arXiv subjects

F. M. Izrailev

Publications and source records attributed to F. M. Izrailev.

At least 19 recordsLinked to original sources

arXiv2018

Distribution of S-matrix poles for one-dimensional disordered wires

By the use of the effective non-Hermitian Hamiltonian approach to scattering we study the distribution of the scattering matrix (S-matrix) poles in one-dimensional (1D) models with various types of diagonal disorder. We consider the case of 1D tight-binding wires, with both on-site uncorrelated and correlated disorder, coupled to the continuum through leads attached to the wire edges. In particular, we focus on the location of the S-matrix poles in the complex plane as a function of the coupling strength and the disorder strength. Specific interest is paid to the super-radiance transition emerging at the perfect coupling between wire and leads. We also study the effects of correlations intentionally imposed to the wire disorder.

cond-mat.dis-nn↗

arXiv2017

Double-sided unidirectional reflectivity

We study the effect of unidirectional reflectivity in the bilayer optical model with the balanced loss/gain terms. It was found that if the impedances characterizing the scattering part are different from those describing the leads, a new effect of double-sided unidirectional reflectivity emerges. In this case the vanishing of reflectivity occurs either for the left or right reflectivity, depending on the frequency of scattering wave. It is shown that the alternation of the unidirectional reflectivity from the left to the right can occur even if the corresponding Hamiltonian is non-PT-symmetric. Our analytical results are demonstrated by numerical data.

physics.optics↗

arXiv2016

Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles

This review is devoted to the problem of thermalization in a small isolated conglomerate of interacting constituents. A variety of physically important systems of intensive current interest belong to this category: complex atoms, molecules (including biological molecules), nuclei, small devices of condensed matter and quantum optics on nano- and micro-scale, cold atoms in optical lattices, ion traps. Physical implementations of quantum computers, where there are many interacting qubits, also fall into this group. Statistical regularities come into play through inter-particle interactions, which have two fundamental components: mean field, that along with external conditions, forms the regular component of the dynamics, and residual interactions responsible for the complex structure of the actual stationary states. At sufficiently high level density, the stationary states become exceedingly complicated superpositions of simple quasiparticle excitations. At this stage, regularities typical of quantum chaos emerge and bring in signatures of thermalization. We describe all the stages and the results of the processes leading to thermalization, using analytical and massive numerical examples for realistic atomic, nuclear, and spin systems, as well as for models with random parameters. The structure of stationary states, strength functions of simple configurations, and concepts of entropy and temperature in application to isolated mesoscopic systems are discussed in detail. We conclude with a schematic discussion of the time evolution of such systems to equilibrium.

cond-mat.stat-mech↗

arXiv2016

PT-symmetric transport in non-PT-symmetric bi-layer optical arrays

We study transport properties of an array created by alternating $(a,b)$ layers with balanced loss/gain characterized by the key parameter $γ$. It is shown that for non-equal widths of $(a,b)$ layers, i.e., when the corresponding Hamiltonian is non-PT-symmetric, the system exhibits the scattering properties similar to those of truly PT-symmetric models provided that without loss/gain the structure presents the matched quarter stack. The inclusion of the loss/gain terms leads to an emergence of a finite number of spectral bands characterized by real values of the Bloch index. Each spectral band consists of a central region where the transmission coefficient $T_N \geq 1$, and two side regions with $T_N \leq 1$. At the borders between these regions the unidirectional reflectivity occurs. Also, the set of Fabry-Perrot resonances with $T_N=1$ are found in spite of the presence of loss/gain.

physics.optics↗

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

Transport through quasi-one-dimensional wires with correlated disorder

We study transport properties of bulk-disordered quasi-one-dimensional (Q1D) wires paying main attention to the role of long-range correlations embedded into the disorder. First, we show that for stratified disorder for which the disorder is the same for all individual chains forming the Q1D wire, the transport properties can be analytically described provided the disorder is weak. When the disorder in every chain is not the same, however, has the same binary correlator, the general theory is absent. Thus, we consider the case when only one channel is open and all others are closed. For this situation we suggest a semi-analytical approach which is quite effective for the description of the total transmission coefficient. Our numerical data confirm the validity of our approach. Such Q1D disordered structures with anomalous transport properties can be the subject of an experimental study.

cond-mat.dis-nn↗

arXiv2013

Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder

We study coherent wave scattering through waveguides with a step-like surface disorder and find distinct enhancements in the reflection coefficients at well-defined resonance values. Based on detailed numerical and analytical calculations, we can unambiguously identify the origin of these reflection resonances to be higher-order correlations in the surface disorder profile which are typically neglected in similar studies of the same system. A remarkable feature of this new effect is that it relies on the longitudinal correlations in the step profile, although individual step heights are random and thus completely uncorrelated. The corresponding resonances are very pronounced and robust with respect to ensemble averaging, and lead to an enhancement of wave reflection by more than one order of magnitude.

cond-mat.dis-nn↗

arXiv2013

Gain/loss induced localization in one-dimensional PT-symmetric tight-binding models

We investigate the properties of PT-symmetric tight-binding models by considering both bounded and unbounded models. For the bounded case, we obtain closed form expressions for the corresponding energy spectra and we analyze the structure of eigenstates as well as their dependence on the gain/loss contrast parameter. For unbounded PT-lattices, we explore their scattering properties through the development of analytical models. Based on our approach we identify a mechanism that is responsible to the emergence of localized states that are entirely due to the presence of gain and loss. The derived expressions for the transmission and reflection coefficients allow one to better understand the role of PT-symmetry in energy transport problems occurring in such PT-symmetric tight-binding settings. Our analytical results are further exemplified via pertinent examples.

cond-mat.mes-hall↗

arXiv2013

Resonant enhancement of Anderson localization: Analytical approach

We study localization properties of the eigenstates and wave transport in one-dimensional system consisting of a set of barriers/wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced Anderson localization, is the presence of the resonances emerging due to the coherent interaction of the waves reflected from the interfaces between wells/barriers. Our theoretical approach allows to derive the localization length in infinite samples both out of the resonances and close to them. We examine how the transport properties of finite samples can be described in terms of this length. It is shown that the analytical expressions obtained by standard methods for continuous random potentials can be used in our discrete model, in spite of the presence of resonances that cannot be described by conventional theories. We also discuss whether the single parameter scaling is valid in view of the suggested modification of the theory. All our results are illustrated with numerical data manifesting an excellent agreement with the theory.

cond-mat.dis-nn↗

arXiv2013

Non-conventional Anderson localization in a matched quarter stack with metamaterials

We study the problem of non-conventional Anderson localization emerging in bilayer periodic-on-average structures with alternating layers of materials with positive and negative refraction indices $n_a$ and $n_b$. Main attention is paid to the model of the so-called quarter stack with perfectly matched layers (the same unperturbed by disorder impedances, $Z_a=Z_b$, and optical path lengths, $n_ad_a=|n_b| d_b$, with $d_a$, $d_b$ being the thicknesses of basic layers). As was recently numerically discovered, in such structures with weak fluctuations of refractive indices (compositional disorder) the localization length $L_{loc}$ is enormously large in comparison with the conventional localization occurring in the structures with positive refraction indices only. In this paper we develop a new approach which allows us to derive the expression for $L_{loc}$ for weak disorder and any wave frequency $ω$. In the limit $ω\rightarrow 0$ one gets a quite specific dependence, $L^{-1}_{loc}\proptoσ^4ω^8$ which is obtained within the fourth order of perturbation theory. We also analyze the interplay between two types of disorder, when in addition to the fluctuations of $n_a$, $n_b$ the thicknesses $d_a$, $d_b$ slightly fluctuate as well (positional disorder). We show how the conventional localization recovers with an addition of positional disorder.

cond-mat.dis-nn↗

arXiv2012

Surface scattering and band gaps in rough waveguides and nanowires

The boundaries of waveguides and nanowires have drastic influence on their coherent scattering properties. Designing the boundary profile is thus a promising approach for transmission and band-gap engineering with many applications. By performing an experimental study of microwave transmission through rough waveguides we demonstrate that a recently proposed surface scattering theory can be employed to predict the measured transmission properties from the boundary profiles and vice versa. A new key ingredient of this theory is a scattering mechanism which depends on the squared gradient of the surface profiles. We demonstrate the non-trivial effects of this scattering mechanism by detailed mode-resolved microwave measurements and numerical simulations.

cond-mat.mes-hall↗

arXiv2012

From closed to open 1D Anderson model: Transport versus spectral statistics

Using the phenomenological expression for the level spacing distribution with only one parameter, $0 \leq β\leq \infty$, covering all regimes of chaos and complexity in a quantum system, we show that transport properties of the one-dimensional Anderson model of finite size can be expressed in terms of this parameter. Specifically, we demonstrate a strictly linear relation between $β$ and the normalized localization length for the whole transition from strongly localized to extended states. This result allows one to describe all transport properties in the open system entirely in terms of the parameter $β$ and strength of coupling to continuum. For non-perfect coupling, our data show a quite unusual interplay between the degree of internal chaos defined by $β$, and degree of openness of the model. The results can be experimentally tested in single-mode waveguides with either bulk or surface disorder.

cond-mat.dis-nn↗

arXiv2012

Onset of chaos and relaxation in isolated systems of interacting spins-1/2: energy shell approach

We study the onset of chaos and statistical relaxation in two isolated dynamical quantum systems of interacting spins-1/2, one of which is integrable and the other chaotic. Our approach to identifying the emergence of chaos is based on the level of delocalization of the eigenstates with respect to the energy shell, the latter being determined by the interaction strength between particles or quasi-particles. We also discuss how the onset of chaos may be anticipated by a careful analysis of the Hamiltonian matrices, even before diagonalization. We find that despite differences between the two models, their relaxation process following a quench is very similar and can be described analytically with a theory previously developed for systems with two-body random interactions. Our results imply that global features of statistical relaxation depend on the degree of spread of the eigenstates within the energy shell and may happen to both integrable and non-integrable systems.

cond-mat.stat-mech↗

arXiv2012

Coherent transport in multi-branch circuits

A multi-branch quantum circuit is considered from the viewpoint of coherent electron or wave transport. Starting with the closed system, we give analytical conditions for the appearance of two isolated localized states out of the energy band. In the open system, using the method of the effective non-Hermitian Hamiltonian, we study signal transmission through such a circuit. The super-radiant transition occurs when the average level width becomes comparable to the mean level spacing. We consider also the case with on-site disorder and find an analytical estimate, confirmed by numerical data, for the robustness of the isolated states and their role in transport processes.

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↗

arXiv2011

Non-Conventional Anderson Localization in Bilayered Structures with Metamaterials

We have developed an approach allowing us to resolve the problem of non-conventional Anderson localization emerging in bilayered periodic-on-average structures with alternating layers of right-handed and left-handed materials. Recently, it was numerically discovered that in such structures with weak fluctuations of refraction indices, the localization length $L_{loc}$ can be enormously large for small wave frequencies $ω$. Within the fourth order of perturbation theory in disorder, $σ^2 \ll 1$, we derive the expression for $L_{loc}$ valid for any $ω$. In the limit $ω\rightarrow 0$ one gets a quite specific dependence, $L^{-1}_{loc} \propto σ^4 ω^8$. Our approach allows one to establish the conditions under which this effect can be observed.

cond-mat.dis-nn↗

arXiv2011

Chaos and statistical relaxation in quantum systems of interacting particles

We propose a method to study the transition to chaos in isolated quantum systems of interacting particles. It is based on the concept of delocalization of eigenstates in the energy shell, controlled by the Gaussian form of the strength function. We show that although the fluctuations of energy levels in integrable and non-integrable systems are principally different, global properties of the eigenstates may be quite similar, provided the interaction between particles exceeds some critical value. In this case the quench dynamics can be described analytically, demonstrating the universal statistical relaxation of the systems irrespectively of whether they are integrable or not.

quant-ph↗