Measuring billiard eigenfunctions with arbitrary trajectories

Details Measuring billiard eigenfunctions with arbitrary trajectories Measuring billiard eigenfunctions with arbitrary trajectories

2001-11-29

arxiv.org/abs/nlin/0111065v1

Phys. Rev. E 67, 026208 (2003)

Nonlinear Sciences

Chaotic Dynamics

revtex, 4 figures

Scientific paper

10.1103/PhysRevE.67.026208

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.

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