Universality in chaos: Lyapunov spectrum and random matrix theory

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...

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Bibliographic Details
Published in:Physical review. E 2018-02, Vol.97 (2-1), p.022224-022224, Article 022224
Main Authors: Hanada, Masanori, Shimada, Hidehiko, Tezuka, Masaki
Format: Article
Language:English
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Summary: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.
ISSN:2470-0045
2470-0053
DOI:10.1103/physreve.97.022224