[Monodromie fractionnelle des oscillateurs résonnants classiques et quantiques]
We introduce fractional monodromy for a class of integrable fibrations which naturally arise for classical nonlinear oscillator systems with resonance. We show that the same fractional monodromy characterizes the lattice of quantum states in the joint spectrum of the corresponding quantum systems. Results are presented on the example of a two-dimensional oscillator with resonance 1:(−1) and 1:(−2).
La monodromie fractionnelle est introduite pour une classe de fibrations intégrables, qui apparaissent naturellement en mécanique classique dans le cas d'un oscillateur nonlinéaire avec résonance. On démontre, que la même monodromie fractionnelle caractérise de façon qualitative le réseau des états quantiques dans le spectre conjoint des observables pour les systèmes quantiques correspondants. Les résultats sont présentés en utilisant l'exemple d'un oscillateur à deux degrés de liberté avec la résonance 1 :(−1) et 1 :(−2).
Révisé le :
Publié le :
Nikolaı́ N. Nekhoroshev 1, 2 ; Dmitriı́ A. Sadovskiı́ 2 ; Boris I. Zhilinskii 2
@article{CRMATH_2002__335_11_985_0,
author = {Nikola{\i}́ N. Nekhoroshev and Dmitri{\i}́ A. Sadovski{\i}́ and Boris I. Zhilinskii},
title = {Fractional monodromy of resonant classical and quantum oscillators},
journal = {Comptes Rendus. Math\'ematique},
pages = {985--988},
publisher = {Elsevier},
volume = {335},
number = {11},
year = {2002},
doi = {10.1016/S1631-073X(02)02584-0},
language = {en},
}
TY - JOUR AU - Nikolaı́ N. Nekhoroshev AU - Dmitriı́ A. Sadovskiı́ AU - Boris I. Zhilinskii TI - Fractional monodromy of resonant classical and quantum oscillators JO - Comptes Rendus. Mathématique PY - 2002 SP - 985 EP - 988 VL - 335 IS - 11 PB - Elsevier DO - 10.1016/S1631-073X(02)02584-0 LA - en ID - CRMATH_2002__335_11_985_0 ER -
%0 Journal Article %A Nikolaı́ N. Nekhoroshev %A Dmitriı́ A. Sadovskiı́ %A Boris I. Zhilinskii %T Fractional monodromy of resonant classical and quantum oscillators %J Comptes Rendus. Mathématique %D 2002 %P 985-988 %V 335 %N 11 %I Elsevier %R 10.1016/S1631-073X(02)02584-0 %G en %F CRMATH_2002__335_11_985_0
Nikolaı́ N. Nekhoroshev; Dmitriı́ A. Sadovskiı́; Boris I. Zhilinskii. Fractional monodromy of resonant classical and quantum oscillators. Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 985-988. doi : 10.1016/S1631-073X(02)02584-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02584-0/
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