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Theses

Polymères Dirigés et Réseaux Conducteurs de Chaleur - Systèmes de mécanique statistique à l'équilibre et hors équilibre

Abstract : This PhD thesis presents two examples arising in statistical mechanics. Directed polymers in random environment are a model of an equilibrium system. We give a criterium based on the comparison between network and environment entropies to provide an improved lower bound on the critical temperature. We also use some well-known results about Anderson Parabolic Equation to obtain an asymptotic on the free energy. We also use directed polymers to give a simple proof of the independance on the initial condition of the Lyapunov function in the Anderson Parabolic Equation.

Heat conduction networks are studied out of equilibrium. When the interacting potentials are harmonic, we give a geometric interpretation of the existence and uniqueness of the invariant measure using a completeness theorem. When this geometric condition fails to occur, we give an explicit invariant of the Hamiltonian flow. We generalize the uniqueness results to analytic potentials. We also show that the Hörmander condition is sufficient to obtain uniqueness of the invariant measure via weak controlability. Lasalle's principle is used to avoid Hörmander's condition. We will also bring up the problem of existence.
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https://tel.archives-ouvertes.fr/tel-00344652
Contributor : Alain Camanes <>
Submitted on : Friday, December 5, 2008 - 1:55:48 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
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Alain Camanes. Polymères Dirigés et Réseaux Conducteurs de Chaleur - Systèmes de mécanique statistique à l'équilibre et hors équilibre. Mathématiques [math]. Université de Nantes, 2008. Français. ⟨tel-00344652⟩

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