Laprise, J.F., Hosseinizadeh, A., Lamy-Poirier, J., Zomorrodi, R., Kröger, J. and Kröger, H., (2010) Universality in Level Spacing Fluctuations of a Chaotic Optical Billiard. Physics Letters A, 374, 2000-2004.
http://dx.doi.org/10.1016/j.physleta.2010.02.057

has been cited by the following article:

• TITLE: Universality in Statistical Measures of Trajectories in Classical Billiard Systems

  AUTHORS: Jean-François Laprise, Ahmad Hosseinizadeh, Helmut Kröger

  KEYWORDS: Classical Chaos, Dynamical Billiards, Random Matrix Theory, Level Spacing Fluctuations, Universality

  JOURNAL NAME: Applied Mathematics, Vol.6 No.8, July 30, 2015

  ABSTRACT: For classical billiards, we suggest that a matrix of action or length of trajectories in conjunction with statistical measures, level spacing distribution and spectral rigidity, can be used to distinguish chaotic from integrable systems. As examples of 2D chaotic billiards, we considered the Bunimovich stadium billiard and the Sinai billiard. In the level spacing distribution and spectral rigidity, we found GOE behaviour consistent with predictions from random matrix theory. We studied transport properties and computed a diffusion coefficient. For the Sinai billiard, we found normal diffusion, while the stadium billiard showed anomalous diffusion behaviour. As example of a 2D integrable billiard, we considered the rectangular billiard. We found very rigid behaviour with strongly correlated spectra similar to a Dirac comb. These findings present numerical evidence for universality in level spacing fluctuations to hold in classically integrable systems and in classically fully chaotic systems.