arXiv subjects

F. M. Izrailev

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

At least 55 records · Page 3Linked to original sources

arXiv2007

Transition from isolated to overlapping resonances in the open system of interacting fermions

We study the statistical properties of resonance widths and spacings in an open system of interacting fermions at the transition between isolated and overlapping resonances, where a radical change in the width distribution occurs. Our main interest is to reveal how this transition is influenced by the onset of chaos in the internal dynamics as the strength of random two-body interaction between the particles increases. We have found that in the region of overlapped resonances, the fluctuations of the widths (rather than their mean values) are strongly affected by the onset of an internal chaos. The results may be applied to the analysis of neutron cross sections, as well as in the physics of mesoscopic devices with strongly interacting electrons.

cond-mat.mes-hall↗

arXiv2007

Open system of interacting fermions: Statistical properties of cross sections and fluctuations

Statistical properties of cross sections are studied for an open system of interacting fermions. The description is based on the effective non-Hermitian Hamiltonian that accounts for the existence of open decay channels preserving the unitarity of the scattering matrix. The intrinsic interaction is modelled by the two-body random ensemble of variable strength. In particular, the crossover region from isolated to overlapping resonances accompanied by the effect of the width redistribution creating super-radiant and trapped states is studied in detail. The important observables, such as average cross section, its fluctuations, autocorrelation functions of the cross section and scattering matrix, are very sensitive to the coupling of the intrinsic states to the continuum around the crossover. A detailed comparison is made of our results with standard predictions of statistical theory of cross sections, such as the Hauser-Feshbach formula for the average cross section and Ericson theory of fluctuations and correlations of cross sections. Strong deviations are found in the crossover region, along with the dependence on intrinsic interactions and degree of chaos inside the system.

cond-mat.dis-nn↗

arXiv2007

Generation of Correlated Binary Sequence from White Noise

We suggest a method for generation of random binary sequences with prescribed correlation properties. It is based on a kind of modification of the widely used convolution method of constructing continuous random processes. Apart from the theoretical interest, this method can be used in various applications such as the design of one-dimensional devices giving rise to selective transport properties.

cond-mat.dis-nn↗

arXiv2006

Square-gradient mechanism of surface scattering in quasi-1D rough waveguides

We develop a perturbative approach that allows one to study the surface scattering in quasi-1D waveguides with rough boundaries. Our approach is based on the construction of an effective ``bulk'' potential of a very complicated structure. The detailed analysis of this potential reveals that apart from the well known terms considered in the previous studies, one should keep specific terms that depend on the square of the derivative of the boundaries. As was found, in spite of an apparent smallness of these square-gradient scattering (SGS) terms, there is a physically important region of parameters, in which they can not be neglected. Our approach also demonstrates that the contribution of the SGS-mechanism of scattering strongly depends on the type of the rough boundaries (uncorrelated, symmetric or antisymmetric)

cond-mat.mes-hall↗

arXiv2006

Nonlinear electron dynamics in a rippled channel with time-dependent electric field: Quantum Arnol'd diffusion

We study the electron dynamics in a 2D waveguide bounded by a periodically rippled surface in the presence of the time-periodic electric field. The main attention is paid to a possibility of a weak quantum diffusion along the coupling resonance, that can be associated with the classical Arnol'd diffusion. It was found that quantum diffusion is possible only when the perturbation is large enough in order to mix many near-separatrix levels. The rate of the quantum diffusion turns out to be less than the corresponding classical one, thus indicating the influence of quantum coherent effects. Another important effect is the dynamical localization of the quantum diffusion, that may be compared with the famous Anderson localization occurring in 1D random potentials. Our estimates show that the quantum Arnol'd diffusion can be observed in semi-metal rippled channels, for which the scattering and decoherence times are larger than the saturation time due to the dynamical localization.

cond-mat.mes-hall↗

arXiv2006

Memory Function versus Binary Correlator in Additive Markov Chains

We study properties of the additive binary Markov chain with short and long-range correlations. A new approach is suggested that allows one to express global statistical properties of a binary chain in terms of the so-called memory function. The latter is directly connected with the pair correlator of a chain via the integral equation that is analyzed in great detail. To elucidate the relation between the memory function and pair correlator, some specific cases were considered that may have important applications in different fields.

cond-mat.stat-mech↗

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↗

arXiv2005

Manifestation of the Roughness-Square-Gradient Scattering in Surface-Corrugated Waveguides

We study a new mechanism of wave/electron scattering in multi-mode surface-corrugated waveguides/wires. This mechanism is due to specific square-gradient terms in an effective Hamiltonian describing the surface scattering, that were neglected in all previous studies. With a careful analysis of the role of roughness slopes in a surface profile, we show that these terms strongly contribute to the expression for the inverse attenuation length (mean free path), provided the correlation length of corrugations is relatively small. The analytical results are illustrated by numerical data.

cond-mat.dis-nn↗

arXiv2005

Return probability: Exponential versus Gaussian decay

We analyze, both analytically and numerically, the time-dependence of the return probability in closed systems of interacting particles. Main attention is paid to the interplay between two regimes, one of which is characterized by the Gaussian decay of the return probability, and another one is the well known regime of the exponential decay. Our analytical estimates are confirmed by the numerical data obtained for two models with random interaction. In view of these results, we also briefly discuss the dynamical model which was recently proposed for the implementation of a quantum computation.

cond-mat.dis-nn↗

arXiv2005

Quantum Arnol'd diffusion in a rippled waveguide

We study the quantum Arnol'd diffusion for a particle moving in a quasi-1D waveguide bounded by a periodically rippled surface, in the presence of the time-periodic electric field. It was found that in a deep semiclassical region the diffusion-like motion occurs for a particle in the region corresponding to a stochastic layer surrounding the coupling resonance. The rate of the quantum diffusion turns out to be less than the corresponding classical one, thus indicating the influence of quantum coherent effects. Another result is that even in the case when such a diffusion is possible, it terminates in time due to the mechanism similar to that of the dynamical localization. The quantum Arnol'd diffusion represents a new type of quantum dynamics, and may be experimentally observed in measurements of a conductivity of low-dimensional mesoscopic structures.

quant-ph↗

arXiv2005

Anomalous transport in low-dimensional systems with correlated disorder

We review recent results on the anomalous transport in one-dimensional and quasi-one-dimensional systems with bulk and surface disorder. Main attention is paid to the role of long-range correlations in random potentials for the bulk scattering, and in corrugated profiles for the surface scattering. It is shown that with a proper choice of correlations one can construct such a disorder that results in a selective transport with given properties. A particular interest is in the possibility to arrange windows of a complete transparency (or reflection) in the dependence on the wave number of incoming classical waves or electrons.

cond-mat.dis-nn↗

arXiv2005

Gradient and Amplitude Scattering in Surface-Corrugated Waveguides

We investigate the interplay between amplitude and square-gradient scattering from the rough surfaces in multi-mode waveguides (conducting quantum wires). The main result is that for any (even small in height) roughness the square-gradient terms in the expression for the wave scattering length (electron mean free path) are dominant, provided the correlation length of the surface disorder is small enough. This important effect is missed in existing studies of the surface scattering.

cond-mat.dis-nn↗

arXiv2005

The Fermi-Pasta-Ulam problem: 50 years of progress

A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other physical problems. We focus on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective. Starting from the first numerical results of FPU, both theoretical and numerical findings are discussed in close connection with the problems of ergodicity, integrability, chaos and stability of motion. New directions related to the Bose-Einstein condensation and quantum systems of interacting Bose-particles are also considered.

nlin.CD↗

arXiv2004

Rough surface scattering in many-mode conducting channels: Gradient versus amplitude scattering

We study the effect of surface scattering on transport properties in many-mode conducting channels (electron waveguides). Assuming a strong roughness of the surface profiles, we show that there are two independent control parameters that determine statistical properties of the scattering. The first parameter is the ratio of the amplitude of the roughness to the transverse width of the waveguide. The second one, which is typically omitted, is determined by the mean value of the derivative of the profile. This parameter may be large, thus leading to specific properties of scattering. Our results may be used in experimental realizations of the surface scattering of electron waves, as well as for other applications (e.g., for optical and microwave waveguides)

cond-mat.dis-nn↗

arXiv2004

Many-particle localization by constructed disorder: enabling quantum computing with perpetually coupled qubits

We demonstrate that, in a many-particle system, particles can be strongly confined to their sites. The localization is obtained by constructing a sequence of on-site energies that efficiently suppresses resonant hopping. The time during which a many-particle state remains strongly localized in an infinite chain can exceed the reciprocal hopping frequency by $\agt 10^6$ already for a narrow energy bandwidth. The results show viability of quantum computers with time-independent qubit coupling.

cond-mat.mes-hall↗

arXiv2004

Strong many-particle localization and quantum computing with perpetually coupled qubits

We demonstrate the onset of strong on-site localization in a one-dimensional many-particle system. The localization is obtained by constructing, in an explicit form, a bounded sequence of on-site energies that eliminates resonant hopping between both nearest and remote sites. This sequence leads to quasi-exponential decay of the single-particle transition amplitude. It also leads to strong localization of stationary many-particle states in a finite-length chain. For an {\it infinite} chain, we instead study the time during which {\it all} many-particle states remain strongly localized. We show that, for any number of particles, this time exceeds the reciprocal frequency of nearest-neighbor hopping by a factor $\sim 10^5$ already for a moderate bandwidth of on-site energies. The proposed energy sequence is robust with respect to small errors. The formulation applies to fermions as well as perpetually coupled qubits. The results show viability of quantum computing with time-independent qubit coupling.

quant-ph↗

arXiv2004

Entropy production and fidelity for quantum many-body systems with noise

We study dynamical properties of systems with many interacting Fermi-particles under the influence of static imperfections. Main attention is payed to the time dependence of the Shannon entropy of wave packets, and to the fidelity of the dynamics. Our question is how the entropy and fidelity are sensitive to the noise. In our study, we use both random matrix models with two-body interaction and dynamical models of a quantum computation. Numerical data are compared with analytical predictions.

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↗