Low-energy density of states and long-time behaviour of random chanins: a scaling approach

Abstract

The asymptotic low-energy and long-time properties of random one-dimensional systems with harmonic chain-type eigenvalue equations are discussed. For a general class of random distributions of the coupling constants W, rho (W), an inherent length scale can be defined, and the corresponding systems exhibit conventional (universal) asymptotic properties. If rho (W) is such that no intrinsic length is defined, a unique energy-dependent localisation length can be determined which leads to anomalous (non-universal) diffusion and density-of-states indices, or at least to non-universal corrections to the conventional asymptotic behaviour. Some implications for the thermodynamic properties of random magnetic chains are also discussed.