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Journal of Statistical Mechanics: Theory and Experiment (2009) L07001
Unexpected features of quantum degeneracies in a pairing model with two integrable limits
J. Dukelsky1, J. Okolowicz2, M. Ploszajczak3

The evolution pattern of level crossings and exceptional points is studied in a non-integrable pairing model with two different integrable limits. One of the integrable limits has two independent parameter-dependent integrals of motion. We demonstrate, and illustrate in our model, that quantum integrability of a system with more than one parameter-dependent integral of motion is always signaled by level crossings of a complex-extended Hamiltonian. We also find that integrability implies a reduced number of exceptional points. Both properties could uniquely characterize quantum integrability in small Hilbert spaces.
1 :  IEM - Instituto de Estructura de la Materia
2 :  Institute of Nuclear Physics
3 :  GANIL - Grand Accélérateur National d'Ions Lourds
Physique/Physique Quantique

Mathématiques/Algèbres quantiques
algebraic structures of integrable models – quantum chaos