arXiv subjects

L. Tessieri

Publications and source records attributed to L. Tessieri.

At least 19 recordsLinked to original sources

arXiv2021

Quantum boomerang effect: beyond the standard Anderson model

It was recently shown that wavepackets with skewed momentum distribution exhibit a boomerang-like dynamics in the Anderson model due to Anderson localization: after an initial ballistic motion, they make a U-turn and eventually come back to their starting point. In this paper, we study the robustness of the quantum boomerang effect in various kinds of disordered and dynamical systems: tight-binding models with pseudo-random potentials, systems with band random Hamiltonians, and the kicked rotor. Our results show that the boomerang effect persists in models with pseudo-random potentials. It is also present in the kicked rotor, although in this case with a specific dependency on the initial state. On the other hand, we find that random hopping processes inhibit any drift motion of the wavepacket, and consequently the boomerang effect. In particular, if the random nearest-neighbor hopping amplitudes have zero average, the wavepacket remains in its initial position.

cond-mat.dis-nn↗

arXiv2015

The band-centre anomaly in the 1D Anderson model with correlated disorder

We study the band-centre anomaly in the one-dimensional Anderson model with weak correlated disorder. Our analysis is based on the Hamiltonian map approach; the correspondence between the discrete model and its continuous counterpart is discussed in detail. We obtain analytical expressions of the localisation length and of the invariant measure of the phase variable, valid for energies in a neighbourhood of the band centre. By applying these general results to specific forms of correlated disorder, we show how correlations can enhance or suppress the anomaly at the band centre.

cond-mat.dis-nn↗

arXiv2015

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 $κ$ 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 $κ\sim N^{\varepsilon}$, with the scaling exponent $\varepsilon$ being arbitrarily small (although not strictly zero), so that normal conduction is almost recovered even in this case.

cond-mat.dis-nn↗

arXiv2014

Transmission in waveguides with compositional and structural disorder: experimental effects of disorder cross-correlations

We analyse the single-mode transmission of microwaves in a guide with internal random structure. The waveguide contains scatterers characterised by random heights and positions, corresponding to compositional and structural disorder. We measure the effects of cross-correlations between two kinds of disorder, showing how they enhance or attenuate the experimentally found transmission gaps generated by long-range self-correlations. The results agree with the theoretical predictions obtained for the aperiodic Kronig-Penney model and prove that self- and cross-correlations have relevant effects also in finite disordered samples of small size.

cond-mat.mes-hall↗

arXiv2011

Anomalous localisation near the band centre in the 1D Anderson model: Hamiltonian map approach

We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns out to be more effective than other known methods. The analytical expressions are supported by numerical data. We also discuss the implications of our results for the single-parameter scaling hypothesis.

cond-mat.dis-nn↗

arXiv2010

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.

cond-mat.dis-nn↗

arXiv2010

Anomalous thermal properties of a harmonic chain with correlated isotopic disorder

We analyse the thermal properties of a harmonic chain with weak correlated disorder. With the use of a perturbative approach we derive analytical expressions for the time-evolution of the chain temperature and of the heat flow when both ends of the chain are coupled to heat baths. Our analytical and numerical results demonstrate that specific long-range correlations of the isotopic disorder can suppress or enhance the vibrational modes in pre-defined frequency windows. In this way one can arrange a frequency-selective heat flow through disordered chains.

cond-mat.dis-nn↗

arXiv2010

Electronic states and transport properties in the Kronig-Penney model with correlated compositional and structural disorder

We study the structure of the electronic states and the transport properties of a Kronig-Penney model with weak compositional and structural disorder. Using a perturbative approach we obtain an analytical expression for the localisation length which is valid for disorder with arbitrary correlations. We show how to generate disorder with self- and cross-correlations and we analyse both the known delocalisation effects of the long-range self-correlations and new effects produced by cross-correlations. We finally discuss how both kinds of correlations alter the transport properties in Kronig-Penney models of finite size.

cond-mat.dis-nn↗

arXiv2008

Anomalous properties of the Kronig-Penney model with compositional and structural disorder

We study the localization properties of the eigenstates in the Kronig-Penney model with weak compositional and structural disorder. The main result is an expression for the localization length that is valid for any kind of self- and inter-correlations of the two types of disorder. We show that the interplay between compositional and structural disorder can result in anomalous localization.

cond-mat.dis-nn↗

arXiv2006

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.

cond-mat.dis-nn↗

arXiv2004

Exact norm-conserving stochastic time-dependent Hartree-Fock

We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise-interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method we calculate the low energy spectrum of Helium. An extension of the method to bosons is outlined.

quant-ph↗

arXiv2004

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.

physics.class-ph↗

arXiv2002

Decoherence in a spin--spin-bath model with environmental self-interaction

A low temperature model system consisting of a central spin coupled to a spin-bath is studied to determine whether interaction among bath spins has an effect on central spin dynamics. In the absence of intra-environmental coupling, decoherence of the central spin is fast and irreversible. Strong intra-environmental interaction results in an effective decoupling of the central spin from the bath and suppression of decoherence. Weaker intra-environmental coupling reduces but does not eliminate decoherence. We believe that similar behaviour will be observed in any system with a self-interacting environment.

quant-ph↗

arXiv2002

Suppression of decoherence via strong intra-environmental coupling

We examine the effects of intra-environmental coupling on decoherence by constructing a low temperature spin--spin-bath model of an atomic impurity in a Debye crystal. The impurity interacts with phonons of the crystal through anti-ferromagnetic spin-spin interactions. The reduced density matrix of the central spin representing the impurity is calculated by dynamically integrating the full Schroedinger equation for the spin--spin-bath model for different thermally weighted eigenstates of the spin-bath. Exact numerical results show that increasing the intra-environmental coupling results in suppression of decoherence. This effect could play an important role in the construction of solid state quantum devices such as quantum computers.

quant-ph↗

arXiv2002

Delocalisation phenomena in one-dimensional models with long-range correlated disorder: a perturbative approach

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

cond-mat.dis-nn↗

arXiv2002

A perturbative study of delocalisation transition in one-dimensional models with long-range correlated disorder

We study the delocalisation transition which takes places in one-dimensional disordered systems when the random potential exhibits specific long-range correlations. We consider the case of weak disorder; using a systematic perturbative approach, we show how the delocalisation transition brings about a change of the scaling law of the inverse localisation length which ceases to be a quadratic function of the disorder strength and assumes a quartic form when the threshold separating the localised phase from the extended one is crossed.

cond-mat.dis-nn↗

arXiv2001

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.

cond-mat.dis-nn↗

arXiv1999

Anderson localization as a parametric instability of the linear kicked oscillator

We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric instability of the oscillator, with the localization length determined by an increment of the exponential growth of the energy. Analytical expression for a weak disorder is obtained, which is valid both inside the energy band and at the band edge.

cond-mat.dis-nn↗