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Long-time dynamics of the perturbed Schr\"odinger equation on negatively curved surfaces by Riviere, Gabriel is a scholarly article available to read on EtoBox.

What is Long-time dynamics of the perturbed Schr\"odinger equation on negatively curved surfaces about?

We consider perturbations of the semiclassical Schr{\"o}dinger equation on a compact Riemannian surface with constant negative curvature and without boundary. We show that, for scales of times which are logarithmic in the size of the perturbation, the solutions associated to initial data in a small spectral window become equidistributed in the semiclassical limit. As an application of our method, we also derive some properties of the quantum Loschmidt echo below and beyond the Ehrenfest time for initial data in a small spectral window.

Author

Riviere, Gabriel

Published

2014

Language

EN