Quantum-classical correspondences of the Berry-Robnik parameter through bifurcations in lemon billiard systems

H. Makino, Takahisa Harayama, Y. Aizawa

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16 Citations (Scopus)

Abstract

The correspondence between classical and quantum mechanics in the statistical properties of energy levels was established. The effect of bifurcations on quantum level statistics was studied by means of Lemon Billiards Model. Hamiltonian dynamics, energy level statistics, analysis of the cusp at the bifurcation point, analysis of volume ratio of the regular and chaotic regions was performed. The volume ratio rhoi of the phase space component was compared with quantum mechanical data for the Berry-Robnik parameter and comparisons made for various energy ranges. Results indicate that the statistical properties of energy levels in the high energy range are reflected sensitively by the local enhancement of island tori in the classical phase.

Original languageEnglish
Pages (from-to)562031-5620311
Number of pages5058281
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume63
Issue number5 II
Publication statusPublished - 2001 May
Externally publishedYes

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ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

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