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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 interplay between the strong intralayer covalent-ionic bonds and the weak interlayer van der Waals (vdW) forces between the neighboring layers of vdW crystals gives rise to unique physical and chemical properties. Here, the intralayer and interlayer bondings in α and β polytypes of In2Se3 are studied, a vdW material with potential applications in advanced electronic and optical devices. Picosecond ultrasonic experiments are conducted to probe the sound velocity in the direction perpendicular to the vdW layers. The measured sound velocities are different in α- and β-In2Se3, suggesting a significant difference in their elastic properties. Density functional theory and an effective spring model are used to calculate the elastic stiffness of the layer and vdW gap in α- and β-In2Se3. The calculated elastic moduli show good agreement with experimental values and reveal the dominant contribution of interlayer atomic bonding to the different elastic properties of the two polytypes. The findings show the power of picosecond ultrasonics for probing the fundamental elastic properties of vdW materials. The data and analysis also provide a reliable description of the intra- and interlayer forces in complex crystal structures, such as the polytype phases of In2Se3.

We investigate the effect of hypersonic (> 1 GHz) acoustic phonon wavepackets on electron transport in a semiconductor superlattice. Our quantum mechanical simulations demonstrate that a GHz train of picosecond deformation strain pulses propagating through a superlattice can generate current oscillations whose frequency is several times higher than that of the strain pulse train. The shape and polarity of the calculated current pulses agree well with experimentally measured electric signals. The calculations also explain and accurately reproduce the measured variation of the induced current pulse magnitude with the strain pulse amplitude and applied bias voltage. Our results open a route to developing acoustically-driven semiconductor superlattices as sources of millimetre and sub-millimetre electromagnetic waves., 5 pages, 4 figures, submitted to Phys Rev App

Diffusive memristors, which have been recently fabricated and measured, attract a significant interest being among 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 the contribution of deterministic and stochastic dynamics to the functional properties of a diffusive memristor is still an open problem. To study the deterministic mechanisms governing the dynamics of diffusive memristors, we analyze a model of a memristive circuit when the effects of the temperature noise are neglected. We reveal instabilities, which shape the current-voltage characteristic of the device and imply the onset of current self-oscillations. Finally, the results of modeling are compared with experimentally measured current-voltage characteristics.

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.

The spatially discrete-continuous dynamical systems, that are composed of a spatially extended medium coupled with a set of lumped elements, are frequently met in different fields, ranging from electronics to multicellular structures in living systems. Due to the natural heterogeneity of such systems, the calculation of Lyapunov exponents for them appears to be a challenging task, since the conventional techniques in this case often become unreliable and inaccurate. The paper suggests an effective approach to calculate Lyapunov exponents for discrete-continuous dynamical systems, which we test in stability analysis of two representative models from different fields. Namely, we consider a mathematical model of a 1D transferred electron device coupled with a lumped resonant circuit, and a phenomenological neuronal model of spreading depolarization, which involves 2D diffusive medium. We demonstrate that the method proposed is able reliably recognize regular, chaotic and hyperchaotic dynamics in the systems under study.

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.

© 2020 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH 2D materials have unique structural and electronic properties with potential for transformative device applications. However, such devices are usually bespoke structures made by sequential deposition of exfoliated 2D layers. There is a need for scalable manufacturing techniques capable of producing high-quality large-area devices comprising multiple 2D materials. Additive manufacturing with inks containing 2D material flakes is a promising solution. Inkjet-printed devices incorporating 2D materials have been demonstrated, however there is a need for greater understanding of quantum transport phenomena as well as their structural properties. Experimental and theoretical studies of inkjet-printed graphene structures are presented. Detailed electrical and structural characterization is reported and explained by comparison with transport modeling that include inter-flake quantum tunneling transport and percolation dynamics. The results reveal that the electrical properties are strongly influenced by the flakes packing fraction and by complex meandering electron trajectories, which traverse several printed layers. Controlling these trajectories is essential for printing high-quality devices that exploit the properties of 2D materials. Inkjet-printed graphene is used to make a field effect transistor and Ohmic contacts on an InSe phototransistor. This is the first time that inkjet-printed graphene has successfully replaced single layer graphene as a contact material for 2D metal chalcogenides.

The effect of the bandgap width between the first and second energy minibands on the charge transport in a semiconducting superlattice to which electric and tilted magnetic fields are applied is studied theoretically. The time dependences of the current passing through the superlattice are calculated, and the dependences of the amplitude and frequency of electric current oscillations on the applied voltage are constructed. It is found that the interminiband electron tunneling facilitates a decrease in the amplitude of current oscillations, but simultaneously increases their frequency.

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.

We study high-frequency generation in a system of electromagnetically coupled semiconductor superlattices fabricated on the same doped substrate. Applying a bias voltage to a single superlattice generates high-frequency current oscillations. We demonstrate that within a certain range of the applied voltage, the current oscillations within the superlattices can be self-synchronized, which leads to a dramatic rise in the generated microwave power. These results, which are in good agreement with our numerical model, open a promising practical route towards the design of high-power miniature microwave generators.

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.

A mathematical model for describing the collective dynamics of charge carriers in a semiconductor superlattice with ohmic emitter and collector contacts is proposed. The model is based on a hydrodynamic description of electron transport. The effect the emitter and collector characteristics have on the oscillation regimes observed in this system is analyzed using the proposed approach.

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 investigate excitation of microwave generation in a semiconductor superlattice under the effect of the applied constant voltage at near-zero temperature in the absence of the external magnetic field. It is shown that the generation is caused by the positive feedback arising from the total constant voltage drop across the superlattice.

We considered the nonstationar charge transport through the nanoscaled heterostructrure, consisting of the muniband semiconductor superlattices (SL), divided by the layers of heavy doped semiconductor. We demonstrate that compared with the regular SL, such design provides simultaneously the significant increase of both the output power and the frequency of the produced current oscillation.

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 examine the feasibility of amplification of the electromagnetic signal in semiconductor superlattice by moving charge domains, which are generated in superlattice by applied DC bias. We show that an external resonator connected to the semiconductor superlattice significantly broadens the frequency range of amplified signals to the higher harmonics of domain transient frequency. These promising results open the way to use semiconductor superlattices as the efficient sub-THz/THz amplifiers.

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 study the effect of a time-delayed feedback upon a Van der Pol oscillator under the influence of white noise in the regime below the Hopf bifurcation where the deterministic system has a stable fixed point. We show that both the coherence and the frequency of the noise-induced oscillations can be controlled by varying the delay time and the strength of the control force. Approximate analytical expressions for the power spectral density and the coherence properties of the stochastic delay differential equation are developed, and are in good agreement with our numerical simulations. Our analytical results elucidate how the correlation time of the controlled stochastic oscillations can be maximized as a function of delay and feedback strength.

We propose a method to control noise-induced motion, based on using delayed feedback in the form of the difference between the delayed and the current states of the system. The method is applied to two different types of systems, namely, a self-oscillator near Andronov–Hopf bifurcation and a threshold system. In both cases, we demonstrate that by variation of time delay one can effectively control coherence and timescales of stochastic oscillations. The entrainment of the basic period of oscillations by time delay is discovered. We give explanations of the phenomena observed and provide a theory for the system near bifurcation.

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.

Using techniques from dynamical systems analysis we explore numerically the solution space, under parametric variation, of a neutral differential delay equation that arises naturally in the Cosserat description of torsional waves on a driven drill-string.

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.

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.