Duality between quantum and classical dynamics for integrable billiards

Details Duality between quantum and classical dynamics for integrable billiards Duality between quantum and classical dynamics for integrable billiards

2006-01-10

arxiv.org/abs/nlin/0601022v1

Phys. Rev. E 73, 046201 (2006)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, 4 figures

Scientific paper

10.1103/PhysRevE.73.046201

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 auto-correlation 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.

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