference in time scale which has to be taken into account (giving rise to the periodicity). This result is important in the physical justification for the use of the thermodynamic formalism in the weak coupling regime developed in [Lebowitz and Spohn, Irreversible thermodynamics for quantum systems weakly coupled to thermal reservoirs, Adv. Chem. Phys. 38 (1978)].
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Contributor : Rodrigo Vargas <>
Submitted on : Wednesday, December 16, 2009 - 12:10:28 PM
Last modification on : Tuesday, May 11, 2021 - 11:36:03 AM
Long-term archiving on: : Thursday, October 18, 2012 - 11:00:24 AM


  • HAL Id : tel-00441518, version 1



Rodrigo Vargas Le-Bert. Systèmes quantiques d'interactions répétées: l'approche perturbative. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2009. Français. ⟨tel-00441518⟩



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