TWO-MICROLOCAL REGULARITY OF QUASIMODES ON THE TORUS

Fabricio Macià (1) , Gabriel Riviere (2)

1 UPM - Universidad Politécnica de Madrid
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We study the regularity of stationary and time-dependent solutions to strong perturbations of the free Schrödinger equation on two-dimensional flat tori. This is achieved by performing a second microlocalization related to the size of the perturbation and by analysing concentration and nonconcentration properties at this new scale. In particular, we show that sufficiently accurate quasimodes can only concentrate on the set of critical points of the average of the potential along geodesics.

Mots clés: Schrödinger equation; semiclassical analysis; integrable systems; two-microlocal defect measure

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

Fabricio Macià, Gabriel Riviere. TWO-MICROLOCAL REGULARITY OF QUASIMODES ON THE TORUS. 2017. ⟨hal-01578916⟩