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

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

Anomalous localisation in the aperiodic Kronig-Penney model

We analyse the anomalous properties of specific electronic states in the Kronig-Penney model with weak compositional and structural disorder. Using the Hamiltonian map approach, we show that the localisation length of the electronic states exhibits a resonant effect close to the band centre and anomalous scaling at the band edges. These anomalies are akin to the corresponding ones found in the Anderson model with diagonal disorder. We also discuss how specific cross-correlations between compositional and structural disorder can generate an anomalously localised state near the middle of the energy band. The tails of this state decay with the same stretched-exponential law which characterises the band-centre state in the Anderson model with purely off-diagonal disorder.Comment: 30 pages, 8 figures. The revised version includes an enlarged bibliography and an extended discussion of the anomalously localised state

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

Delocalisation transition in quasi-1D models with correlated disorder

We introduce a new approach to analyse the global structure of electronic states in quasi-1D models in terms of the dynamics of a system of parametric oscillators with time-dependent stochastic couplings. We thus extend to quasi-1D models the method previously applied to 1D disordered models. Using this approach, we show that a ``delocalisation transition'' can occur in quasi-1D models with weak disorder with long-range correlations.Comment: 33 pages, no figure

Two qubits entanglement dynamics in a symmetry-broken environment

We study the temporal evolution of entanglement pertaining to two qubits interacting with a thermal bath. In particular we consider the simplest nontrivial spin bath models where symmetry breaking occurs and treat them by mean field approximation. We analytically find decoherence free entangled states as well as entangled states with an exponential decay of the quantum correlation at finite temperature.Comment: 10 pages, 2 figure