Séminaire de Physique ThéoriqueFinite-gap periodic quantum systems and hidden supersymmetry
Mikhail Plushchay (Universidad de Santiago de Chile)
Friday 23 October 2009 14:00 - Tours - Salle 1180 (Bât E2)
I will discuss a hidden, bosonized supersymmetry of a linear and nonlinear nature. It was revealed recently in some quantum mechanical spinless models, whose list includes the Aharonov-Bohm system, the Dirac delta and reflectionless Poschl-Teller potential problems, finite-gap periodic Lamé system and its generalizations. Spin-1/2 extension of a finite-gap system, constructed by a certain Crum-Darboux transformation, is described then by a rich tri-supersymmetric structure, that reflects coherently the band structure and peculiarities of the initial system. Tri-supersymmetry is shown to be realized in a planar model of a non-relativistic electron in periodic magnetic and electric fields of a special form, that produce a 1D crystal for spin components separated by a half-period spacing.