Universality of Level Spacing Distributions in Classical Chaos

Details Universality of Level Spacing Distributions in Classical Chaos Universality of Level Spacing Distributions in Classical Chaos

2007-02-16

arxiv.org/abs/nlin/0702037v1

Phys. Lett. A 372 (2008) 4574-4577

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1016/j.physleta.2008.04.044

We suggest that random matrix theory applied to a classical action matrix can be used in classical physics to distinguish chaotic from non-chaotic behavior. We consider the 2-D stadium billiard system as well as the 2-D anharmonic and harmonic oscillator. By unfolding of the spectrum of such matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe Poissonian behavior in the integrable case and Wignerian behavior in the chaotic case. We present numerical evidence that the action matrix of the stadium billiard displays GOE behavior and give an explanation for it. The findings present evidence for universality of level fluctuations - known from quantum chaos - also to hold in classical physics.

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