Quantitative equidistribution properties of toral eigenfunctions

Hamid Hezari (1) , Gabriel Riviere (2)

1 Department of Mathematics [Irvine]
2 LPP - Laboratoire Paul Painlevé - UMR 8524

In this note, we prove quantitative equidistribution properties for orthonor-mal bases of eigenfunctions of the Laplacian on the rational d-torus. We show that the rate of equidistribution of such eigenfunctions is polynomial. We also prove that equidistribution of eigenfunctions holds for symbols supported in balls with a radius shrinking at a polynomial rate.

Mots clés: Quantum ergodicity; Eigenfunctions of the Laplacian

Domaines: Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Hamid Hezari, Gabriel Riviere. Quantitative equidistribution properties of toral eigenfunctions. Journal of Spectral Theory, 2017. ⟨hal-01130004⟩