Lyapunov Exponent for Products of Markovian Random Matrices

摘要

The effect of finite memory on the Lyapunov exponent of products of random matrices is studied by considering Markov trials. The cases studied include one dimensional Anderson model with correlated random potentials, light propagation in media with correlated random optical indexes, and mime of the deterministic chaos appearing in dynamical systems with few degrees of freedom. The Lyapunov exponent is found to have the same qualitative shape as the inverse of the correlation length of the Markov process.