Time evolution of wave-packets in quasi-1D disordered media

We have investigated numerically the quantum evolution of a wave-packet in a quenched disordered medium described by a tight-binding Hamiltonian with long-range hopping (band random matrix approach). We have obtained clean data for the scaling properties in time and in the bandwidth b of the packet width and its fluctuations with respect to disorder realizations. We confirm that the fluctuations of the packet width in the steady-state show an anomalous scaling and we give a new estimate of the anomalous scaling exponent. This anomalous behaviour is related to the presence of non-Gaussian tails in the distribution of the packet width. Finally, we have analysed the steady state probability profile and we have found finite band corrections of order 1/b with respect to the theoretical formula derived by Zhirov in the limit of infinite bandwidth. In a neighbourhood of the origin, however, the corrections are $O(1/\sqrt{b})$.Comment: 19 pages, 9 Encapsulated Postscript figures; submitted to ``European Physical Journal B'

Recovery of normal heat conduction in harmonic chains with correlated disorder

We consider heat transport in one-dimensional harmonic chains with isotopic disorder, focussing our attention mainly on how disorder correlations affect heat conduction. Our approach reveals that long-range correlations can change the number of low-frequency extended states. As a result, with a proper choice of correlations one can control how the conductivity $\kappa$ scales with the chain length $N$. We present a detailed analysis of the role of specific long-range correlations for which a size-independent conductivity is exactly recovered in the case of fixed boundary conditions. As for free boundary conditions, we show that disorder correlations can lead to a conductivity scaling as $\kappa \sim N^{\varepsilon}$, with the scaling exponent $\varepsilon$ being arbitrarily small (although not strictly zero), so that normal conduction is almost recovered even in this case.Comment: 15 pages, 2 figure

Parametric instability of linear oscillators with colored time-dependent noise

The goal of this paper is to discuss the link between the quantum phenomenon of Anderson localization on the one hand, and the parametric instability of classical linear oscillators with stochastic frequency on the other. We show that these two problems are closely related to each other. On the base of analytical and numerical results we predict under which conditions colored parametric noise suppresses the instability of linear oscillators.Comment: RevTex, 9 pages, no figure

1D quantum models with correlated disorder vs. classical oscillators with coloured noise

We perform an analytical study of the correspondence between a classical oscillator with frequency perturbed by a coloured noise and the one-dimensional Anderson-type model with correlated diagonal disorder. It is rigorously shown that localisation of electronic states in the quantum model corresponds to exponential divergence of nearby trajectories of the classical random oscillator. We discuss the relation between the localisation length for the quantum model and the rate of energy growth for the stochastic oscillator. Finally, we examine the problem of electron transmission through a finite disordered barrier by considering the evolution of the classical oscillator.Comment: 23 pages, LaTeX fil