Zeta function for the Lyapunov exponent of a product of random matrices

1993/01/11 by Ronnie Mainieri, Mainieri, Ronnie
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Protein Structure and Dynamics #Quantum chaos and dynamical systems #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.chao-dyn/9301001

openalex publication_date 1993/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A cycle expansion for the Lyapunov exponent of a product of random matrices is derived. The formula is non-perturbative and numerically effective, which allows the Lyapunov exponent to be computed to high accuracy. In particular, the free energy and the heat capacity are computed for the one-dimensional Ising model with quenched disorder. The formula is derived by using a Bernoulli dynamical system to mimic the randomness.

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