2006/01/10 by W. T. Lu, Weiqiao Zeng, S. Sridhar
Chemistry · Mathematics · Physics and Astronomy · #Classical mechanics #Duality (order theory) #Dynamical billiards #Geometry #Integrable system #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Rectangle #Semiclassical physics #Spectrum (functional analysis) #Wave function #nlin.SI
paper · pdf · doi:10.1103/physreve.73.046201
published as Phys. Rev. E 73, 046201 (2006) · 12 pages, 4 figures
arxiv created 2006/01/10 · openalex publication_date 2006/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the quantum wave vector spectrum. A semiclassical derivation and numerical calculations are presented in support of the results. These classical eigenmodes can be observed in physical experiments through the autocorrelation of the transmission coefficient of waves in quantum billiards. Exact classical trace formulas of the resolvent are derived for the rectangle, equilateral triangle, and circle billiards. We also establish a correspondence between the classical periodic orbit length spectrum and the quantum spectrum for integrable polygonal billiards.