Observation of Periodic Orbits on Curved Two-Dimensional Geometries

被引：8

作者：

Avlund, M. ^{[1
]}

Ellegaard, C. ^{[1
]}

Oxborrow, M. ^{[2
]}

Guhr, T. ^{[3
]}

Sondergaard, N. ^{[4
]}

机构：

[1] Niels Bohr Inst, DK-2100 Copenhagen O, Denmark

[2] Natl Phys Lab, Teddington TW11 0LW, Middx, England

[3] Univ Duisburg Essen, Fak Phys, D-47057 Duisburg, Germany

[4] Lund Univ, LTH, S-22100 Lund, Sweden

来源：

PHYSICAL REVIEW LETTERS | 2010年 / 104卷 / 16期

关键词：

SPECTRAL STATISTICS; VIBRATIONS; WAVES;

D O I：

10.1103/PhysRevLett.104.164101

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页数：4

共 26 条

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[Anonymous], 1999, QUANTUM CHAOS INTRO, DOI DOI 10.1017/CBO9780511524622

[2]

Berline N., 2004, Heat kernels and Dirac operators. Grundlehren Text Editions

[3] Measurement of parametric correlations in spectra of resonating quartz blocks [J].