Introduction au chaos classique et au chaos quantique Article Swipe

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Fréderic Faure ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.5802/xups.2014-01

Depuis les travaux de Henri Poincaré (1892) et ensuite Birkhoff, Anosov (1967), Ruelle etc. il est apparu que les trajectoires issues de lois déterministes mais possédant une « forte sensibilité aux conditions initiales » semblent imprévisibles et qu’il y a des propriétés aléatoires émergeantes. On parle de « chaos déterministe en mécanique classique ». On présentera un modèle assez concret de dynamique chaotique que sont les « billards dispersifs ». On établira les propriétés mathématiques du chaos (mélange et ergodicité) sur un modèle similaire mais plus simple appelé « application du chat d’Arnold ». La problématique du chaos quantique est d’étudier la dynamique des ondes quantiques dans un système dont la dynamique classique associée est chaotique comme décrite plus haut. Plus précisément on souhaite comprendre l’évolution des ondes mais aussi la structure et la répartition spatiale des ondes stationnaires. On posera ces questions en montrant quelques exemples numériques intrigants qui serviront à introduire les exposés suivants. Par exemple le « théorème d’ergodicité quantique » (1974) établit que lorsque la dynamique classique est ergodique alors presque toutes les ondes quantiques stationnaires sont équi-réparties sur l’espace.

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Type: article
Language: fr
Landing Page: https://doi.org/10.5802/xups.2014-01
PDF: https://proceedings.centre-mersenne.org/item/10.5802/xups.2014-01.pdf
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Cited By: 3
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DOI: https://doi.org/10.5802/xups.2014-01

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Title: Introduction au chaos classique et au chaos quantique

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Language: fr

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Publication year: 2024

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Publication date: 2024-08-06

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Authors: Fréderic Faure

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Landing page: https://doi.org/10.5802/xups.2014-01

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Concepts: Humanities, CHAOS (operating system), Philosophy, Physics, Computer science, Computer security

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