Dynamical localization of trajectories on a bond-disordered lattice

The chaotic dynamics of a random walker in a quenched environment is studie d via the thermodynamic formalism of Ruelle, Sinai, and Bowen, in which cha otic properties are expressed in terms of a free energy-type function, psi( beta), of an inverse temperature-like parameter, beta. Localization phenome na in this system are elucidated both analytically and numerically. The inf inite system limit of the Ruelle pressure at beta > 1 and beta < 1 is shown to be controlled by rare configurations of the bond disorder, and this is related, respectively, to the extreme configurations associated to the mini mum and maximum Lyapunov exponent in finite systems. These extreme values a nd the corresponding configurations are obtained numerically from Monte Car lo simulations based on the thermodynamic formalism. (C) 1999 Elsevier Scie nce B.V. All rights reserved.