Granville, A;
Wigman, I;
(2017)
Planck-Scale Mass Equidistribution of Toral Laplace Eigenfunctions.
Communications in Mathematical Physics
, 355
(2)
pp. 767-802.
10.1007/s00220-017-2953-3.
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Abstract
We study the small scale distribution of the L 2 -mass of eigenfunctions of the Laplacian on the two-dimensional flat torus. Given an orthonormal basis of eigenfunctions, Lester and Rudnick (Commun. Math. Phys. 350(1):279–300, 2017) showed the existence of a density one subsequence whose L 2 -mass equidistributes more-or-less down to the Planck scale. We give a more precise version of their result showing equidistribution holds down to a small power of log above Planck scale, and also showing that the L 2 -mass fails to equidistribute at a slightly smaller power of log above the Planck scale. This article rests on a number of results about the proximity of lattice points on circles, much of it based on foundational work of Javier Cilleruelo.
| Type: | Article |
|---|---|
| Title: | Planck-Scale Mass Equidistribution of Toral Laplace Eigenfunctions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00220-017-2953-3 |
| Publisher version: | http://doi.org/10.1007/s00220-017-2953-3 |
| Language: | English |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1568238 |
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