Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold

Details Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold

2006-10-09

arxiv.org/abs/math-ph/0610019v2

Annales de l'Institut Fourier 57, 7 (2007) 2465-2523

Physics

Mathematical Physics

We added the proof of the Entropic Uncertainty Principle. 45 pages, 2 EPS figures

Scientific paper

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.

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