[Comment les états lagrangiens évoluent en ondes aléatoires]
Dans cet article, nous considérons une variété riemannienne connexe, compacte, de courbure sectionnelle négative, et une famille d’états lagrangiens semi-classiques sur . Pour une grande famille de phases , nous montrons que que l’on fait évoluer par l’équation de Schrödinger pendant un temps long ressemble à un champ aléatoire gaussien. Ceci peut être vu comme un analogue de la conjecture des ondes aléatoires de Berry pour les états lagrangiens.
In this paper, we consider a compact connected manifold of negative curvature, and a family of semi-classical Lagrangian states on . For a wide family of phases , we show that , when evolved by the semi-classical Schrödinger equation during a long time, resembles a random Gaussian field. This can be seen as an analogue of Berry’s random waves conjecture for Lagrangian states.
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Keywords: Quantum chaos, semi-classical analysis, Berry’s conjecture, random waves
Mot clés : Chaos quantique, analyse semi-classique, conjecture de Berry, ondes aléatoires
Maxime Ingremeau 1 ; Alejandro Rivera 2
CC-BY 4.0
@article{JEP_2022__9__177_0,
author = {Maxime Ingremeau and Alejandro Rivera},
title = {How {Lagrangian} states evolve into random~waves},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {177--212},
publisher = {\'Ecole polytechnique},
volume = {9},
year = {2022},
doi = {10.5802/jep.181},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.181/}
}
TY - JOUR AU - Maxime Ingremeau AU - Alejandro Rivera TI - How Lagrangian states evolve into random waves JO - Journal de l’École polytechnique — Mathématiques PY - 2022 SP - 177 EP - 212 VL - 9 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.181/ DO - 10.5802/jep.181 LA - en ID - JEP_2022__9__177_0 ER -
%0 Journal Article %A Maxime Ingremeau %A Alejandro Rivera %T How Lagrangian states evolve into random waves %J Journal de l’École polytechnique — Mathématiques %D 2022 %P 177-212 %V 9 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.181/ %R 10.5802/jep.181 %G en %F JEP_2022__9__177_0
Maxime Ingremeau; Alejandro Rivera. How Lagrangian states evolve into random waves. Journal de l’École polytechnique — Mathématiques, Tome 9 (2022), pp. 177-212. doi : 10.5802/jep.181. https://jep.centre-mersenne.org/articles/10.5802/jep.181/
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