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Comptes Rendus Mathématique
Volume 340, n° 1
pages 21-26 (janvier 2005)
Doi : 10.1016/j.crma.2004.11.013
Received : 27 September 2004 ;  accepted : 9 November 2004
A Gutzwiller type formula for a reduced Hamiltonian within the framework of symmetry
Une formule de type Gutzwiller pour un hamiltonien réduit en présence de symétries
 

Roch Cassanas
Laboratoire de mathématiques Jean Leray, UMR CNRS-université de Nantes, faculté des sciences et techniques, 2, rue de la Houssinière, BP 92208, 44322 Nantes cedex 3, France 

Abstract

For a classical Hamiltonian with a finite group of symmetries, we give semi-classical asymptotics in a neighbourhood of an energy E of a regularized spectral density of the quantum Hamiltonian restricted to symmetry subspaces of Peter-Weyl defined by irreducible characters of the group. If we suppose that the energy level   is compact, non-critical, and that its periodic orbits are non-degenerate, we get a Gutzwiller type formula for the reduced Hamiltonian, whose oscillating part involves the symmetry properties of closed trajectories of  . To cite this article: R. Cassanas, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The full text of this article is available in PDF format.
Résumé

Pour un hamiltonien classique comportant des symétries issues dʼun groupe fini, on donne le comportement semi-classique au voisinage dʼune énergie E , dʼune densité spectrale régularisée pour lʼhamiltonien quantique restreint aux espaces de symétries de Peter-Weyl définis par les caractères irréductibles du groupe. Supposant que le niveau dʼénergie   est compact sans point critique, et que ses orbites périodiques sont non dégénérées, on obtient pour lʼopérateur restreint une formule du type Gutzwiller, dont la partie oscillante fait intervenir la symétrie des orbites périodiques de  . Pour citer cet article : R. Cassanas, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The full text of this article is available in PDF format.


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