Semiclassical energy level statistics in the transition region between integrability and chaos: transition from Brody-like to Berry-Robnik behaviour

1994/12/21 by Tomaž Prosen, T Prosen, M Robnik +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Protein Structure and Dynamics #Quantum chaos and dynamical systems #Scientific Research and Discoveries

paper · doi:10.1088/0305-4470/27/24/017

openalex publication_date 1994/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We study the energy level statistics of the generic Hamiltonian systems in the transition region between integrability and chaos and present the theoretical and numerical evidence that in the ultimate (far) semiclassical limit the Berry-Robnik (1984) approach is the asymptotically exact theory. However, before reaching that limit, one observes phenomenologically a quasi-universal behaviour characterized by the fractional power-law level repulsion and globally quite well described by the Brody (or Izrailev) distribution. We offer theoretical arguments explaining this extremely slow transition and demonstrate it numerically in improved statistics of the Robnik billiard and in the standard (Chirikov) map on a torus.

Citations

• Random-matrix physics: spectrum and strength fluctuations

Cited by

• Flooding of Chaotic Eigenstates into Regular Phase Space Islands
• About ergodicity in the family of limaçon billiards

Related

• Energy level statistics in the transition regime between integrability and chaos for systems with broken antiunitary symmetry
• Correspondence between classical dynamics and energy level spacing distribution in the transition billiard systems
• Quantum chaos and semiclassical behavior in mushroom billiards I: Spectral statistics
• Level Repulsion in Integrable Systems
• Topics in quantum chaos of generic systems