1/f noise and spectral singularities in strongly disordered electronic systems

Abstract

Discusses the common origin of 1/f noise in the power spectrum of random walks in a random environment and the 1/E-like spectral anomaly for tight-binding electronic systems with off-diagonal disorder. In one dimension the existence of the Dyson singularity, ( rho (E)) varies as mod ln-3 mod E mod mod / mod E mod , for the density of states of the random chain as mod E mod to 0 is inevitably linked to Sinai ultraslow diffusion with the law (x2(t)) varies as ln4t as t to 0 and the presence of S(f) varies as ln4f/f power spectral density for small frequencies f. Different forms of power-law singularities are expected instead for a correlated disorder model appropriate to describe random symmetric diffusion and magnon or phonon excitations. The two problems are discussed in terms of the averaged moments of the electronic wavefunction. The 1/E behaviour is shown to rely on the underlying very general validity of the log-normal distribution for strongly disordered electronic systems. Analytical arguments are given and numerical evidence reported for the asymptotic presence of these singularities in the dimensions d=2, 3 when the disorder is sufficiently strong.