Title :

Perturbation of the semiclassical Schrödinger equation on negatively curved surfaces

Author(s) :

Eswarathasan, Suresh [Auteur]
Institut des Hautes Études Scientifiques [IHES]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

semiclassical analysis
hyperbolic dynamical systems
quantum chaos

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Systèmes dynamiques [math.DS]
Mathématiques [math]/Physique mathématique [math-ph]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Comment :

48 pages. Compared with version 1, we consider slightly different families of perturbations in order to simplify the exposition.

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL