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.
Keywords
Cite
@article{arxiv.1702.06935,
title = {Universality in Chaos: Lyapunov Spectrum and Random Matrix Theory},
author = {Masanori Hanada and Hidehiko Shimada and Masaki Tezuka},
journal= {arXiv preprint arXiv:1702.06935},
year = {2018}
}
Comments
5 pages + supplementary materials. v2: minor corrections, references added. v3: a lot more evidence added. v4: the version appeared in Phys. Rev. E