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

Abstract

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.

14 pages REVTeX4, 16 figures, version to appear in Phys. Rev. E. Qualities of some figures are lowered to reduce their sizes. Original figures are available at http://www.phys.nitech.ac.jp/~arita/papers/tricirc/

References in corpus (15)

• Nuclear Tetrahedral Symmetry: Possibly Present Throughout the Periodic Table
• Bifurcations of Periodic Orbits and Uniform Approximations
• Tetrahedral Symmetry in Ground- and Low-Lying States of Exotic A ~ 110 Nuclei
• Uniform Approximation for Period-Quadrupling Bifurcations
• Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: I: Elliptic Billiard
• Semiclassical interference of bifurcations
• Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: II -- Spheroidal Cavity --
• Periodic orbits near bifurcations of codimension two: Classical mechanics, semiclassics, and Stokes transitions
• Semiclassical trace formulas in terms of phase space path integrals
• Uniform approximations for pitchfork bifurcation sequences
• Semiclassical Origin of Superdeformed Shell Structure in the Spheroidal Cavity Model
• Effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems
• Periodic orbit theory for the Hénon-Heiles system in the continuum region
• Periodic-Orbit Bifurcation and Shell Structure in Reflection-Asymmetric Deformed Cavity
• Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics

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• Semiclassical origin of nuclear ground-state octupole deformations
• Quantum Mechanical Approach to Bifurcation Point Detection in Hamiltonian Dynamical Systems