Chatterjee, S;
Galkowski, J;
(2018)
Arbitrarily small perturbations of Dirichlet Laplacians are quantum unique ergodic.
Journal of Spectral Theory
, 8
(3)
pp. 909-947.
10.4171/JST/217.
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Abstract
Given an Euclidean domain with very mild regularity properties, we prove that there exist perturbations of the Dirichlet Laplacian of the form $-(I+S_\epsilon)\Delta$ with $\|S_\epsilon\|_{L^2\to L^2}\leq \epsilon$ whose high energy eigenfunctions are quantum uniquely ergodic (QUE). Moreover, if we impose stronger regularity on the domain, the same result holds with $\|S_\epsilon\|_{L^2\to H^\gamma}\leq \epsilon$ for $\gamma>0$ depending on the domain. We also give a proof of a local Weyl law for domains with rough boundaries.
| Type: | Article |
|---|---|
| Title: | Arbitrarily small perturbations of Dirichlet Laplacians are quantum unique ergodic |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4171/JST/217 |
| Publisher version: | https://doi.org/10.4171/JST%2F217 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Quantum unique ergodicity, quantum chaos, Laplacian eigenfunction |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10083901 |
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