Observation of Periodic Orbits on Curved Two - dimensional Geometries

Details Observation of Periodic Orbits on Curved Two - dimensional Geometries Observation of Periodic Orbits on Curved Two - dimensional Geometries

2010-04-26

arxiv.org/abs/1004.4511v1

Phys. Rev. Lett. 104, 164101 (2010)

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevLett.104.164101

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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