A geometric theory of chaotic phase synchronization

A rigorous mathematical treatment of chaotic phase synchronization is still lacking, although it has been observed in many numerical and experimental studies. In this article we address the extension of results on phase synchronization in periodic oscillators to systems with phase coherent chaotic attractors with small phase diffusion. As models of such systems we consider special flows over diffeomorphisms in which the neutral direction is periodically perturbed. A generalization of the Averaging Theorem for periodic systems is used to extend Kuramoto's geometric theory of phase locking in periodically forced limit cycle oscillators to this class of systems. This approach results in reduced equations describing the dynamics of the phase difference between drive and response systems over long time intervals. The reduced equations are used to illustrate how the structure of a chaotic attractor is important in its response to a periodic perturbation, and to conclude that chaotic phase coherent systems may not always be treated as noisy periodic oscillators in this context. Although this approach is strictly justified for periodic perturbations affecting only the phase variable of a chaotic oscillator, we argue that these ideas are applicable much more generally.     

Chaotic atomic tunneling between two periodically driven Bose-Einstein condensates

The chaotic coherent atomic tunneling between two periodically driven and weakly coupled Bose-Einstein condensates has been investigated. The perturbed correction to the homoclinic orbit is constructed and its boundedness conditions are established that contain the Melnikov criterion for the onset of chaos. We analytically reveal that the chaotic coherent atomic tunneling is deterministic but not predictable. Our numerical calculation shows good agreement with the analytical result and exhibits nonphysically numerical instability. By adjusting the initial conditions, we propose a method to control the unboundedness, which leads the quantum coherent atomic tunneling to predictable periodical oscillation.     

Bipartite Entanglement in the Two-Mode Quantum Kicked Top

We show that the bipartite entanglement in the two-mode quantum kicked top can reveal the underlying chaotic and regular structures in phase space： namely, the entanglement displays a rapid rise after a very short time for an initial spin coherent state centred in a chaotic region of the phase space, whereas the entanglement displays a periodic modulation for the coherent state centred at an elliptic fixed point. The quantum-classical correspondence is investigated by studying the mean and maximal linear entropy.     

Effect of noise on the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors

We study the influence of external noise on the relaxation to an invariant probability measure for two types of nonhyperbolic chaotic attractors, a spiral (or coherent) and a noncoherent one. We find that for the coherent attractor the rate of mixing changes under the influence of noise, although the largest Lyapunov exponent remains almost unchanged. A mechanism of the noise influence on mixing is presented which is associated with the dynamics of the instantaneous phase of chaotic trajectories. This also explains why the noncoherent regime is robust against the presence of external noise.     

Stimulated Raman scattering of pre-gaussian light

The quantum theory of a forward Stokes generation by means of stimulated Raman scattering is considered in the case of a pre-gaussian pump composed by two and three telegraphs. As for the case of a colored chaotic pump the mean Stokes intensity is found to be enhanced over that resulting from a coherent pump in both transient and steady-state limits. In the limit that the pre-gaussian bandwidth becomes large, the mean Stokes intensity also becomes identical with that resulting from a coherent pump.     

Dicke模型的量子混沌和单粒子相干动力学特性

量子化的Dicke模型在非旋波近似条件下表现为量子混沌动力学特征.利用单粒子一阶时间关联函数,通过数值计算详细考察了Dicke模型中单粒子相干动力学特性.结果表明:当初始相干态处在混沌区域时,一阶时间关联函数曲线衰减较快,而当初始相干态处在规则区域时,一阶时间关联函数曲线衰减较慢,单粒子相干动力学对初态具有较强的敏感性,经典混沌抑制量子相干.考察单粒子相干动力学在相空间的平均演化性质,得到一种较好的量子经典对应关系.最后研究了相空间单粒子相干的整体动力学性质,更好地揭示了相空间的混沌和规则结构.     

Coherent control of quantum chaotic diffusion

Extensive coherent control over quantum chaotic diffusion using the kicked rotor model is demonstrated and its origin in deviations from random matrix theory is identified. Further, the extent of control in the presence of external decoherence is established. The results are relevant to both areas of quantum chaos and coherent control.     

Generalized Fokker-Planck equation approach to optical parametric processes I. Equations of motion and their solutions

We develop a recursion procedure for solving the generalized Fokker-Planck equation for a system of three interacting one-mode boson fields including the proof of convergence. Approximate formulae for the quantum antinormal characteristic function and the corresponding quasidistribution are obtained for the whole system and as a consequence quantum fluctuations in single fields, correlations among them and various cases of occurrence of the anticorrelation effect are discussed including losses. Initial fields are assumed to be coherent or partly chaotic and it is shown that in some cases the lossy mechanism as well as if some of these fields are chaotic can support the occurrence of the anticorrelation effect. The most important cases are described by the model of the superposition of coherent and chaotic fields although some corrections to this model are also found.     

Fermi-edge singularities in the mesoscopic x-ray edge problem

We study the x-ray edge problem for a chaotic quantum dot or nanoparticle displaying mesoscopic fluctuations. In the bulk, x-ray physics is known to produce Fermi-edge singularities-deviations from the naively expected photoabsorption cross section in the form of a peaked or rounded edge. For a coherent system with chaotic dynamics, we find substantial changes; in particular, a photoabsorption cross section showing a rounded edge in the bulk will change to a slightly peaked edge on average as the system size is reduced to a mesoscopic (coherent) scale.     

Effects of source opacity and expansion on two-pion Bose-Einstein correlations

We examine two-pion Bose-Einstein correlations for partially coherent particle-emitting sources within quantum statistical formalism, where the sources are treated as classical currents with chaotic and coherent components. The two-pion correlation functions of the partially coherent sources contain a phase which is sensitive to the asymmetry of the source emission function. We investigate the influence of source opacity and expansion in high energy heavy ion collisions on the phase by Monte Carlo calculati...     

Zur Korrelationsfunktionn-ter Ordnung für die Überlagerung von Thermischem und Kohärentem Licht

Then-th order correlation function for superimposed coherent and chaotic light is calculated in coherent state formalism. This function reduces to products and sums of the first-order correlations of coherent and chaotic fields alonge. It is demonstrated that superimposed fields cannot have full coherence farther then to the first order.     

Chaotic Entanglement: Entropy and Geometry

In chaotic entanglement, pairs of interacting classically-chaotic systems are induced into a state of mutual stabilization that can be maintained without external controls and that exhibits several properties consistent with quantum entanglement. In such a state, the chaotic behavior of each system is stabilized onto one of the system’s many unstable periodic orbits (generally located densely on the associated attractor), and the ensuing periodicity of each system is sustained by the symbolic dynamics of its partner system, and vice versa. Notably, chaotic entanglement is an entropy-reversing event: the entropy of each member of an entangled pair decreases to zero when each system collapses onto a given period orbit. In this paper, we discuss the role that entropy plays in chaotic entanglement. We also describe the geometry that arises when pairs of entangled chaotic systems organize into coherent structures that range in complexity from simple tripartite lattices to more involved patterns. We conclude with a discussion of future research directions.     

Quantum Signatures of Chaos in Adiabatic Interaction Between a Trapped Ion and a Laser Standing Wave

We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.     

Entanglement and dynamics of spin chains in periodically pulsed magnetic fields: accelerator modes

We study the dynamics of a single excitation in a Heisenberg spin-chain subjected to a sequence of periodic pulses from an external, parabolic, magnetic field. We show that, for experimentally reasonable parameters, a pair of counterpropagating coherent states is ejected from the center of the chain. We find an illuminating correspondence with the quantum time evolution of the well-known paradigm of quantum chaos, the quantum kicked rotor. From this we can analyze the entanglement production and interpret the ejected coherent states as a manifestation of the so-called "accelerator modes" of a classically chaotic system.     

A robust steganographic technique based on improved chaotic-range systems

This paper presents a novel chaos-based technique of steganography in spatial domain. In the last decade, chaos theory has gained utmost importance in multimedia security applications. Generally, 1-D chaotic maps are employed because of computational ease and structural simplicity but their limited chaotic range is an obstacle. In the proposed work, we model the nonlinear combinations of 1-D chaotic maps. These chaotic systems possess chaotic behavior throughout the domain. We, for the first time, propose an effective application of these improved chaotic systems in steganography. These newly synthesized systems are used to embed secret information in the least significant bits (LSBs) of the host image. By comparing with some recent models, we prove that involving improved chaotic systems in steganographic approach really produces extraordinary outcomes. We determine the strength of our steganographic algorithm through the most significant statistical analyses such as information entropy, correlation, contrast, energy, homogeneity, peak signal to noise ratio (PSNR) and mean square error (MSE). We further prove the robustness of the anticipated technique against several image processing attacks. The upshot of these analysis techniques shows that our algorithm is highly reliable and produces coherent results.     

Localized Coherent Structures with Chaotic and Fractal Behaviors in a(2+1)-Dimensional Modified Dispersive Water-Wave System

In this work, we reveal a novel phenomenon that the localized coherent structures of some (2 1 )-dimensionalphysical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (2 1)-dimensional modified dispersive water-wave system as a concrete example. Starting from a variable separation approach,a general variable separation solution of this system is derived. Besides the stable localized coherent soliton excitationslike dromions, lumps, rings, peakons, and oscillating soliton excitations, some new excitations with chaotic and fractalbehaviors are derived by introducing some types of lower dimensional chaotic and fractal patterns.     

Analysis of chaotic saddles in high-dimensional dynamical systems: the Kuramoto-Sivashinsky equation

This paper presents a methodology to study the role played by nonattracting chaotic sets called chaotic saddles in chaotic transitions of high-dimensional dynamical systems. Our methodology is applied to the Kuramoto-Sivashinsky equation, a reaction-diffusion partial differential equation. The paper describes a novel technique that uses the stable manifold of a chaotic saddle to characterize the homoclinic tangency responsible for an interior crisis, a chaotic transition that results in the enlargement of a chaotic attractor. The numerical techniques explained here are important to improve the understanding of the connection between low-dimensional chaotic systems and spatiotemporal systems which exhibit temporal chaos and spatial coherence.     

Secure communication scheme using chaotic laser diodes subject to incoherent optical feedback and incoherent optical injection

We propose a secure communication scheme based on anticipating synchronization of two chaotic laser diodes, one subject to incoherent optical feedback and the other to incoherent optical injection. This scheme does not require fine tuning of the optical frequencies of both lasers as is the case for other schemes based on chaotic laser diodes subject to coherent optical feedback and injection. Our secure communication scheme is therefore attractive for experimental investigation.     

Chaotic itinerancy based on attractors of one-dimensional maps

A general methodology is described for constructing systems that have a slowly converging Lyapunov exponent near zero, based on one-dimensional maps with chaotic attractors. In certain parameter ranges, these relatively simple systems display the properties of intermittent dynamics known as chaotic itinerancy. We show that in addition to the local sensitivity characteristic of chaotic dynamics, these itinerant systems display a global sensitivity, in the sense that fine-scale additive noise may significantly change the natural measure on the large scale.     

Chaotic oscillations associated with the breakup of polarization entangled coherent states in a microchip solid-state laser

We demonstrate the breakup of spatial-polarization entangled lasing patterns, which possess vector phase singularities, and the resultant dynamic instabilities featuring chaotic oscillations. The frequency splitting between a pair of Ince-Gauss (IG) lasing modes, originally forming a coherent entanglement state, and a self-excited additional nonorthogonal IG mode through a new class of transverse effect of self-injection pattern seeding, is shown to result in modal-interference-induced modulation at the beat frequency, leading to chaotic oscillations.