The Quantum-Classical Correspondence in Polygonal Billiards

Abstract

We show that wave functions in planar rational polygonal billiards (all angles rationally related to Pi) can be expanded in a basis of quasi-stationary and spatially regular states. Unlike the energy eigenstates, these states are directly related to the classical invariant surfaces in the semiclassical limit. This is illustrated for the barrier billiard. We expect that these states are also present in integrable billiards with point scatterers or magnetic flux lines.

8 pages, 9 figures (in reduced quality), to appear in PRE

References in corpus (2)

• Singular continuous spectra in a pseudo-integrable billiard
• Distribution of Husimi Zeroes in Polygonal Billiards

Cited by in corpus (6)

• Hexagonal dielectric resonators and microcrystal lasers
• Spectral properties of quantized barrier billiards
• A pseudointegrable Andreev billiard
• Evanescent wave approach to diffractive phenomena in convex billiards with corners
• Quasicrystalline and rational approximant wave patterns in hydrodynamic and quantum nested wells
• Consequences of a wave-correction extended ray dynamics for integrable and chaotic optical microcavities