Chaotic behavior in lemon-shaped billiards with elliptical and hyperbolic boundary arcs

Scientific paper - Original scientific paper

• Author: Vjera Lopac
• Author: Ivana Mrkonjić
• Author: Danko Radić
• Author's institution: University of Zagreb; Faculty of Science; (Department of Physics)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract (english)

Chaotic properties of a new family, ellipse hyperbola billiards (EHB), of lemon-shaped two-dimensional billiards, interpolating between the square and the circle, whose boundaries consist of hyperbolic, parabolic, or elliptical segments, depending on the shape parameter δ, are investigated classically and quantally. Classical chaotic fraction is calculated and compared with the quantal level density fluctuation measures obtained by fitting the calculated level spacing sequences with the Brody, Berry-Robnik, and Berry-Robnik-Brody distributions. Stability of selected classical orbits is investigated, and for some special hyperbolic points in the Poincaré sections, the “blinking island” phenomenon is observed. Results for the EHB billiards are compared with the properties of the family of generalized power-law lemon-shaped billiards.

• Keywords (english): billiards; chaotic behavior
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Physical Review E
• Numbering: vol. 64, no. 1, pp. 16214-8
• p-ISSN: 1539-3755
• DOI: https://doi.org/10.1103/PhysRevE.64.016214
• URN:NBN: urn:nbn:hr:217:691030
• Publication: 2001
• Document URL: http://link.aps.org/doi/10.1103/PhysRevE.64.016214
• Type of resource: Text
• Access conditions: Open access
• Public note: Copyright (2001) by the American Physical Society.
• Created on: 2019-10-11 15:17:40