Fluctuations of the Lyapunov exponent in two-dimensional disordered systems

Slevin, Keith; Asada, Yoichi

doi:10.1103/physrevb.70.054201

Cited by 38 publications

(33 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For deriving estimation LLE is analyzed a time series. Other approaches to estimation LE on bases of deriving a solution dynamic system or fulfillment of the analysis experimental data are described in [6]- [8].…”

Section: Introductionmentioning

confidence: 99%

Estimation of Spectrum Eigenvalues Dynamic System on the Basis of Application Lyapunov Exponents

Karabutov¹,

Лохин²,

Манько³

et al. 2015

IJMMM

View full text Add to dashboard Cite

Abstract-The method is based on identifications of a particular solution of the linear dynamic system on a class of static models with the dynamic specification on an input. On the basis of a particular solution the common decision are search. The common decision is a basis for an estimation of a spectrum system. For identification of a spectrum eigenvalues we introduced special structures, who described a modification of Lyapunov exponents. We gave generalization of the offer methods on the linear non-stationary dynamic systems. The algorithm of decision-making about a type of eigenvalues system is developed. We analyse properties of the offered special functions.Index Terms-Identification, lyapunov exponent, spectrum of eigenvalues, structure.

show abstract

Section: Introductionmentioning

confidence: 99%

Estimation of Spectrum Eigenvalues Dynamic System on the Basis of Application Lyapunov Exponents

Karabutov¹,

Лохин²,

Манько³

et al. 2015

IJMMM

View full text Add to dashboard Cite

show abstract

“…This problem is known as the large fd problem [54] and appears in a wide variety of fields. We discuss in Appendix B two different methods to deal with it, using the Global Matrix method (appearing in the study of the propagation of ultrasonic waves in multilayered media [54]) or the QR decomposition (considered in Anderson localization problems [55]). …”

Section: Quasi-stationary Scattering Modelmentioning

confidence: 99%

“…For sufficiently large optical lattices, this makes that the fundamental matrix becomes singular within computer's relative accuracy, spoiling the calculation. In order to deal with this problem, we consider two methods: QR decomposition [55] and the Global Matrix method [54]. Both methods are based on the following property of the transfer matrix of Eq.…”

Section: Appendix B: Numerical Integration Of the Quasi-stationary Bdmentioning

confidence: 99%

Quantum Transport in the Black‐Hole Configuration of an Atom Condensate Outcoupled Through an Optical Lattice

2017

View full text Add to dashboard Cite

The outcoupling of a Bose-Einstein condensate through an optical lattice provides an interesting scenario to study quantum transport phenomena or the analog Hawking effect as the system can reach a quasi-stationary black-hole configuration. We devote this work to characterize the quantum transport properties of quasi-particles on top of this black-hole configuration by computing the corresponding scattering matrix. We find that most of the features can be understood in terms of the usual Schrödinger scattering. In particular, a transmission band appears in the spectrum, with the normal-normal transmission dominating over the anomalous-normal one. We show that this picture still holds in a realistic experimental situation where the actual Gaussian envelope of the optical lattice is considered. A peaked resonant structure is displayed near the upper end of the transmission band, which suggests that the proposed setup is a good candidate to provide a clear signal of spontaneous Hawking radiation.

show abstract

“…For deriving estimation LLE is analyzed a time series. Other approaches to estimation LE on bases of deriv ing a solution dynamic system or fulfillment of the analysis experimental data are described in [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Identification of Quality Indicators Dynamic System on Basis of Analysis Data "Input-Output"

Karabutov¹

2014

IJISA

View full text Add to dashboard Cite

Abstract-The problem of an estimation quality indicators of linear dynamic system in the conditions of uncertainty is considered. Quality indicators are a point of an equilibrium state and a spectrum of eigenvalues. We offer a method of an estimation a point of an equilibrium state. M ethod is based on identification of the particular solution system on a class of static models with the dynamic specification on an input. We offered on the basis of the general decision of system procedures and criteria of an estimation equilibrium state. After an estimation of equilibrium state system in work the problem of definition a spectrum eigenvalues of linear dynamic system is considered. We form the time series describing a modification of Lyapunov exponents. For identification of a spectrum eigenvalues we introduce special structures which describe a modification of the Lyapunov exponent. We apply a method of the secant structures and we receive spectrum tentative estimations. The special structure, allowing identifying the largest Lyapunov exponent, is offered. Generalization of the offered methods on linear non-stationary dynamic systems is given.

show abstract

Fluctuations of the Lyapunov exponent in two-dimensional disordered systems

Cited by 38 publications

References 28 publications

Estimation of Spectrum Eigenvalues Dynamic System on the Basis of Application Lyapunov Exponents

Estimation of Spectrum Eigenvalues Dynamic System on the Basis of Application Lyapunov Exponents

Quantum Transport in the Black‐Hole Configuration of an Atom Condensate Outcoupled Through an Optical Lattice

Identification of Quality Indicators Dynamic System on Basis of Analysis Data "Input-Output"

Contact Info

Product

Resources

About