Universality in Chaos: Lyapunov Spectrum and Random Matrix Theory

Abstract

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by Random Matrix Theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

5 pages + supplementary materials. v2: minor corrections, references added. v3: a lot more evidence added. v4: the version appeared in Phys. Rev. E

References in corpus (2)

• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Chaotic behavior in classical Yang-Mills dynamics

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