Perturbation of the semiclassical Schrödinger equation on negatively curved surfaces

Suresh Eswarathasan (1) , Gabriel Riviere (2)

1 IHES - Institut des Hautes Études Scientifiques
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We consider the semiclassical Schrödinger equation on a compact negatively curved surface. For any sequence of initial data microlocalized on the unit cotangent bundle, we look at the quantum evolution (below the Ehrenfest time) under small perturbations of the Schrödinger equation, and we prove that, in the semiclassical limit and for typical perturbations, the solutions become equidistributed on the unit cotangent bundle.

Mots clés: semiclassical analysis; hyperbolic dynamical systems; quantum chaos

Domaines: Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Physique mathématique [math-ph]

Suresh Eswarathasan, Gabriel Riviere. Perturbation of the semiclassical Schrödinger equation on negatively curved surfaces. 2014. ⟨hal-00990646v2⟩