From nodal points to non-equidistribution at the Planck scale

Xiaolong Han

doi:10.5802/crmath.311

Théorie spectrale

From nodal points to non-equidistribution at the Planck scale

Xiaolong Han ¹

¹ Department of Mathematics, California State University, Northridge, CA 91330, USA

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 451-458.

Résumé
Abstract

Dans cette note, on observe que les fonctions propres du laplacien ne sont pas équidistribuées à l’échelle de Planck. De plus, l’équidistribution à la même échelle n’est plus valable autour des points où les fonctions propres ont des valeurs grandes.

In this note, we make an observation that Laplacian eigenfunctions fail equidistribution at the Planck scale. Furthermore, equidistribution at the same scale also fails around the points where the eigenfunctions have large values.

Reçu le : 2020-12-09
Révisé le : 2021-12-08
Accepté le : 2021-12-08
Publié le : 2022-05-23

DOI : 10.5802/crmath.311

Classification : 35P20, 58J50

Affiliations des auteurs :

Xiaolong Han ¹

¹ Department of Mathematics, California State University, Northridge, CA 91330, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {From nodal points to non-equidistribution at the {Planck} scale},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {451--458},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.311},
     language = {en},
}

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Xiaolong Han. From nodal points to non-equidistribution at the Planck scale. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 451-458. doi : 10.5802/crmath.311. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.311/

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