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Weyl formula: Experimental test of ray splitting and corner corrections

C. Vaa1, P. M. Koch1, and R. Blümel2

  • 1Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA
  • 2Department of Physics, Wesleyan University, Middletown, Connecticut 06459-0155, USA

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Phys. Rev. E 72, 056211 – Published 17 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.056211

Abstract

The number of resonances N(f) of a resonator below frequency f is an essential concept in physics. Smooth approximations N¯(f) are known as Weyl formulas. An abrupt change in the properties of the wave propagation medium in a resonator was predicted by Prange et al. [Phys. Rev. E 53, 207 (1996)] to produce a universal ray-splitting correction to N¯(f). We confirm this effect experimentally. Our results with a quasi-two-dimensional dielectric-loaded microwave cavity are directly relevant to the ray-splitting correction in two-dimensional quantal ray-splitting billiards. Our experimental spectra have sufficient accuracy and extent to allow, as far as we are aware, the first experimental determination of the corner correction, which we find to agree with theory. We show that our movable-bar setup enhances non-Newtonian periodic orbits, thereby providing an experimental technique for periodic-orbit spectroscopy. This technique, differential spectroscopy, will facilitate the study of non-Newtonian classical physics.

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Phys. Rev. E 72, 056211– Published 17 November, 2005
  • Received 9 June 2005

© 2005 American Physical Society

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