Non-KAM classical chaos topology for electrons in superlattice minibands determines the inter-well quantum transition rates

We investigate the quantum-classical correspondence for a particle tunnelling through a periodic superlattice structure with an applied bias voltage and an additional tilted harmonic oscillator potential. We show that the quantum mechanical tunnelling rate between neighbouring quantum wells of the superlattice is determined by the topology of the phase trajectories of the analogous classical system. This result also enables us to estimate, with high accuracy, the tunnelling rate between two spatially displaced simple harmonic oscillator states using a classical model, and thus gain new insight into this generic quantum phenomenon. This finding opens new directions for exploring and understanding the quantum-classical correspondence principle and quantum jumps between displaced harmonic oscillators, which are important in many branches of natural science.

Gamma radiation-induced nanodefects in diffusive memristors and artificial neurons

Gamma photons with an average energy of 1.25 MeV are well-known to generate large amounts of defects in semiconductor electronic devices. Here we investigate the novel effect of gamma radiation on diffusive memristors based on metallic silver nanoparticles dispersed in a dielectric matrix of silica. Our experimental findings show that after exposure to radiation, the memristors and artificial neurons made of them demonstrate much better performance in terms of stable volatile resistive switching and higher spiking frequencies, respectively, compared to the pristine samples. At the same time we observe partial oxidation of silver and reduction of silicon within the switching silica layer. We propose nanoinclusions of reduced silicon distributed across the silica layer to be the backbone for metallic nanoparticles to form conductive filaments, as supported by our theoretical simulations of radiation-induced changes in the diffusion process. Our findings propose a new opportunity to engineer the required characteristics of diffusive memristors in order to emulate biological neurons and develop bio-inspired computational technology.

Deterministic modeling of the diffusive memristor

Recently developed diffusive memristors have gathered a large amount of research attention due to their unique property to exhibit a variety of spiking regimes reminiscent to that found in biological cells, which creates a great potential for their application in neuromorphic systems of artificial intelligence and unconventional computing. These devices are known to produce a huge range of interesting phenomena through the interplay of regular, chaotic, and stochastic behavior. However, the character of these interplays as well as the instabilities responsible for different dynamical regimes are still poorly studied because of the difficulties in analyzing the complex stochastic dynamics of the memristive devices. In this paper, we introduce a new deterministic model justified from the Fokker-Planck description to capture the noise-driven dynamics that noise has been known to produce in the diffusive memristor. This allows us to apply bifurcation theory to reveal the instabilities and the description of the transition between the dynamical regimes.

Nonlinear dynamics and band transport in a superlattice driven by a plane wave

A quantum particle transport induced in a spatially periodic potential by a propagating plane wave has a number of important implications in a range of topical physical systems. Examples include acoustically driven semiconductor superlattices and cold atoms in an optical crystal. Here we apply a kinetic description of the directed transport in a superlattice beyond standard linear approximation, and utilize exact path-integral solutions of the semiclassical transport equation. We show that the particle drift and average velocities have nonmonotonic dependence on the wave amplitude with several prominent extrema. Such nontrivial kinetic behavior is related to global bifurcations developing with an increase of the wave amplitude. They cause dramatic transformations of the system phase space and lead to changes of the transport regime. We describe different types of phase trajectories contributing to the directed transport and analyze their spectral content.

Subterahertz chaos generation by coupling a superlattice to a linear resonator

We investigate the effects of a linear resonator on the high-frequency dynamics of electrons in devices exhibiting negative differential conductance. We show that the resonator strongly affects both the dc and ac transport characteristics of the device, inducing quasiperiodic and high-frequency chaotic current oscillations. The theoretical findings are confirmed by experimental measurements of a GaAs/AlAs miniband semiconductor superlattice coupled to a linear microstrip resonator. Our results are applicable to other active solid state devices and provide a generic approach for developing modern chaos-based high-frequency technologies including broadband chaotic wireless communication and superfast random-number generation.

Controlling high-frequency collective electron dynamics via single-particle complexity

We demonstrate, through experiment and theory, enhanced high-frequency current oscillations due to magnetically-induced conduction resonances in superlattices. Strong increase in the ac power originates from complex single-electron dynamics, characterized by abrupt resonant transitions between unbound and localized trajectories, which trigger and shape propagating charge domains. Our data demonstrate that external fields can tune the collective behavior of quantum particles by imprinting configurable patterns in the single-particle classical phase space.

Noise-controlled signal transmission in a multithread semiconductor neuron

We report on stochastic effects in a new class of semiconductor structures that accurately imitate the electrical activity of biological neurons. In these devices, electrons and holes play the role of K+ and Na+ ions that give the action potentials in real neurons. The structure propagates and delays electrical pulses via a web of spatially distributed transmission lines. We study the transmission of a periodic signal through a noisy semiconductor neuron. Using experimental data and a theoretical model we demonstrate that depending on the noise level and the amplitude of the useful signal, transmission is enhanced by a variety of nonlinear phenomena, such as stochastic resonance, coherence resonance, and stochastic synchronization.

Fock-Darwin-like quantum dot states formed by charged Mn interstitial ions

We report a method of creating electrostatically induced quantum dots by thermal diffusion of interstitial Mn ions out of a p-type (GaMn)As layer into the vicinity of a GaAs quantum well. This approach creates deep, approximately circular, and strongly confined dotlike potential minima in a large (200 microm) mesa diode structure without need for advanced lithography or electrostatic gating. Magnetotunneling spectroscopy of an individual dot reveals the symmetry of its electronic eigenfunctions and a rich energy level spectrum of Fock-Darwin-like states with an orbital angular momentum component |lz| from 0 to 11.

Bifurcations and chaos in semiconductor superlattices with a tilted magnetic field

We study the effects of dissipation on electron transport in a semiconductor superlattice with an applied bias voltage and a magnetic field that is tilted relative to the superlattice axis. In previous work, we showed that, although the applied fields are stationary, they act like a terahertz plane wave, which strongly couples the Bloch and cyclotron motion of electrons within the lowest miniband. As a consequence, the electrons exhibit a unique type of Hamiltonian chaos, which creates an intricate mesh of conduction channels (a stochastic web) in phase space, leading to a large resonant increase in the current flow at critical values of the applied voltage. This phase-space patterning provides a sensitive mechanism for controlling electrical resistance. In this paper, we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term. We demonstrate that, even in the presence of dissipation, deterministic chaos plays an important role in the electron transport process. We identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories. When the Bloch and cyclotron frequencies are commensurate, complex multistability phenomena occur in the system. In particular, for fixed values of the control parameters several distinct stable regimes can coexist, each corresponding to different initial conditions. We show that this multistability has clear, experimentally observable, signatures in the electron transport characteristics.

Long-term correlations in stochastic systems with extended time-delayed feedback

The effects of a feedback with multiple time delays on noise-induced dynamics are studied in a nonlinear system close to the Hopf instability. We show analytically and numerically that such a feedback creates two distinct time scales, which can be tuned independently by the feedback parameters. In this way, the coherence of noise-induced oscillations can be drastically improved, and an arbitrarily large correlation of oscillations can be achieved without inducing a bifurcation. This opens up new perspectives for control of stochastic dynamical systems.

Delayed feedback control of noise-induced patterns in excitable media

We show that characteristic features of noise-induced spatiotemporal patterns in excitable media can be effectively controlled by applying delayed feedback. Actually, by variation of the time delay and of the strength of the feedback one can deliberately change both spatial and temporal coherence, as well as adjust the characteristic time scales.

Delayed feedback control of stochastic spatiotemporal dynamics in a resonant tunneling diode

The influence of time-delayed feedback upon the spatiotemporal current density patterns is investigated in a model of a semiconductor nanostructure, namely a double-barrier resonant tunneling diode. The parameters are chosen below the Hopf bifurcation, where the only stable state of the system is a spatially inhomogeneous "filamentary" steady state. The addition of weak Gaussian white noise to the system gives rise to spatially inhomogeneous self-sustained temporal oscillations that can be quite coherent. We show that applying a time-delayed feedback can either increase or decrease the regularity of the noise-induced dynamics in this spatially extended system. Using linear stability analysis, we can explain these effects, depending on the length of the delay interval. Furthermore, we study the influence of this additional control term upon the deterministic behavior of the system, which can change significantly depending on the choice of parameters.

Role of saddle tori in the mutual synchronization of periodic oscillations

We show that in the mutual synchronization of periodic oscillators, besides an attracting torus, there is also a saddle torus that plays an equally important role. We demonstrate that the saddle and stable tori form an elegant structure, allowing for a variety of phenomena, both known and new, related to the origin and evolution of coexisting synchronous regimes (phase multistability).

Noise-induced pattern formation in a semiconductor nanostructure

We investigate the influence of noise upon the dynamics of the current density distribution in a model of a semiconductor nanostructure, namely, a double barrier resonant tunneling diode. We fix the parameters of the device below the Hopf bifurcation, where the only stable state of the system is a spatially inhomogeneous "filamentary" steady state. We show that the addition of weak Gaussian white noise to the system gives rise to spatially inhomogeneous oscillations that can be quite coherent. As the noise intensity grows, the oscillations tend to become more and more spatially homogeneous, while simultaneously the temporal correlation of the oscillations decreases. Thus, while on one hand noise destroys temporal coherence, on the other hand it enhances the spatial coherence of the current density pattern.

Delayed feedback control of chaos: bifurcation analysis

We study the effect of time delayed feedback control in the form proposed by Pyragas on deterministic chaos in the Rössler system. We reveal the general bifurcation diagram in the parameter plane of time delay tau and feedback strength K which allows one to explain the phenomena that have been discovered in some previous works. We show that the bifurcation diagram has essentially a multileaf structure that constitutes multistability: the larger the tau, the larger the number of attractors that can coexist in the phase space. Feedback induces a large variety of regimes nonexistent in the original system, among them tori and chaotic attractors born from them. Finally, we estimate how the parameters of delayed feedback influence the periods of limit cycles in the system.

Delayed feedback as a means of control of noise-induced motion

Time-delayed feedback is exploited for controlling noise-induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the time scales of noise-induced motion by changing the time delay.

Regions of cardiorespiratory synchronization in humans under paced respiration

Cardiorespiratory synchronization under paced respiration is studied systematically as the respiration frequency is changed between 3 and 30 breaths per min. We plot a one-dimensional cut of the classical picture of synchronization regions along the line defining the current breathing amplitude. The existence of n:m synchronization regions of finite width is demonstrated for each of six subjects studied. The statistics of the different types of synchronization and their stability are discussed.

Coherence resonance versus synchronization in a periodically forced self-sustained system

A fundamental relationship between coherence resonance (CR) and phase synchronization in a self-sustained system in the presence of noise is addressed. A Van der Pol system synchronized by external forcing is taken as an example. It is shown that, in breaking down synchronization, applied noise creates a new ordered motion whose coherence depends resonantly on its intensity, i.e., CR occurs. The same is true for both types of synchronization, via phase locking and via suppression: only the mechanisms of CR differ. The result is valid for any order n:m of synchronization.

Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory

A general approach is developed for the detection of phase relationships between two or more different oscillatory processes interacting within a single system, using one-dimensional time series only. It is based on the introduction of angles and radii of return times maps, and on studying the dynamics of the angles. An explicit unique relationship is derived between angles and the conventional phase difference introduced earlier for bivariate data. It is valid under conditions of weak forcing. This correspondence is confirmed numerically for a nonstationary process in a forced Van der Pol system. A model describing the angles' behavior for a dynamical system under weak quasiperiodic forcing with an arbitrary number of independent frequencies is derived.

Phase relationships between two or more interacting processes from one-dimensional time series. II. Application to heart-rate-variability data

The recently proposed approach to detect synchronization from univariate data is applied to heart-rate-variability (HRV) data from ten healthy humans. The approach involves introducing angles for return times map and studying their behavior. For filtered human HRV data, it is demonstrated that: (i) in many of the subjects studied, interactions between different processes within the cardiovascular system can be considered as weak, and the angles can be well described by the derived model; (ii) in some of the subjects the strengths of the interactions between the processes are sufficiently large that the angles map has a distinctive structure, which is not captured by our model; (iii) synchronization between the processes involved can often be detected; (iv) the instantaneous radii are rather disordered.

Modelling the dynamics of angles of human R-R intervals

Heart rate variability (HRV) data from young healthy humans is expanded into two components, namely, the angles and radii of a map of R-R intervals. It is shown that. for most subjects at rest breathing spontaneously, the map of successive angles reveals a highly deterministic structure after the frequency range below approximately 0.05 Hz has been filtered out. However, no obvious low-dimensional structure is found in the map of successive radii. A recently proposed model describing the map of angles for a periodic self-oscillator under external periodic and quasiperiodic forcing is successfully applied to model the dynamics of such angles.

Phase synchronization between several interacting processes from univariate data

A novel approach is suggested for detecting the presence or absence of synchronization between two or three interacting processes with different time scales in univariate data. It is based on an angle-of-return-time map. A model is derived to describe analytically the behavior of angles for a periodic oscillator under weak periodic and quasiperiodic forcing. An explicit connection is demonstrated between the return angle and the phase of the external periodic forcing. The technique is tested on simulated nonstationary data and applied to human heart rate variability data.

Desynchronization in coupled systems with quasiperiodic driving

We describe the development of coexisting attractors in coupled quasiperiodically forced maps. The process of loss of complete synchronization in the systems, which individually demonstrates strange nonchaotic behavior, is studied. With this process, the complex structure of the basin of attraction is observed.

Loss of lag synchronization in coupled chaotic systems

Lag synchronization denotes a particular form of synchronization in which the amplitudes of two interacting, nonidentical chaotic oscillators are correlated but there is a characteristic time delay between them. We study transitions to and between different forms of synchronization for the attractors defined as "in-phase" and "out-of-phase" and investigate the processes by which lag synchronization is lost in two coupled Rössler systems. With a small frequency mismatch between the two systems, these processes are related to the occurrence of a peculiar form of basin structure as more and more periodic orbits embedded into the synchronized chaotic state become unstable in a transverse direction.

Role of multistability in the transition to chaotic phase synchronization

In this paper we describe the transition to phase synchronization for systems of coupled nonlinear oscillators that individually follow the Feigenbaum route to chaos. A nested structure of phase synchronized regions of different attractor families is observed. With this structure, the transition to nonsynchronous behavior is determined by the loss of stability for the most stable synchronous mode. It is shown that the appearance of hyperchaos and the transition from lag synchronization to phase synchronization are related to the merging of chaotic attractors from different families. Numerical examples using Rossler systems and model maps are given. (c) 1999 American Institute of Physics.