Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Série IPHT-PHM
Domaines math-ph
Date Lundi 27 Octobre 2014
Heure 11:00
Institut IPHT
Salle Salle Claude Itzykson, Bât. 774, Orme des Merisiers
Nom de l'orateur Sasha Turbiner
Prenom de l'orateur
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Institution de l'orateur
Titre Solvability, Integrability, discrete symmetry in planar (elliptic) quantum dynamics
Résumé Algebraic-rational nature of two-dimensional, Weyl-invariant integrable quantum Hamiltonians (rational, trigonometric and elliptic) is revealed and reviewed. If written in special Weyl invariants (polynomial, exponential and elliptic), all similarity-transformed Hamiltonians (and integrals) are in algebraic form: they are the second order differential operators with polynomial coefficients; the flat metric in the Laplace-Beltrami operator is polynomial, their potentials are rational functions with singularities at the boundaries of the configuration space. Ground state eigenfunctions are algebraic functions in a form of product of polynomials in some degrees. \par It is shown that $A_2$ and $BC_2$ models possess the hidden algebra $gl(3)$, their coupling constants are defined by spin of representation. For quantized values of coupling constants the representation becomes finite-dimensional and a number of polynomial eigenfunctions occur. \par For the elliptic Hamiltonian there exists a single finite-dimensional invariant subspace. While the rational and trigonometric Hamiltonians preserve the same infinite flag of polynomial spaces. Unusual particular integral common for all three models is derived.
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