Anomalous shell effect in the transition from a circular to a triangular billiard

Details Anomalous shell effect in the transition from a circular to a triangular billiard Anomalous shell effect in the transition from a circular to a triangular billiard

2007-10-27

arxiv.org/abs/0710.5231v2

Phys.Rev.E77:056211,2008

Nonlinear Sciences

Chaotic Dynamics

14 pages REVTeX4, 16 figures, version to appear in Phys. Rev. E. Qualities of some figures are lowered to reduce their sizes.

Scientific paper

10.1103/PhysRevE.77.056211

We apply periodic orbit theory to a two-dimensional non-integrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing triangular deformation, it exhibits an astonishingly pronounced shell effect on its way through the shape transition. A semiclassical analysis reveals that this shell effect emerges from a codimension-two bifurcation of the triangular periodic orbit. Gutzwiller's semiclassical trace formula, using a global uniform approximation for the bifurcation of the triangular orbit and including the contributions of the other isolated orbits, describes very well the coarse-grained quantum-mechanical level density of this system. We also discuss the role of discrete symmetry for the large shell effect obtained here.

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