2019/09/21 by Omer Friedland, Friedland, Omer, Henrik Ueberschär +1
Materials Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.1909.09798
openalex publication_date 2019/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a continuous family of quasimodes for the Laplace-Beltrami operator on a translation surface. We apply our result to rational polygonal quantum billiards and thus construct a continuous family of quasimodes for the Neumann Laplacian on such domains with spectral width Oε(λ3/8+ε). We show that the semiclassical measures associated with this family of quasimodes project to a finite sum of Dirac measures on momentum space, hence, they satisfy Bogomolny and Schmit's superscar conjecture for rational polygons.