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PERTURBATION OF THE SEMICLASSICAL SCHRÖDINGER EQUATION ON NEGATIVELY CURVED SURFACES

Published online by Cambridge University Press:  27 August 2015

Suresh Eswarathasan
Affiliation:
Institut des Hautes Études Scientifiques, Le Bois-Marie 35, route de Chartres, 91440 Bures-sur-Yvette, France Department of Mathematics and Statistics, McGill University, Montréal, Canada (suresh@ihes.fr; suresh@math.mcgill.ca) School of Mathematics, Cardiff University, Senghennyd Road, Cardiff, Wales, CF244AG, UK
Gabriel Rivière
Affiliation:
Laboratoire Paul Painlevé (U.M.R. CNRS 8524), U.F.R. de Mathématiques, Université Lille 1, 59655 Villeneuve d’Ascq Cedex, France (gabriel.riviere@math.univ-lille1.fr)

Abstract

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.

Type
Research Article
Copyright
© Cambridge University Press 2015 

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