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.
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.
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Xiaolong Han 1
@article{CRMATH_2022__360_G5_451_0, author = {Xiaolong Han}, 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}, }
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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