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Deux applications du chaos quantique : etude des fonctions d'ondes aleatoires via SLE et description de cavites dielectriques

Abstract : We studied here two problem of quantum chaos. First we gave another argument for the percolation model in order to describe the nodal lines of a wavefunction of a quantum system whose classical counterpart is chaotic. We described the lines via the Schramm Loewner Evolution process and our numerical results show no contradiction with Smirnov's theorem relating SLE and the critical percolation .
Secondly we were interested in dielectric cavities and how to generalize well-known results about billiards to these open systems. We gave the two first terms for the Weyl's expansion of the resonance counting function and generalize the trace formula for these systems. Our results agree with both numerical and experimental data.
This thesis show how fundamental the quantum chaos is for very topical issues.
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https://tel.archives-ouvertes.fr/tel-00343367
Contributor : Remy Dubertrand <>
Submitted on : Monday, December 1, 2008 - 1:11:27 PM
Last modification on : Wednesday, September 16, 2020 - 4:04:44 PM
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R. Dubertrand. Deux applications du chaos quantique : etude des fonctions d'ondes aleatoires via SLE et description de cavites dielectriques. Physique mathématique [math-ph]. Université Paris Sud - Paris XI, 2008. Français. ⟨tel-00343367⟩

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