Random moments for the new eigenfunctions of point scatterers on rectangular flat tori

Abstract

We define a random model for the moments of the new eigenfunctions of a point scat-terer on a 2-dimensional rectangular flat torus. In the deterministic setting,Seba conjectured these moments to be asymptotically Gaussian, in the semi-classical limit. This conjecture was disproved by Kurlberg-Uebersch{ä}r on Diophantine tori. In our model, we describe the accumulation points in distribution of the randomized moments, in the semi-classical limit. We prove that asymptotic Gaussianity holds if and only if some function, modeling the multiplicities of the Laplace eigenfunctions, diverges to +$\infty$.

References in corpus (7)

• Value distribution of the eigenfunctions and spectral determinants of quantum star graphs
• Statistics of wave functions for a point scatterer on the torus
• Eigenfunction statistics for a point scatterer on a three-dimensional torus
• Eigenfunctions and Random Waves in the Benjamini-Schramm limit
• Local Weak Limits of Laplace Eigenfunctions
• Quantum Ergodicity for Point Scatterers on Arithmetic Tori
• Small scale equidistribution for a point scatterer on the torus

Cited by in corpus (1)

• Quantum Transport in a Crystal With Short-Range Interactions: The Boltzmann-Grad Limit