2017/02/28 by Masanori Hanada, Hidehiko Shimada, Masaki Tezuka
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Chaotic #Cosmology and Gravitation Theories #Eigenvalues and eigenvectors #Lyapunov exponent #Mathematical physics #Mathematics #Nonlinear system #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Random matrix #Statistical physics #String theory #Universality (dynamical systems) #hep-th #math-ph #math.MP #nlin.CD
paper · pdf · doi:10.1103/physreve.97.022224
published as Phys. Rev. E 97, 022224 (2018) · 5 pages + supplementary materials. v2: minor corrections, references added. v3: a lot more evidence added. v4: the version appeared in Phys. Rev. E
openalex publication_date 2018/02/28 · arxiv created 2018/03/12 · arxiv updated 2018/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.