Chaotic-like Behavior Research Articles

Nonlinear three-state quantum walks

The dynamics of a three-state quantum walk with amplitude-dependent phase shifts is investigated. We consider two representative inputs whose linear evolution is known to display either full dispersion of the wave packet or intrinsic localization on the initial position. The nonlinear counterpart presents much more involved dynamics featuring self-trapping, solitonic pulses, radiation, and chaotic-like behavior. We show that nonlinearity leads to a metastable self-trapped wavepacket component that radiates in the long-time regime with the survival probability $\propto t^{-1/2}$. A sudden dynamical transition from such metastable state to the point when the radiation process is triggered is found for a set of parameters.

Multidimensional scaling and visualization of patterns in global large-scale accidents

Catastrophic events have been commonly referred to as phase transitions in complex systems (CS). This paper proposes an approach based on unsupervised machine learning to identify phases and phase transitions in the dynamics of CS. The testbed is a dataset of causalities and events associated with global large-scale accidents. Multidimensional time-series are generated from the raw data and are interpreted as the output of a CS. The time-series are normalized and segmented in the time-domain, and the resulting objects are used to characterize the behavior of the dynamical process. The objects are compared through a number of distances and the information by the multidimensional scaling (MDS) technique, respectively. The time is displayed as a parametric variable. The generated portraits have a complex nature, with periods of chaotic-like behavior, and are analyzed in terms of the emerging patterns. The results show that the adoption of MDS is a relevant modeling tool using present day computational resources.

Dynamics of modulated waves and localized energy in a Burridge and Knopoff model of earthquake with velocity-dependant and hydrodynamics friction forces

We investigate both analytically and numerically the dynamics of modulated waves in a modified Burridge and Knopoff mechanical model of earthquake. We take into account the velocity-dependent and hydrodynamics friction forces between the rock blocks of the system. The theoretical framework for the analysis is presented using the multiple scale expansion method. We show that the system can be governed by the complex Ginzburg–Landau equation, which admits soliton solutions. The modulational instability of the system is performed, showing that the bandwidth of instability increases with the friction forces parameter. The planar wave solution used as the initial condition leads to more unstable waves in the system with chaotic-like behaviour, allowing energy localization. It is also found that the wave parameters, namely, the frequency, magnitude and velocity (as well as the energy of the system) strongly depend on η. In the non-friction limit, the obtained waves propagate with a coherent behaviour for a very short time, before disappearing. Our results suggest that the damages caused by an earthquake can be important as the friction forces increase and may excite the possibility of relative predictions for the dynamics of waves propagating in the earth in the field of nonlinear science.

Computer Analysis of Human Belligerency

War is a cause of gains and losses. Economic historians have long stressed the extreme importance of considering the economic potential of society for belligerency, the role of management of chaos to bear the costs of battle and casualties, and ingenious and improvisation methodologies for emergency management. However, global and inter-temporal studies on warring are missing. The adoption of computational tools for data processing is a key modeling option with present day resources. In this paper, hierarchical clustering techniques and multidimensional scaling are used as efficient instruments for visualizing and describing military conflicts by electing different metrics to assess their characterizing features: time, time span, number of belligerents, and number of casualties. Moreover, entropy is adopted for measuring war complexity over time. Although wars have been an important topic of analysis in all ages, they have been ignored as a subject of nonlinear dynamics and complex system analysis. This paper seeks to fill these gaps in the literature by proposing a quantitative perspective based on algorithmic strategies. We verify the growing number of events and an explosion in their characteristics. The results have similarities to those exhibited by systems with increasing volatility, or evolving toward chaotic-like behavior. We can question also whether such dynamics follow the second law of thermodynamics since the adopted techniques reflect a system expanding the entropy.

Metamorphoses of Electron Systems Hosting a Fermion Condensate

We present a unified theory of strongly correlated electron systems with a fermion condensate. This theoretical framework facilitates quantitative analysis and explanation, on an equal footing, of (i) non-Fermi-liquid behavior of high-Tc superconductors in which the critical temperature for superconductivity is proportional to the Fermi energy TF and (ii) the so-called quantum electron solid state in the two-dimensional electron liquid of MOSFETs and SiGe/Si/SiGe quantum wells. In this framework, low-temperature chaotic-like behavior that is documented in experimental studies of these systems is attributed to a spontaneous topological rearrangement of the conventional Landau state, quite in contrast to models in which the chaotic element is introduced deliberately in terms of a chaotic distribution of interaction matrix elements.

A Quantification of the Butterfly Effect in Cosmological Simulations and Implications for Galaxy Scaling Relations

Abstract We study the chaotic-like behavior of cosmological simulations by quantifying how minute perturbations grow over time and manifest as macroscopic differences in galaxy properties. When we run pairs of “shadow” simulations that are identical except for random minute initial displacements to particle positions (e.g., of order ), the results diverge from each other at the individual galaxy level (while the statistical properties of the ensemble of galaxies are unchanged). After cosmological times, the global properties of pairs of “shadow” galaxies that are matched between the simulations differ from each other, generally at a level of ∼2–25%, depending on the considered physical quantity. We perform these experiments using cosmological volumes of evolved either purely with dark matter, or with baryons and star formation but no feedback, or else using the full feedback model of the IllustrisTNG project. The runs cover four resolution levels spanning a factor of 512 in mass. We find that, without feedback, the differences between shadow galaxies generally become smaller as the resolution increases—but with the IllustrisTNG model, the results mostly converge toward a “floor.” This hints at the role of feedback in setting the chaotic properties of galaxy formation. Importantly, we compare the macroscopic differences between shadow galaxies to the overall scatter in various galaxy scaling relations, and conclude that, for the star formation-mass and the Tully–Fisher relations, the butterfly effect in our simulations contributes significantly to the overall scatter. We find that our results are robust to whether random numbers are used in the subgrid models or not. We discuss the implications for galaxy formation theory in general and for cosmological simulations in particular.

Graphene-Based Active Random Metamaterials for Cavity-Free Lasing.

Manipulating and controlling the optical energy flow inside random media is a research frontier of photonics and the basis of novel laser designs. Here, we show that a metamaterial consisting of randomly dispersed graphene nanoflakes embedded within an optically pumped gain medium (rhodamine 6G) can operate as a cavity-free laser thanks to its extraordinarily low threshold for saturable absorption. The emitted light is self-organized into a well-determined spatial pattern, which depends on the graphene flake density and can be externally controlled through the optical pump. We provide different examples of tunable laser operation ranging from stable single-mode to chaoticlike behavior. Our metamaterial design holds great potential for the optical control of light amplification, as well as for the development of single-mode beam-engineered cavity-free lasers.

Sequential dynamics of master–slave systems

Following on previous work, we discuss a scenario in which two neural ensembles have a master–slave arrangement. We will consider a more particular case in which the master system exhibits transient dynamics due to a stable heteroclinic sequence (SHS) and the slave system has attractors in the form of limit cycles. We will give sufficient conditions that guarantee the existence of a SHS in the form of a tube in the full phase space, together with an open stable heteroclinic channel that surrounds it. We present a numerical observation of chaotic-like transient behaviour different from well-known transient chaos.

Nonlinear Dynamics of Vertical-Cavity Surface-Emitting Lasers

Nonlinear dynamics of Vertical-Cavity Surface-Emitting Lasers (VCSELs) induced by optical injection, optical feedback, current modulation and mutual coupling is reviewed. Due to the surface emission and cylindrical symmetry VCSELs lack strong polarization anisotropy and may undergo polarization switching. Furthermore, VCSELs may emit light in multiple transverse modes. These VCSEL properties provide new features to the rich nonlinear dynamics induced by an external perturbation. We demonstrate for the case of orthogonal optical injection that new Hopf bifurcation on a two-polarization-mode solution delimits the injection locking region and that polarization switching and injection locking of first-order transverse mode lead to a new resonance tongue for large positive detunings. Similarly, the underlying polarization mode competition leads to chaotic-like behavior in case of gain switching and the presence of two transverse modes additionally reduces the possibility of regular dynamics. The bistable property of VCSEL makes it possible to investigate very fundamental problems of bistable systems with time-delay, such as the coherence resonance phenomenon. We also demonstrate that the synchronization quality between unidirectionally coupled VCSELs can be significantly enhanced when the feedback-induced chaos in the master laser involves both orthogonal LP fundamental transverse modes.

Performance reproducibility of organic light-emitting devices under exposure to atmospheric water vapor during fabrication: Sensitivity and chaotic-like behaviour of the quantum yield

Organic electronic devices are generally sensitive to atmospheric conditions, especially to water vapor when combined with oxygen. Organic light-emitting devices are such an example. Usually, atmospheric water vapor has detrimental consequences on the devices performance. However, as shown by our experimental results, in some (still uncontrolled) circumstances, oxidation processes accelerated by water vapor can be beneficial to performance. Thus, high humidity level is not only a detrimental issue to OLEDs. In addition, it appears that the occurrence of antagonist mechanisms and the devices sensitivity to initial structural conditions of organic materials and electrodes leads to an unpredictable, chaotic-like, behaviour of organic light-emitting quantum yield when they are exposed to atmospheric water vapor.

Polarization- and Transverse-Mode Dynamics in Optically Injected and Gain-Switched Vertical-Cavity Surface-Emitting Lasers

In this paper, we summarize our recent results on nonlinear polarization- and transverse-mode dynamics of vertical-cavity surface-emitting lasers (VCSELs) induced by optical injection (OI) or current modulation. Due to the surface emission and cylindrical symmetry, VCSELs lack strong polarization anisotropy and may undergo polarization switching (PS). Furthermore, VCSELs may emit light in multiple transverse modes. This provides new features to the rich nonlinear dynamics induced in VCSELs by an external perturbation. We demonstrate for the case of orthogonal OI that new Hopf bifurcation on a two-polarization-mode solution delimits the injection locking (IL) region and that PS and IL of first-order transverse mode lead to a new resonance tongue for large positive detunings. Similarly, the underlying polarization-mode competition leads to chaotic-like behavior in case of gain switching and the presence of two transverse modes additionally reduces the possibility of regular dynamics.

Expression of Cassini's third law for Callisto, and theory of its rotation

The rotation of the main natural satellites of the Solar System is widely assumed to be synchronous, because this corresponds to an equilibrium state. In the case of the Moon, 3 laws have been formulated by Cassini, assuming a spin–orbit resonance and a 1:1 nodal resonance. The recent gravitational data collected by the spacecrafts Galileo (in the jovian system) and Cassini (in the saturnian system) allows us to study the rotation of other natural satellites, and to check the universality of Cassini's laws. This paper deals with the rotation of the Galilean satellites of Jupiter J-4 Callisto. In this study we use both analytical (like Lie transforms) and numerical methods (numerical detection of chaos, numerical integration, frequency analysis) to first check the reliability of Cassini Laws for Callisto, and then to give a first theory of its rotation, Callisto's being considered as a rigid body. We first show that the Third Cassini Law (i.e. the nodal resonance), is not satisfied in every reference frame, in particular in the most natural one (i.e. the J2000 jovian equator). The difference of the nodes presents a chaotic-like behavior, that we prove to be just a geometrical illusion. Moreover, we give a mathematical condition ruling the choice of an inertial reference frame in which the Third Cassini Law is fulfilled. Secondly, we give a theory of Callisto's rotation in the International Celestial Reference Frame (ICRF). We highlight a small motion (i.e. <200 m) of its rotation axis about its body figure, a 11.86-yr periodicity in Callisto's length-of-day, and the proximity of a resonance that forces 182-yr librations in Callisto's obliquity.

Modulated waves and chaotic-like behaviours in the discrete electrical transmission line

The dynamics of a weakly nonlinear modulated wave in a discrete electrical transmission line with negative nonlinear resistance and dissipative effects is investigated. This leads to the propagation of envelope modulation in the line modelled by the discrete complex Ginzburg–Landau equation. For an initial modulated plane wave propagating in the line, the criteria for modulational instability as well as the threshold amplitude are derived. The evolution of modulated waves which have the shape of an envelope soliton and the chaotic-like behaviour of the system are also examined. We show that dissipation can affect patterns propagating into the system. Numerical simulations demonstrate the validity of theoretical predictions.

Recovery of classical chaoticlike behavior in a conservative quantum three-body problem

Recovering trajectories of quantum systems whose classical counterparts display chaotic behavior has been a subject that has received a lot of interest over the last decade. However, most of these studies have focused on driven and dissipative systems. The relevance and impact of chaotic-like phenomena to quantum systems has been highlighted in recent studies which have shown that quantum chaos is significant in some aspects of quantum computation and information processing. In this paper we study a three-body system comprising of identical particles arranged so that the system's classical trajectories exhibit Hamiltonian chaos. Here we show that it is possible to recover very nearly classical-like, conservative, chaotic trajectories from such a system through an unravelling of the master equation. First, this is done through continuous measurement of the position of each system. Second, and perhaps somewhat surprisingly, we demonstrate that we still obtain a very good match between the classical and quantum dynamics by weakly measuring the position of only one of the oscillators.

Signatures of chaoticlike and nonchaoticlike behavior in a nonlinear quantum oscillator through photon detection

The driven nonlinear Duffing oscillator is a very good, and standard, example of a quantum mechanical system from which classical-like orbits can be recovered from unravelings of the master equation. In order to generate such trajectories in the phase space of this oscillator, in this paper we use the quantum jump unraveling together with a suitable application of the correspondence principle. We analyze the measured readout by considering the power spectra of photon counts produced by the quantum jumps. Here we show that localization of the wave packet from the measurement of the oscillator by the photon detector produces a concomitant structure in the power spectra of the measured output. Furthermore, we demonstrate that this spectral analysis can be used to distinguish between different modes of the underlying dynamics of the oscillator.

Drift Intermittent Synchronization and Controllability in a Simple Model**Theproject supported by National Natural Science Foundation of China under GrantNo. 10475009 and partially by the Program for New Century Excellent Talents inUniversity (NCET)

A simple model of three coupled oscillatorsas an approximation of mainmodes behaviors in a spatial extended system is proposed. Multi-loopinggeneralized synchronization and drift intermittent lag phase synchronizationphenomena are found in this simple model. For a certain of parameters inwhich chaotic-like intermittent behavior exhibit the amplitudes and phasesof three modes are controlled to be synchronized states via coupling themwith an external periodic mode.

Persistent entanglement in the classical limit

The apparent difficulty in recovering classical nonlinear dynamics and chaos from standard quantum mechanics has been the subject of a great deal of interest over the last 20 years. For open quantum systems—those coupled to a dissipative environment and/or a measurement device—it has been demonstrated that chaotic-like behaviour can be recovered in the appropriate classical limit. In this paper, we investigate the entanglement generated between two nonlinear oscillators, coupled to each other and to their environment. Entanglement—the inability to factorize coupled quantum systems into their constituent parts—is one of the defining features of quantum mechanics. Indeed, it underpins many of the recent developments in quantum technologies. Here, we show that the entanglement characteristics of two ‘classical’ states (chaotic and periodic solutions) differ significantly in the classical limit. In particular, we show that significant levels of entanglement are preserved only in the chaotic-like solutions.

Chaotic-like behavior of modulated waves in a nonlinear discrete LC transmission line

Modulational instability (MI) in a discrete nonlinear LC transmission line is investigated. The higher order nonlinear Schrödinger (NLS) equation modeling modulated waves propagation in the network allows to predict the MI conditions, with additional features, compared to the standard NLS model. More precisely, a chaotic-like behavior of the system, which is observed in a particular frequency domain, is related to the nonrepeatability of the numerical experiments.

Molecular-dynamics simulation of homogeneous nucleation in the vapor phase

Ten independent quenches of a gas of 40 000 Lennard-Jones particles are followed until the systems exhibit droplet growth. The cluster distributions and the kinetics are determined for the quenched quasi-equilibrium state, at the onset of nucleation and at droplet growth. All the distributions are isomorphic with the particle distribution in the equilibrium gas state and asymptotically given by simple exponentials. The kinetics show detailed balance of particles and clusters which join and which leave the successful critical nuclei. The systems exhibit chaoticlike behavior with respect to the onset of nucleation, so that only marginal changes in a system will change the onset of nucleation.

Nonlinear-driven instability of dynamical plasma in solids: Emergence of spatially self-organized order and chaotic-like behavior

We analyze in detail the nonlinear kinetics of a carrier system in a photoinjected plasma in semiconductors under the action of constant illumination with ultraviolet light. We show that the spatially homogeneous steady-state becomes unstable, and a charge density wave emerges after a critical intensity of the incident radiation is achieved. It is shown that this instability can only follow in doped p-type materials. In bulk systems the critical intensity was found to be too high making the phenomenon not observable under realistic experimental conditions. However, a more efficient electron excitation can be obtained in low dimensional p-type systems, like some molecular and biological polymers, where the interaction may follow by chemical interaction with the medium. We show that for intensities beyond the critical threshold an increasing number of modes provide further contributions (subharmonics) to the space inhomogeneity. It is conjectured that this process could lead the system to display chaotic-like behavior.