Lyapunov exponent of random walkers on a bond-disordered lattice

The chaotic properties of a random walker in a quenched random environment are studied analytically, following the work of Gaspard et al. on Lorentz gases, for systems with closed (periodic) or open (absorbing) boundaries. The model of interest describes random walkers hopping on a disordered lattice, on which the hopping probabilities across bonds are quenched random variables. For closed systems an exact expression for the Lyapunov exponent is derived, which not only depends on the composition, but also on the number of clusters of certain type. For open systems escape rates and Lyapunov exponents are calculated from a mean-field approximation. The theoretical predictions are compared with the results of extensive computer simulations, based on the thermodynamic formalism. For large systems the agreement is excellent.