2019/05/31 by Nadav Yesha · 1 citation
Mathematics · Physics and Astronomy · #Eigenfunction #Eigenvalues and eigenvectors #Geometry #Laplace operator #Mathematical analysis #Mathematics #Physics #Planck scale #Point (geometry) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Scale (ratio) #Spectral Theory in Mathematical Physics #Torus #math-ph #math.AP #math.MP #math.NT #nlin.CD
paper · pdf · doi:10.1007/s00220-019-03669-0
published in Communications in Mathematical Physics 377(1), 199-224 (Springer Science+Business Media) · 29 pages. Minor revision. To appear in Communications in Mathematical Physics
arxiv created 2019/12/23 · openalex publication_date 2020/01/06 · arxiv updated 2020/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the small scale distribution of the eigenfunctions of a point scatterer (the Laplacian perturbed by a delta potential) on two- and three-dimensional flat tori. In two dimensions, we establish small scale equidistribution for the "new" eigenfunctions holding all the way down to the Planck scale. In three dimensions, small scale equidistribution is established for all of the "new" eigenfunctions at certain scales.