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Progress in the creation of large scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are non-perturbative. Analysis of multiparticle quantum correlations in a large system in the presence of decoherence and external driving is especially topical. Still, scaling behaviour of dynamics and related emergent phenomena are not yet well understood. We investigate how the dynamics of a driven system of several quantum elements (e.g., qubits or Rydberg atoms) changes with increasing number of elements. Surprisingly, a two-element system exhibits chaotic behaviours. For larger system sizes a highly stochastic, far from equilibrium, {\em hyperchaotic} regime emerges. Its complexity systematically scales with the size of the system, proportionally to the number of elements. Finally, we demonstrate that these chaotic dynamics can be efficiently controlled by a periodic driving field. The insights provided by our results indicate the possibility of a reduced description for the behaviour of a large quantum system in terms of the transitions between its qualitatively different dynamical regimes, which are controlled by a relatively small number of parameters, and may prove useful in the design, characterization and control of large artificial quantum structures., 17 pages, 13 figures, 2 tables

The effect doping density perturbations have on the current characteristics in a semiconductor superlattice is studied. The current characteristics are shown to depend on the localization and form of the perturbation. The effect of perturbations is strongest near the superlattice emitter. The effect grows along with the density profile integral and depends weakly on the form of the profile.

Partially quantum coherent arrays of artificial atoms (e.g., superconducting qubits) may be used as analogue simulators of other quantum systems, when the behaviour of the latter cannot be directly observed or modeled by classical means. Here we show that a chain of superconducting qubits can simulate the chaotic behaviour predicted in chains of Rydberg atoms. We investigate the transition from periodic to chaotic dynamics and show the increase of the number of positive Lyapunov exponents as the number of atoms grows. The possibility of an external control and suppression of hyperchaos in the chain is demonstrated.

Recently fabricated and measured diffusive memristors have attracted a significant interest as one of the best candidates to mimic neuron activities and to implement novel computing paradigms. Such devices are capable of exhibiting a combination of dynamical chaotic, and stochastic phenomena needed for efficient neuromorphic computational systems. However, understanding of contribution and interplay of deterministic and stochastic dynamics to the functional properties of a diffusive memristor is still an open problem. Here, we propose a perturbative approach allowing to separate an influence of noise from regular motion of nanoparticles in diffusive memristors. We demonstrate that noise, coupled with a deterministic degree of freedom in artificial neurons based on diffusive memristors, originates a novel spiking mechanism absent in noiseless systems. The developed formalism suggests an approach towards deterministic modeling of stochastic artificial neurons.

A transition to self-sustained current oscillations was investigated in a circuit with a NbOx thin film device, acting as an artificial neuron. Above a threshold of the applied voltage, the circuit begins to demonstrate persistent but rather random current spiking, which becomes more regular with increasing applied voltage. Experimental measurements reveal two scaling regions of the interspike interval dependence on source voltage: an initial logarithmic dependence, which transitions to a power law with an exponent of -1/2. Using a numerical model of the artificial neuron circuit, we observe good agreement with our experimental data. We show that the logarithmic scaling behavior is associated with noise-induced spiking, while the power law is attributed to noisy self-sustained oscillations, which would exist in the system even with the absence of noise. These findings stress the importance of noise in the dynamics of NbOx threshold switches and shed light on their spiking response to variation of the input signals. The reported approach to spiking control in NbOx artificial oscillation neurons can help to develop an optimal design for neuromorphic neural networks and oscillator-based computing systems.

Inspired by rapid experimental development of diffusive memristors, we propose a computational model of a memristive artificial neuron that takes into consideration inertia of metallic nanoparticles within the dielectric layer of the core-memristor. This model displays rich nonlinear dynamics, which has been speculated to be key for successful emulation of living biological neurons by neuromorphic devices. We found out four characteristic dynamical regimes realized in the system depending on inertness of the nanoparticles. For low-inertia particles, the artificial neuron biased by an applied DC-voltage demonstrates either steady state or regular periodic oscillations. For higher inertia, metastable and intermittent chaos can appear in the system. We analyse the transitions between these regimes and draw parallels between our model and biological neurons.

A very simple model describing steady-state electron transport along a quantum superlattice of a finite length taking into account an arbitrary electrical characteristic of the injecting contact is considered. In the singleminiband approximation, exact formulas for the spatial distribution of the electric field in the superlattice are derived for different types of contact. Conditions under which the field is uniform are identified. Analytical expressions for the current–voltage characteristics are obtained. In the context of the developed theory, the possibility of attaining uniform-field conditions in a diode structure with a natural silicon-carbide superlattice is discussed.

The transition between different modes of current oscillations in a semiconductor superlattice, from close-to-harmonic (near the generation onset) to relaxation oscillations, has been investigated. The transition type is shown to change with an increase in temperature. A period-doubling bifurcation is observed at low temperatures. With an increase in temperature, the period-doubling bifurcation is observed at increasingly larger values of the voltage across the superlattice. The doubling bifurcation ceases to be observed at voltages at which the generation of oscillations of the current through the semiconductor superlattice is suppressed.

The paper studies instabilities of charge transport in strongly coupled semiconductor superlattices with an applied electric and a tilted magnetic field. We reveal the bifurcation phenomena, which are associated with the transitions between different regimes of charge dynamics, and also investigate effects of the temperature on these bifurcations. In addition, we find out that the development of an instability can be accompanied by a graduate change of the dominant transport mechanism.

Spectra of current oscillations caused by the transport of the electron domains induced by an applied voltage in a semiconductor superlattice with the absence and presence of the tilted magnetic field are numerically investigated with allowance for the interband tunneling.

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.

The transition to chaos in a semiconductor superlattice coupled to an external resonator is studied. It is shown that the transition to chaos proceeds through intermittency. It is found that the system exhibits broadband generation regimes, which is of direct interest for the practical use of nanostructures in data transmission systems.

The mechanisms of transitions between different regimes of current oscillations in a semiconductor superlattice in the presence of a tilted magnetic field at various temperatures have been studied. At relatively low temperatures, an increase in the applied voltage leads to a period-doubling bifurcation that causes a change in the dynamic regime. At increased temperatures, the transition takes place with the quenching of current oscillations.

The dynamics of a semiconductor superlattice in an external resonator is studied. It is shown that the external electrodynamic system considerably complicates the behavior of the superlattice by exciting random oscillations and leads to additional negative differential conductivity in the I–V characteristic that is not observed in an autonomous system.

The stability of the steady state of a semiconductor superlattice described using a semiclassical approach is analyzed. It is shown that generation arises due to the appearance of perturbations characterized by a positive increment of growth. The relationship between the frequency of the current oscillations and the frequency of the perturbation oscillation is determined.

We theoretically show that two semiconductor superlattices arranged on the same substrate and coupled with the same resistive load can be used for a generation of high-frequency periodic and quasiperiodic signals. Each superlattice involved is capable to generate current oscillations associated with drift of domains of high charge concentration. However, the coupling with the common load can eventually lead to synchronization of the current oscillations in the interacting superlattices. We reveal how synchronization depends on detuning between devices and the resistance of the common load, and discuss the effects of coupling and detuning on the high-frequency power output from the system.

We found the full analytical solution of the semiclassical model, described the stationary profile of the electric field in the miniband semiconductors, subjected to the DC voltage. The analysis of obtained solution shown the three different types of the field distribution, taken place in the semiconductor depending on the emitter current-field characteristics. Among the observed profiles we found the spatially-homogeneous solutions, existed in the condition of the negative differential conductivity (NDC), and represented themselves as the key condition for the THz Bloch oscillations. We applied our theory for the estimation of the current field-condition in the natural SiC superlattice, demonstrated the terahertz electroluminescence and confirmed its Bloch mechanism.

The space-time dynamics of electron domains in a semiconductor superlattice is studied in a tilted magnetic field with regard to the effect of temperature. It is shown that an increase in temperature substantially changes the space-time dynamics of the system. This leads to a decrease in the frequency and amplitude of oscillations of a current flowing through the semiconductor superlattice. The quenching of oscillations is observed, which is attributed to the change in the drift velocity as a function of electric-field strength under the variation of temperature.

We report on the transmission of electrical pulses through a semiconductor structure which emulates biological neurons. The ‘neuron’ emits bursts of electrical spikes whose coherence we study as a function of the amplitude and frequency of a sine wave stimulus and noise. Noise is found to enhance the transmission of pulses below the firing threshold of the neuron. We demonstrate stochastic resonance when the power of the output signal passes through a maximum at an optimum noise value. Under appropriate conditions, we observe coherence resonance and stochastic synchronization. Data are quantitatively explained by modelling the FitzHugh–Nagumo equations derived from the electrical equivalent circuit of the soma. We have therefore demonstrated a physically realistic neuron structure that provides first principles feedback on mathematical models and that is well suited to building arborescent networks of pulsing neurons.

We show that the reflection of quantum-mechanical waves from semiconductor surfaces creates new regimes of nonlinear dynamics, which offer sensitive control of electrons and ultra-cold atoms. For electrons in superlattices, comprising alternating layers of different semiconductor materials, multiple reflections of electron waves from the layer interfaces induce a unique type of chaotic electron motion when a bias voltage and tilted magnetic field are applied. Changing the field parameters switches the chaos on and off abruptly, thus producing a sharp increase in the measured current flow by creating unbounded electron orbits. These orbits correspond to either intricate web patterns or attractors in phase space depending on the electron decoherence rate. We show that related dynamics provide a mechanism for controlling the transmission of electromagnetic waves through spatially-modulated photonic crystals. Finally, we consider the quantum dynamics of a Bose-Einstein condensate, comprising 120,000 rubidium atoms cooled to 10 nK, incident on a stadium billiard etched in a room-temperature silicon surface. Despite the huge temperature difference between the condensate and the billiard, quantum-mechanical reflection can shield the cold atoms from the disruptive influence of the surface, thus enabling the billiard to imprint signatures of single-particle classical trajectories in the collective motion of the reflected atom cloud.

We investigate the onset of broadband microwave chaos in the miniband semiconductor superlattice coupled to an external resonator. Our analysis shows that the transition to chaos, which is confirmed by calculation of Lyapunov exponents, is associated with the intermittency scenario. The evolution of the laminar phases and the corresponding Poincare maps with variation of a supercriticality parameter suggest that the observed dynamics can be classified as type I intermittency. We study the spatiotemporal patterns of the charge concentration and discuss how the frequency band of the chaotic current oscillations in semiconductor superlattice depends on the voltage applied.

We consider noise-induced charge density dynamics in a semiconductor superlattice. The parameters are fixed in the regime below the Hopf bifurcation that gives birth to spatio-temporal oscillations, where in the absence of noise of the system rests at a fixed point. It is shown that in this case noise can induce in the superlattice quite coherent oscillations of the current through the device. While the regularity of these oscillations depends on the noise intensity, their dominant frequency remains almost constant with variation of the noise level in the system. Further, we demonstrate that a time-delayed feedback scheme that was previously used to control purely temporal oscillations induced by noise, can not only enhance or deteriorate the regularity of stochastic spatio-temporal patterns but also allow for the manipulation of the system's time scales with varying time delay.

We investigate the way in which noise destroys phase synchronization in chaotic systems. Two cases are considered: where the route to synchronization involves frequency locking; and where it occurs via a suppression of the natural dynamics. We show that, just as in the case of synchronization of periodic oscillations, noise induces a new motion whose coherence depends non-monotonically (resonantly) on the noise intensity.

The impedance and absorption of a semiconductor superlattice under an external harmonic perturbation are investigated. It is shown that a weak external periodic signal synchronizes the domain motion in a semiconductor superlattice, and this process is accompanied by an increase in absorption and a reduction in the amplitude of the superlattice impedance. The characteristic dependence of the active and reactive impedance components on the frequency and amplitude of the external harmonic perturbation is presented.

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.

A new method, employing one-dimensional time series, is proposed for diagnostics of the presence or absence of phase synchronization between several interacting self-sustained oscillators. The procedure is based on introducing a polar coordinate system into the residence time mapping and studying the angle dynamics in this system. The method is verified by application to realizations reflecting the dynamics of two and three interacting processes in the presence of noise.

We study the mechanism of synchronization for a periodic Van der Pol oscillator driven by a strong chaotic forcing from a Rossler system. It is demonstrated how the system with increasing coupling strength adjusts its motion in accordance with the external forcing via the suppression of its natural dynamics by the chaotic signal. This transition is traced both in the power spectrum and in the spectrum of Lyapunov exponents. We identify the underlying mechanism as a set of inverse Hopf bifurcations of saddle orbits embedded in the synchronized chaotic set.

We show that a phonon wave propagating through a semiconductor superlattice can induce a charge current even when no static electric field is applied. When the energy amplitude of the phonon wave is less than the width of the lowest superlattice miniband, we find strong resonant enhancement of electron transport, accompanied by very high frequency oscillations of the electron orbits. In this regime, the phonon wave drags the electrons through the superlattice, causing them to undergo quasi-periodic trajectories with a single dominant temporal frequency several orders of magnitude higher than that of the phonon deformation wave itself. This transformation of GHz frequency wave motion into highly coherent THz frequency electron dynamics provides a mechanism for frequency up-conversion, with a multiplication factor of ~20 in our present samples. For phonon wave amplitudes higher than the miniband width, the electrons perform Bloch-like oscillations, which dramatically suppresses transport.

Department of Physics, The Technical University of Denmark, 2800 Lyngby, Denmark~Received 21 October 1998!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 studytransitions 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 Ro¨sslersystems. With a small frequency mismatch between the two systems, these processes are related to theoccurrence of a peculiar form of basin structure as more and more periodic orbits embedded into the synchro-nized chaotic state become unstable in a transverse direction. @S1063-651X~99!03711-3#PACS number~s!: 05.45.2aI. INTRODUCTION

We investigate generic aspects of chaos synchronization in an externally forced Rossler system. By comparing different diagnostic methods, we show the existence of a well-defined cut-off of synchronization associated with the transition from weak to fully developed chaos. Chaotic synchronization is found to be lost at this cut-off only after the last band-merging bifurcation has occurred. Everywhere at the boundary of phase synchronization, one of the Lyapunov exponents becomes equal to zero. Two types of chaotic behavior, differing by the number of vanishing Lyapunov exponents, are observed outside the synchronization region.

We discuss a numerical method for the calculation of the spectrum of Lyapunov exponents for spatially extended systems described by coupled Poisson and continuity equations. This approach was applied to the model of collective charge transport in semiconductor superlattices operating in the miniband transport regime. The method is in very good agreement with analytical results obtained for the steady state. As an illustrative example, we consider the collective electron dynamics in the superlattice subjected to an ac voltage and a tilted magnetic field, and conclusively show that, depending on the field parameters, the dynamics can exhibit periodic, quasiperiodic, or chaotic behavior.

We study theoretically how the dynamics of the resistive state in narrow superconducting channels shunted by an external resistor depends on channel's length $L$, the applied current $j$, and parameter $u$ characterizing the penetration depth of the electric field in nonequilibrium superconductors. We show that changing $u$ dramatically affects both the behavior of the current-voltage characteristics of the superconducting channels and the dynamics of their order parameter. Previously, it was demonstrated that when $u$ is less than the critical value ${u}_{c1}$, which does not depend on $L$, the phase slip centers appear simultaneously at different spots of the channel. Herewith, for $ug{u}_{c1}$ these centers arise consecutively at the same place. In our work we demonstrate that there is another critical value for $u$. Actually, if $u$ does not exceed a certain value ${u}_{c2}$, which depends on $L$, the current-voltage characteristic exhibits the step-like behavior. However, for $ug{u}_{c2}$ it becomes hysteretic. In this case, with increase of $j$ the steady state, which corresponds to the time-independent distribution of the order parameter along the channel, losses its stability at switching current value ${j}_{sw}$, and time-periodic oscillations of both the order parameter and electric field occur in the channel. As $j$ sweeps down, the periodic dynamics ceases at certain retrapping current value ${j}_{r}l{j}_{sw}$. Shunting the channel by a resistor increases the value of ${j}_{r}$, while ${j}_{sw}$ remains unchanged. Thus, for some high-enough conductivity of the shunt, ${j}_{r}$ and ${j}_{sw}$ eventually coincide, and the hysteretic loop disappears. We reveal dynamical regimes involved in the hysteresis and discuss the bifurcation transitions between them.

We show theoretically that the dynamics of cold atoms in the lowest-energy band of a stationary optical lattice can be transformed and controlled by a second, weaker, periodic potential moving at a constant speed along the axis of the stationary lattice. The atom trajectories exhibit complex behavior, which depends sensitively on the amplitude and speed of the propagating lattice. When the speed and amplitude of the moving potential are low, the atoms are dragged through the static lattice and perform drifting orbits with frequencies an order of magnitude higher than that corresponding to the moving potential. Increasing either the speed or amplitude of the moving lattice induces Bloch-like oscillations within the energy band of the static lattice, which exhibit complex resonances at critical values of the system parameters. In some cases, a very small change in these parameters can reverse the atom's direction of motion. In order to understand these dynamics we present an analytical model, which describes the key features of the atom transport and also accurately predicts the positions of the resonant features in the atom's phase space. The abrupt controllable transitions between dynamical regimes, as well as the associated set of resonances, provide a mechanism for transporting atoms between precise locations in a lattice, as required for using cold atoms to simulate condensed matter or as a stepping stone to quantum information processing. The system also provides a direct quantum simulator of acoustic waves propagating through semiconductor nanostructures in sound analogs of the optical laser (saser).

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., 5 pages, 4 figures

The current-voltage characteristics of long and narrow superconducting channels are investigated using the time-dependent Ginzburg-Landau equations for complex order parameter. We found out that the steps in the current voltage characteristic can be associated with bifurcations of either steady or oscillatory solution. We revealed typical instabilities which induced the singularities in current-voltage characteristics, and analytically estimated period of oscillations and average voltage in the vicinity of the critical currents. Our results show that these bifurcations can substantially complicate dynamics of the order parameter and eventually lead to appearance of such phenomena as multistability and chaos. The discussed bifurcation phenomena sheds a light on some recent experimental findings.

We have investigated the properties of the resistive state of the narrow superconducting channel of the length L/\xi=10.88 on the basis of the time-dependent Ginzburg-Landau model. We have demonstrated that the bifurcation points of the time-dependent Ginzburg-Landau equations cause a number of singularities of the current-voltage characteristic of the channel. We have analytically estimated the averaged voltage and the period of the oscillating solution for the relatively small currents. We have also found the range of currents where the system possesses the chaotic behavior.

We show that resonant electron transport in semiconductor superlattices with an applied electric and tilted magnetic field can, surprisingly, become more pronounced as the lattice and conduction electron temperature increases from 4.2 K to room temperature and beyond. It has previously been demonstrated that at certain critical field parameters, the semiclassical trajectories of electrons in the lowest miniband of the superlattice change abruptly from fully localised to completely unbounded. The unbounded electron orbits propagate through intricate web patterns, known as stochastic webs, in phase space, which act as conduction channels for the electrons and produce a series of resonant peaks in the electron drift velocity versus electric field curves. Here, we show that increasing the lattice temperature strengthens these resonant peaks due to a subtle interplay between thermal population of the conduction channels and transport along them. This enhances both the electron drift velocity and the influence of the stochastic webs on the current-voltage characteristics, which we calculate by making self-consistent solutions of the coupled electron transport and Poisson equations throughout the superlattice. These solutions reveal that increasing the temperature also transforms the collective electron dynamics by changing both the threshold voltage required for the onset of self-sustained current oscillations, produced by propagating charge domains, and the oscillation frequency., Comment: 8 figures, 12 pages

We show that GHz acoustic waves in semiconductor superlattices can induce THz electron dynamics that depend critically on the wave amplitude. Below a threshold amplitude, the acoustic wave drags electrons through the superlattice with a peak drift velocity overshooting that produced by a static electric field. In this regime, single electrons perform drifting orbits with THz frequency components. When the wave amplitude exceeds the critical threshold, an abrupt onset of Bloch-like oscillations causes negative differential velocity. The acoustic wave also affects the collective behavior of the electrons by causing the formation of localised electron accumulation and depletion regions, which propagate through the superlattice, thereby producing self-sustained current oscillations even for very small wave amplitudes. We show that the underlying single-electron dynamics, in particular the transition between the acoustic wave dragging and Bloch oscillation regimes, strongly influence the spatial distribution of the electrons and the form of the current oscillations. In particular, the amplitude of the current oscillations depends non-monotonically on the strength of the acoustic wave, reflecting the variation of the single-electron drift velocity., Comment: 10 pages, 8 figures

Using a combination of modeling and tunneling spectroscopy, we investigate how electrostatic potential fluctuations generated by randomly distributed ionized donors close to a quantum well can produce deep and strongly confined quantum-dot-like potential minima with a rich spectrum of zero-dimensional electronic energy levels. We consider different types of random distribution of donors and how the electronic properties can be controlled and investigated in appropriately designed double barrier resonant tunneling diodes.

We show that electrons in a semiconductor superlattice can be used to realize and exploit the unique dynamics of the driven harmonic oscillator that were discovered and explored by George Zaslavsky and colleagues. Under the action of an electric and tilted magnetic field, the semiclassical dynamics of electrons in an energy band of the superlattice exhibit non-KAM chaos, which strongly affects the electrical conductivity. At certain critical field parameters, the electron trajectories change abruptly from fully localized to completely unbounded, and map out intricate stochastic webs in phase space, which act as conduction channels for the electrons. Delocalization of the electron paths produces a series of strong resonant peaks in the electron drift velocity versus electric field curves. We use these drift velocity characteristics to make self-consistent drift-diffusion calculations of the current-voltage and differential conductance-voltage curves of the superlattices, which agree well with our experimental data and reveal strong resonant features originating from the sudden delocalization of the stochastic single-electron paths. We show that this delocalization has a pronounced effect on the distribution of space charge and electric field domains within the superlattices. Inter-miniband tunneling greatly reduces the amount of space-charge buildup, thus enhancing the domain structure and both the strength and number of the current resonances.

We report on the stochastic dynamics of a semiconductor neuron that uses the non‐linear conductances of modulation doped semiconductors to compute electrical spikes. This GaAs‐based neuron has pn wires which propagate and delay electrical pulses and a soma which sums and regenerates pulses through the positive feedback of a quantum tunnel amplifier vertically integrated with the wire. The neuron exhibits the property of excitability: it responds with a spike to a perturbation that exceeds a certain threshold value, and remains silent if the perturbation is small. When exciting the neuron with a sub‐threshold periodic signal, a superimposed random noise is shown to enhance the coherence of the output pulse train. We perform a systematic study of stochastic resonance and coherence resonance as a function of excitation parameters and analyze output spectra using statistical tools.

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.

We show that a tilted magnetic field transforms the structure and THz dynamics of charge domains in a biased semiconductor superlattice. At critical field values, strong coupling between the Bloch and cyclotron motion of a miniband electron triggers chaotic delocalization of the electron orbits, causing strong resonant enhancement of their drift velocity. This dramatically affects the collective electron behavior by inducing multiple propagating charge domains and GHz-THz current oscillations with frequencies ten times higher than with no tilted field., Comment: 5 pages, 5 figures

Earlier we discussed synchronization phenomena in periodically forced periodic oscillators, when the forcing frequency was close to the natural frequency of unforced oscillations. A natural question arises: “What happens if we are perturbing the system with a frequency which is substantially different from its natural frequency? Are there any synchronization phenomena in that case?” The answer is “yes,” and below we will illustrate this.

Generally anisochronicity means that the phase velocity on a limit cycle depends on the instantaneous values of the amplitude. In other words, a phase trajectory slows down in some parts of the limit cycle and accelerates in others. It is clear that the response of such an oscillator to perturbations should depend on the current position of the phase point on the limit cycle. In this chapter we discuss non-linear effects that appear due to anisochronicity of individual oscillatory units and introduce some useful methods for their analysis.

In this chapter we study the simplest case of synchronization: synchronization of unidirectionally coupled periodic oscillators. Another name for this phenomenon is forced synchronization, which reflects the fact that one system influences the other, but does not experience any influence from the other system in return.