Hamiltonian dynamics and spectral theory for spin-oscillators - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Communications in Mathematical Physics Année : 2012

Hamiltonian dynamics and spectral theory for spin-oscillators

Résumé

We study the Hamiltonian dynamics and spectral theory of spin\--oscillators. Because of their rich structure, spin\--oscillators display fairly general properties of integrable systems with two degrees of freedom. Spin-oscillators have infinitely many transversally elliptic singularities, exactly one elliptic-elliptic singularity and one focus-focus singularity. The most interesting dynamical features of integrable systems, and in particular of spin-oscillators, are encoded in their singularities. In the first part of the paper we study the symplectic dynamics around the focus-focus singularity. In the second part of the paper we quantize the coupled spin-oscillators systems and study their spectral theory. The paper combines techniques from semiclassical analysis with differential geometric methods.
Fichier principal
Vignette du fichier
spin050310-arkiv.pdf (540.93 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00480299 , version 1 (03-05-2010)

Identifiants

Citer

Alvaro Pelayo, San Vu Ngoc. Hamiltonian dynamics and spectral theory for spin-oscillators. Communications in Mathematical Physics, 2012, 309 (1), pp.123-154. ⟨10.1007/s00220-011-1360-4⟩. ⟨hal-00480299⟩
345 Consultations
125 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More