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.
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.
Accepted:
Published online:
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
@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, Volume 9 (2022), pp. 177-212. doi : 10.5802/jep.181. https://jep.centre-mersenne.org/articles/10.5802/jep.181/
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