Observation of periodic orbits on curved two-dimensional geometries

TY - JOUR

T1 - Observation of periodic orbits on curved two-dimensional geometries

AU - Avlund, Mikkel

AU - Ellegaard, Clive Sigurd

AU - Oxborrow, M.

AU - Søndergaard, N.

PY - 2010/4/20

Y1 - 2010/4/20

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevLett.104.164101

DO - 10.1103/PhysRevLett.104.164101

M3 - Journal article

SN - 0031-9007

VL - 104

SP - 164101

JO - Physical Review Letters

JF - Physical Review Letters

IS - 16

ER -