arXiv subjects

F. M. Izrailev

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

At least 73 records · Page 4Linked to original sources

arXiv2003

Controlled transparency of many-mode waveguides with rough surface

In a unified approach we consider transport properties of 1D and quasi-1D waveguides with rough surfaces. Main attention is paid to the possibility of perfect transmission of waves due to specific long-range correlations in the surface profiles. First, we show how to construct random profiles that lead to a complete transparency of waveguides with one open channel. Then, we present analytical results for many-mode waveguides. It was revealed that by a proper choice of correlations in surface profiles the transmission through such quasi-1D waveguides is described by a coset of non-interacting 1D channels with a perfect transmission along each one. The number of these conducting modes is governed by the control parameter, and can be equal to the total number of channels. Therefore, the waveguides can be completely transparent in some region of frequency of incoming waves. This unexpected phenomenon is discussed in connection with the violation of the single-parameter scaling for surface scattering.

cond-mat.mes-hall↗

arXiv2003

Irregular Dynamics in a One-Dimensional Bose System

We study many-body quantum dynamics of $δ$-interacting bosons confined in a one-dimensional ring. Main attention is payed to the transition from the mean-field to Tonks-Girardeau regime using an approach developed in the theory of interacting particles. We analyze, both analytically and numerically, how the Shannon entropy of the wavefunction and the momentum distribution depend on time for a weak and strong interactions. We show that the transition from regular (quasi-periodic) to irregular ("chaotic") dynamics coincides with the onset of the Tonks-Girardeau regime. In the latter regime the momentum distribution of the system reveals a statistical relaxation to a steady state distribution. The transition can be observed experimentally by studying the interference fringes obtained after releasing the trap and letting the boson system expand ballistically.

cond-mat.stat-mech↗

arXiv2003

Resistance of a 1D random chain: Hamiltonian version of the transfer matrix approach

We study some mesoscopic properties of electron transport by employing one-dimensional chains and Anderson tight-binding model. Principal attention is paid to the resistance of finite-length chains with disordered white-noise potential. We develop a new version of the transfer matrix approach based on the equivalency of a discrete Schroedinger equation and a two-dimensional Hamiltonian map describing a parametric kicked oscillator. In the two limiting cases of ballistic and localized regime we demonstrate how analytical results for the mean resistance and its second moment can be derived directly from the averaging over classical trajectories of the Hamiltonian map. We also discuss the implication of the single-parameter scaling hypothesis to the resistance.

cond-mat.mes-hall↗

arXiv2003

From Chaos to Disorder in Quasi-1D Billiards with Corrugated Surfaces

We study chaotic properties of eigenstates depending on the degree of complexity in boundaries of a 2D periodic billiard. Main attention is paid to the situation when the motion of a classical particle is strongly chaotic. Our approach allows to explore the transition from deterministic to disordered chaos, and to link chaos to the degree of ergodicity in eigenstates of the billiard. We have found that bouncing balls strongly reduce chaotic properties of eigenstates, thus leading to a serious problem in statistical description for global properties of eigenstates. A quite unexpected effect of rough surfaces on the form of eigenstates has been discovered and explained by a strong localization of a subset of eigenstates in the energy representation.

cond-mat↗

arXiv2003

Amplitude and Gradient Scattering in Waveguides with Corrugated Surfaces

We study chaotic properties of eigenstates for periodic quasi-1D waveguides with "regular" and "random" surfaces. Main attention is paid to the role of the so-called "gradient scattering" which is due to large gradients in the scattering walls. We demonstrate numerically and explain theoretically that the gradient scattering can be quite strong even if the amplitude of scattering profiles is very small in comparison with the width of waveguides.

cond-mat.dis-nn↗

arXiv2003

Selective Transport and Mobility Edges in Quasi-1D Systems with a Stratified Correlated Disorder

We present analytical results on transport properties of many-mode waveguides with randomly stratified disorder having long-range correlations. To describe such systems, the theory of 1D transport recently developed for a correlated disorder is generalized. The propagation of waves through such waveguides may reveal a quite unexpected phenomena of a complete transparency for a subset of propagating modes. We found that with a proper choice of long-range correlations one can arrange a perfect transparency of waveguides inside a given frequency window of incoming waves. Thus, mobility edges are shown to be possible in quasi-1D geometry with correlated disorder. The results may be important for experimental realizations of a selective transport in application to both waveguides and electron/optic nanodevices.

cond-mat↗

arXiv2003

Ballistic Localization in Quasi-1D Waveguides with Rough Surfaces

Structure of eigenstates in a periodic quasi-1D waveguide with a rough surface is studied both analytically and numerically. We have found a large number of "regular" eigenstates for any high energy. They result in a very slow convergence to the classical limit in which the eigenstates are expected to be completely ergodic. As a consequence, localization properties of eigenstates originated from unperturbed transverse channels with low indexes, are strongly localized (delocalized) in the momentum (coordinate) representation. These eigenstates were found to have a quite unexpeted form that manifests a kind of "repulsion" from the rough surface. Our results indicate that standard statistical approaches for ballistic localization in such waveguides seem to be unappropriate.

cond-mat.dis-nn↗

arXiv2002

Transport properties of 1D disordered models: a novel approach

A new method is developed for the study of transport properties of 1D models with random potentials. It is based on an exact transformation that reduces discrete Schrödinger equation in the tight-binding model to a two-dimensional Hamiltonian map. This map describes the behavior of a classical linear oscillator under random parametric delta-kicks. We are interested in the statistical properties of the transmission coefficient $T_L$ of a disordered sample of length $L$. In the ballistic regime we derive expressions for the mean value of the transmission coefficient $T_L$, its second moment and variance, that are more accurate than the existing ones. In the localized regime we analyze the global characteristics of $\ln T_L$, and demonstrate that its distribution function approaches the Gaussian form if $L\to \infty$. For any finite $L$ there are deviations from the Gaussian law that originate from the subtle correlation effects between different trajectories of the Hamiltonian map.

cond-mat↗

arXiv2002

Onset of Delocalization in Quasi-1D Waveguides with Correlated Surface Disorder

We present first analytical results on transport properties of many-mode waveguides with rough surfaces having long-range correlations. We show that propagation of waves through such waveguides reveals a quite unexpected phenomena of a complete transparency for a subset of propagating modes. These modes do not interact with each other and effectively can be described by the theory of 1D transport with correlated disorder. We also found that with a proper choice of model parameters one can arrange a perfect transparency of waveguides inside a given window of energy of incoming waves. The results may be important in view of experimental realizations of a selective transport in application to both waveguides and electron/optic nanodevices.

cond-mat↗

arXiv2002

Fluctuations of wave functions about their classical average

Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes. We compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators. The expectation is broadly confirmed, but deviations due to scars are observed.

nlin.CD↗

arXiv2002

Dynamical fidelity of a solid-state quantum computation

In this paper we analyze the dynamics in a spin-model of quantum computer. Main attention is paid to the dynamical fidelity (associated with dynamical errors) of an algorithm that allows to create an entangled state for remote qubits. We show that in the regime of selective resonant excitations of qubits there is no any danger of quantum chaos. Moreover, in this regime a modified perturbation theory gives an adequate description of the dynamics of the system. Our approach allows to explicitly describe all peculiarities of the evolution of the system under time-dependent pulses corresponding to a quantum protocol. Specifically, we analyze, both analytically and numerically, how the fidelity decreases in dependence on the model parameters.

quant-ph↗

arXiv2002

Quantum Arnol'd Diffusion in a Simple Nonlinear System

We study the fingerprint of the Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators with a two-frequency external force. In the classical description, this peculiar diffusion is due to the onset of a weak chaos in a narrow stochastic layer near the separatrix of the coupling resonance. We have found that global dependence of the quantum diffusion coefficient on model parameters mimics, to some extent, the classical data. However, the quantum diffusion happens to be slower that the classical one. Another result is the dynamical localization that leads to a saturation of the diffusion after some characteristic time. We show that this effect has the same nature as for the studied earlier dynamical localization in the presence of global chaos. The quantum Arnol'd diffusion represents a new type of quantum dynamics and can be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.

quant-ph↗

arXiv2001

Chaotic Electron Motion in Superlattices. Quantum-Classical Correspondence of the Structure of Eigenstates and LDOS

We investigate the classical-quantum correspondence for particle motion in a superlattice in the form of a 2D channel with periodic modulated boundaries. Its classical dynamics undergoes the generic transition to chaos of Hamiltonian systems as the amplitude of the modulation is increased. We show that for strong chaotic motion, the classical counterpart of the structure of eigenstates (SES) in energy space reveals an excellent agreement with the quantum one. This correspondence allows us to understand important features of the SES in terms of classical trajectories. We also show that for typical 2D modulated waveguides there exist, at any energy range, extremely localized eigenstates (in energy) which are practically unperturbed by the modulation. These states contribute to the strong fluctuations around the classical SES. The approach to the classical limit is discussed.

cond-mat.dis-nn↗

arXiv2001

Manifestation of the Arnol'd Diffusion in Quantum Systems

We study an analog of the classical Arnol'd diffusion in a quantum system of two coupled non-linear oscillators one of which is governed by an external periodic force with two frequencies. In the classical model this very weak diffusion happens in a narrow stochastic layer along the coupling resonance, and leads to an increase of total energy of the system. We show that the quantum dynamics of wave packets mimics, up to some extent, global properties of the classical Arnol'd diffusion. This specific diffusion represents a new type of quantum dynamics, and may be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.

quant-ph↗

arXiv2001

Time dependence of occupation numbers and thermalization time in closed chaotic many-body systems

We study the time evolution of occupation numbers for interacting Fermi-particles in the situation when exact compound states are "chaotic". This situation is generic for highly excited many-particles states in heavy nuclei, complex atoms, quantum dots, spin systems and quantum computer models. Numerical data show perfect agreement with a simple theory for the onset of thermalization in close systems of interacting particles.

quant-ph↗

arXiv2001

A semiquantal approach to finite systems of interacting particles

A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well defined classical analog which can be easily obtained from the classical equations of motion. Therefore, the occupation numbers for single-particle states can be represented as a convolution of the classical SE with the quantum occupation number operator for non-interacting particles. The latter takes into account the wavefunctions symmetry and depends on the unperturbed energy spectrum only. As a result, the distribution of occupation numbers $n_s$ can be numerically found for a very large number of interacting particles. Using the model of interacting spins we demonstrate that this approach gives a correct description of $n_s$ even in a deep quantum region with few single-particle orbitals.

nlin.CD↗

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↗

arXiv2001

Selective Transparence of Single-Mode Waveguides with Surface Scattering

A random surface scattering in a one-mode waveguide is studied in the case when the surface profile has long-range correlations along the waveguide. Analytical treatment of this problem shows that with a proper choice of the surface, one can arrange any desired combination of transparent and non-transparent frequency windows. We suggest a method to find such profiles, and demonstrate its effectiveness by making use of direct numerical simulations.

cond-mat↗