Perturbation theory for the random dimer model

Abstract

The authors study a one-dimensional tight binding model with a random potential taking two values +or- nu , with the restriction that on pairs of two neighbouring sites the potentials take the same value. This random dimer model, proposed by Dunlap, Phillips and Wu (1990), has a vanishing Lyapunov exponent for the energy E=+or- nu . They compute the Lyapunov exponent and the density of states perturbatively in the vicinity of this energy using the invariant measure formalism.