Observation of Periodic Orbits on Curved Two-Dimensional Geometries

M. Avlund, C. Ellegaard, M. Oxborrow, T. Guhr, and N. Søndergaard
Phys. Rev. Lett. 104, 164101 – Published 20 April 2010

Abstract

We measure elastomechanical spectra for a family of thin shells. We show that these spectra can be described by a “semiclassical” trace formula comprising periodic orbits on geodesics, with the periods of these orbits consistent with those extracted from experiment. The influence of periodic orbits on spectra in the case of two-dimensional curved geometries is thereby demonstrated, where the parameter corresponding to Planck’s constant in quantum systems involves the wave number and the curvature radius. We use these findings to explain the marked clustering of levels when the shell is hemispherical.

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  • Received 19 December 2009

DOI:https://doi.org/10.1103/PhysRevLett.104.164101

©2010 American Physical Society

Authors & Affiliations

M. Avlund1, C. Ellegaard1, M. Oxborrow2, T. Guhr3, and N. Søndergaard4

  • 1Niels Bohr Institutet, Blegdamsvej 17, 2100 København Ø, Denmark
  • 2National Physical Laboratory, Hampton Road, Teddington, TW11 0LW, United Kingdom
  • 3Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1 47057 Duisburg, Germany
  • 4Matematisk Fysik, LTH, Lunds Universitet, Box 118, 22100 Lund, Sweden

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Vol. 104, Iss. 16 — 23 April 2010

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