Space–time, spectral, and energy characteristics of a gold-vapor ultraviolet laser

Abstract

We study the nature of electronic states in one-dimensional continuous models with weak correlated disorder. Using a perturbative approach, we compute the inverse localization length (Lyapunov exponent) up to terms proportional to the fourth power of the potential; this makes it possible to analyse the delocalization transition which takes place when the disorder exhibits specific long-range correlations. We find that the transition consists of a change of the Lyapunov exponent, which switches from a quadratic to a quartic depending on the strength of the disorder. Within the framework of the fourth-order approximation we also discuss the different localization properties which distinguish Gaussian from non-Gaussian random potentials.