Spectral theory
From nodal points to non-equidistribution at the Planck scale
Comptes Rendus. Mathématique, Volume 360 (2022) no. G5, pp. 451-458.

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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DOI: 10.5802/crmath.311
Classification: 35P20, 58J50
Han, Xiaolong 1

1 Department of Mathematics, California State University, Northridge, CA 91330, USA
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Han, Xiaolong. From nodal points to non-equidistribution at the Planck scale. Comptes Rendus. Mathématique, Volume 360 (2022) no. G5, pp. 451-458. doi : 10.5802/crmath.311. http://www.numdam.org/articles/10.5802/crmath.311/

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