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Lundi 14 mai 10:30-11:30 Alix Deleporte 
Concentration of eigenfunctions for semiclassical Toeplitz operators

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Lieu : Salle 3L15, IMO

Résumé : Toeplitz operators are a generalisation of the FBI point of view on pseudodifferential operators ; they also allow to quantize compact phase spaces, with applications to spin systems in the large spin limit. Motivated by the Heisenberg Antiferromagnet, we proved a series of results on the subprincipal effects on concentration for low-energy eigenfunctions in the general setting of Toeplitz operators. An example is the « miniwell » situation, studied by Helffer and Sjöstrand for Schrödinger operators but never in the general pseudodifferential case, where the principal symbol (classical energy) is minimal along a submanifold, but the ground state concentrates only at one point, a physical effect known as « quantum selection ».
In this talk, we will present Toeplitz operators, the physical problem of interest, and some of the tools used in our work.

Concentration of eigenfunctions for semiclassical Toeplitz operators  Version PDF