Delocalization of quasimodes on the disk

2015/04/16 by Nalini Anantharaman, Anantharaman, Nalini, Matthieu Léautaud +3 · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #math-ph #math.AP #math.MP #math.OC

paper · pdf · doi:10.48550/arxiv.1504.04234

arXiv admin note: text overlap with arXiv:1406.0681

arxiv created 2015/04/16 · arxiv updated 2015/04/17

Abstract

This note deals with semiclassical measures associated to (sufficiently accurate) quasimodes (u_h) for the Laplace-Dirichlet operator on the disk. In this time-independent set-up, we simplify the statements of our preprint arXiv:1406.0681 and their proofs. We describe the restriction of semiclassical measures to every invariant torus in terms of two-microlocal measures. As corollaries, we show regularity and delocalization properties for limit measures of |u_h|² dx: these are absolutely continuous in the interior of the disk and charge every open set intersecting the boundary.

Citations

• Wigner measures and observability for the Schrödinger equation on the disk

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