Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold
Mathematical Physics
2011-11-10 v2 Dynamical Systems
math.MP
Chaotic Dynamics
Abstract
We study the high-energy eigenfunctions of the Laplacian on a compact Riemannian manifold with Anosov geodesic flow. The localization of a semiclassical measure associated with a sequence of eigenfunctions is characterized by the Kolmogorov-Sinai entropy of this measure. We show that this entropy is necessarily bounded from below by a constant which, in the case of constant negative curvature, equals half the maximal entropy. In this sense, high-energy eigenfunctions are at least half-delocalized.
Keywords
Cite
@article{arxiv.math-ph/0610019,
title = {Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold},
author = {Nalini Anantharaman and Stéphane Nonnenmacher},
journal= {arXiv preprint arXiv:math-ph/0610019},
year = {2011}
}
Comments
We added the proof of the Entropic Uncertainty Principle. 45 pages, 2 EPS figures