2013/01/22 by Stefan Giller, Giller, Stefan, Jarosław Janiak +1
Mathematics · Physics and Astronomy · #81Q20 #81Q50 #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Nuclear physics research studies #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #math-ph #math.MP #msc:81Q20 #msc:81Q50 #nlin.CD #quant-ph
paper · pdf · doi:10.48550/arxiv.1301.5212
52 pages, 20 figures. arXiv admin note: substantial text overlap with arXiv:1108.2527
openalex publication_date 2013/01/22 · arxiv created 2013/01/30 · arxiv updated 2013/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Semiclassical wave functions in billiards based on the Maslov-Fedoriuk approach are constructed. They are defined on classical constructions called skeletons which are the billiards generalization of the Arnold tori. Skeletons in the rational polygon billiards considered in the phase space can be closed with a definite genus or can be open being a cylinder-like or Moebius-like bands. The skeleton formulation is applied to calculate semiclassical wave functions and the corresponding energy spectra for the integrable and pseudointegrable billiards as well as in the limiting forms in some cases of chaotic ones. The superscars of Bogomolny and Schmit are shown to be simply singular semiclassical solutions of the eigenvalue problem in the billiards well built on the singular skeletons in the billiards with flat boundaries in both the integrable and the pseudointegrable billiards as well as in the chaotic cases of such billiards.