Analyse spectrale et analyse semi-classique pour l'étude de la métastabilité en dynamique moléculaire

Abstract : This thesis is dedicated to the study of the sharp asymptotic behaviour in the low temperature regime of the exit event from a metastable domain $Omegasubset mathbb R^d$ (exit point and exit time) for the overdamped Langevin process. In practice, the overdamped Langevin dynamics can be used to describe for example the motion of the atoms of a molecule or the diffusion of interstitial impurities in a crystal. The obtention of sharp asymptotic approximations of the first exit point density in the small temperature regime is the main result of this thesis. These results justify the use of the Eyring-Kramers law to model the exit event. The Eyring-Kramers law is used for example to compute the transition rates between the states of a system in a kinetic Monte-Carlo algorithm in order to sample efficiently the state-to-state dynamics. The cornerstone of our analysis is the quasi stationary distribution associated with the overdamped Langevin dynamics in $Omega$. The proofs are based on tools from semi-classical analysis. This thesis is divided into three independent chapters. The first chapter (in French) is dedicated to an introduction to the mathematical results. The other two chapters (in English) are devoted to the precise statements and proofs
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Boris Nectoux. Analyse spectrale et analyse semi-classique pour l'étude de la métastabilité en dynamique moléculaire. Chemo-informatique. Université Paris-Est, 2017. Français. ⟨NNT : 2017PESC1228⟩. ⟨tel-01749125⟩

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