Non-equilibrium steady states for Hamiltonian chains and networks

Diplôme Thèse Non-equilibrium steady states for Hamiltonian chains and networks eng 2016-04-08 author Cuneo Noé 773132 director Eckmann Jean-Pierre 0000-0001-6118-1077 24759 director Velenik Yvan Alain 0000-0002-6459-3197 42242 Yvan Velenik 10.13097/archive-ouverte/unige:83489 urn:nbn:ch:unige-834896 Sc. 4916 In this thesis, we consider heat-conducting chains and networks, which are prototypical examples of non-equilibrium systems. We prove the existence and uniqueness of an invariant measure (also called non-equilibrium steady state) for some classical systems made of interacting oscillators and rotors coupled with stochastic heat baths at (possibly) different temperatures. We start by introducing the models of interest and putting them into context. We then focus on the uniqueness problem for networks of oscillators, by introducing a set of tools to verify Hörmander's bracket condition. Next, we prove the existence and uniqueness of a steady state for chains of 3 rotors. We show that the system converges to this steady state at a stretched exponential rate. Finally, we extend these results (existence, uniqueness and convergence to the steady state) to chains of 4 rotors, which requires to deal with resonances. Mathematical physics Statistical mechanics Stochastic process Non-equilibrium systems Dewey 500.2 37 Département de physique théorique 133 false bbacbaf4-4e79-4db4-a697-2ebd206e5935 Thesis Restricted thesis_final_version_PDF.pdf 2928118 application/pdf d5372f26e3f066e401bb82e90c4f7f7cecf6ce49f763f44a724b58f7a185337c restrictedAccess Faculté des sciences / Section de physique / Département de physique théorique

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Non-equilibrium steady states for Hamiltonian chains and networks				2016	661	14

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