SUPERSCARRED QUASIMODES ON FLAT SURFACES WITH CONICAL SINGULARITIES
Résumé
We construct a continuous family of quasimodes for the Laplace-Beltrami operator on a translation surface. We apply our result to rational polygonal quantum billiards and thus construct a continuous family of quasimodes for the Neumann Laplacian on such domains with spectral width O ε (λ 3/8+ε). We show that the semiclassical measures associated with this family of quasimodes project to a finite sum of Dirac measures on momentum space, hence, they satisfy Bogomolny and Schmit's superscar conjecture for rational polygons.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)