Low-energy spectrum of Toeplitz operators with a miniwell

Alix Deleporte (1)

1 IRMA - Institut de Recherche Mathématique Avancée

In the semiclassical limit, it is well-known that the first eigenvector of a Toeplitz operator concentrates on the minimal set of the symbol. In this paper, we give a more precise criterion for concentration in the case where the minimal set of the symbol is a submanifold, in the spirit of the " miniwell condition " of Helffer-Sjöstrand.

Mots clés: Berezin-Toeplitz; Semiclassical Analysis

Domaines: Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Alix Deleporte. Low-energy spectrum of Toeplitz operators with a miniwell. 2017. ⟨hal-01383403v2⟩