Density of states and localization lengths in one-dimensional linear chains

The integral equation for computing the density of states of a disordered linear chain of harmonic oscillators is interpreted as describing a stochastic Markov process, and its solution is determined by means of Monte Carlo simulation of the process. It is also shown that, in addition to the localization lengths of the eigenstates, the method allows the computation of the generalized Ljapunov exponents. Many different examples of application, ranging from systems with uncorrelated disorder to deterministic aperiodic chains, are reported.