Scaling Law for the Maximum Lyapunov Characteristic Exponent of Infinite Product of Random Matrices

摘要

A simple derivation for the scaling behavior of the maximum Lyapunov characteristic exponent lambda of infinite product of symplectic random matrices is presented. The considered random matrices depend on a parameter Sigma and for Sigma = 0 lambda = 0, lambda varies as Sigma to the power Beta is obtained with either Beta = 1/2 or Beta = 2/3 depending on the probability distribution of the matrix elements. The results agree with previous numerical simulation.