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Observation of Periodic Orbits on Curved Two-Dimensional Geometries

Avlund, M.; Ellegaard, C.; Oxborrow, M.; Guhr, T. and Søndergaard, Niels LU (2010) In Physical Review Letters 104(16).
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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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review Letters
volume
104
issue
16
publisher
American Physical Society
external identifiers
  • wos:000277007700025
  • scopus:77951126808
ISSN
1079-7114
DOI
10.1103/PhysRevLett.104.164101
language
English
LU publication?
yes
id
d23df60c-5101-411d-89c5-48917ac4e266 (old id 1601076)
date added to LUP
2010-05-20 10:49:36
date last changed
2018-06-17 03:07:59
@article{d23df60c-5101-411d-89c5-48917ac4e266,
  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.},
  articleno    = {164101},
  author       = {Avlund, M. and Ellegaard, C. and Oxborrow, M. and Guhr, T. and Søndergaard, Niels},
  issn         = {1079-7114},
  language     = {eng},
  number       = {16},
  publisher    = {American Physical Society},
  series       = {Physical Review Letters},
  title        = {Observation of Periodic Orbits on Curved Two-Dimensional Geometries},
  url          = {http://dx.doi.org/10.1103/PhysRevLett.104.164101},
  volume       = {104},
  year         = {2010},
}