Measuring billiard eigenfunctions with arbitrary trajectories

Abstract

We propose a method of measuring approximate quantum eigenfunctions in polygonalized billiard geometries, based on a quasiclassical evolution operator having a (smoothened) Perron-Frobenius kernel modulated by a phase arising from quantum considerations. We show that quasiclassical evolution differs from semiclassical (or quantum) evolution but the operators have the same set of eigenfunctions. We demonstrate this by determining the quasiclassical eigenfunctions of the polygonalized stadium billiard using arbitrary trajectories and comparing this with the exact quantum stadium eigenfunctions.

revtex, 4 figures

References in corpus (2)

• The Arbitrary Trajectory Quantization Method
• Semiclassical Inequivalence of Polygonalized Billiards

Cited by in corpus (1)

• Classical projected phase space density of billiards and its relation to the quantum Neumann spectrum