Anomalous diffusion and scaling behavior of dynamically perturbed one-dimensional disordered quantum systems

Abstract

Coherent oscillatory perturbations enhance the localization length of one-dimensional quantum disordered systems to a numerically undetectable level and result in an anomalous diffusion. The transition to the normal diffusion occurs continuously with the perturbation strength and/or the number of frequency components of the oscillatory perturbation. The corresponding space( x)-time( t) distribution function P( x, t) reduces to the unified scaling form P(x,t) ∼ exp[−const × ( x t α 2 ) β] , which contains the localization and the normal diffusion as two extreme cases and interpolates the two limits in the general case.