Bloch oscillations and Wannier-Stark ladder in the coupled LC circuits

We present a new scheme for realizing Bloch oscillations and Wannier-Stark ladder based on a lattice of coupled LC circuits. By converting the second order dynamical ODEs of the system into a first order Schrödinger-like equation, we propose an equivalent tight binding Hamiltonian to describe the circuit. We show that a synthesized electric field is produced by introducing a frequency mismatch into the resonant frequency of the adjacent LC resonators. The Wannier-Stark modes are the normal modes of the circuit and the Bloch oscillations can be observed in a coupled LC lattice. By addition of coupling capacitors between nodes of the circuit, we study the Bloch oscillation in the presence of long-range couplings. We also show that the circuit converts to a transmission line simulating synthetic electric fields in the continuum limit. The coupled LC circuit is, in some sense, amongst the simplest physical systems exhibiting Bloch oscillation and Wannier-Stark Ladder.     

Oscillation death in coupled oscillators

We study dynamical behaviors in coupled nonlinear oscillators and find that under certain conditions, a whole coupled oscillator system can cease oscillation and transfer to a globally nonuniform stationary state [i.e., the so-called oscillation death (OD) state], and this phenomenon can be generally observed. This OD state depends on coupling strengths and is clearly different from previously studied amplitude death (AD) state, which refers to the phenomenon where the whole system is trapped into homogeneously steady state of a fixed point, which already exists but is unstable in the absence of coupling. For larger systems, very rich pattern structures of global death states are observed. These Turing-like patterns may share some essential features with the classical Turing pattern.      

Quantum Transport through a Rigidly Connected Double Quantum-Dot Shuttle

We design a double quantum-dot （QD） shuttle （DQDS） model including two rigidly connected QDs that are softly linked to two leads via deformable organic materiaJs. Based on the full quantum mechanical approaches we explore the influences on the electron transport induced by the electrical and mechanical degrees of freedom. First of a/l the modified rate equations of the DQDS are derived theoretically and then a numerical investigation on the quantum transport through the DQDS is performed. For the classical DQDS, the time-dependent evolutions of the electron- occupation probabilities and the currents flowing through the DQDS show the periodic oscillations with their periods determined by the oscillation period of the DQDS. Both the mechanical oscillation amplitude and the interdot coupling can play crucial roles in adjusting the peak shapes of the currents and the probabilities. For the quantum DQDS, the current and electron-occupation probabilities of the DQDS evolve into a stationary state as time goes on, with no periodical oscillations observed. As a consequence, the sharp differences of the time-dependent properties between the c/assica/ and quantum DQDS systems are clearly demonstrated, which should be greatly helpful in designing new nanoelectromechanical devices. Also, this work is of great significance to understanding the kind of rigidly connected QD shuttle systems that have more than two QDs.     

Short- and long period oscillations in the exchange coupling of Fe across epitaxially grown Al- and Au-interlayers

We have investigated the exchange coupling of Fe films across Al- and Au-interlayers with good epitaxial growth. For the first time coupling across Al was found to be antiferromagnetic (a.f.). In addition to the long period oscillations of the coupling now well known from many other systems there are short period oscillations which are clearly visible for Au and faintly visible also for Al. This observation can be correlated with the much better growth of Au interlayers. In both cases we find also a strong contribution of biquadratic coupling, previously identified for the Fe/Cr system. The results strongly support an RKKY-type mechanism as the microscopic origin of these couplings.     

Resurgence of oscillation in coupled oscillators under delayed cyclic interaction

This paper investigates the emergence of amplitude death and revival of oscillations from the suppression states in a system of coupled dynamical units interacting through delayed cyclic mode. In order to resurrect the oscillation from amplitude death state, we introduce asymmetry and feedback parameter in the cyclic coupling forms as a result of which the death region shrinks due to higher asymmetry and lower feedback parameter values for coupled oscillatory systems. Some analytical conditions are derived for amplitude death and revival of oscillations in two coupled limit cycle oscillators and corresponding numerical simulations confirm the obtained theoretical results. We also report that the death state and revival of oscillations from quenched state are possible in the network of identical coupled oscillators. The proposed mechanism has also been examined using chaotic Lorenz oscillator.     

Ordering in nematic liquid crystals from NMR cross-polarization studies

The measurement of dipolar couplings between nuclei is a convenient way of obtatining directly liquid crystalline ordering through NMR since the coupling is dependent on the average orientation of the dipolar vector in the magnetic field which also aligns the liquid crystal. However, measurement of the dipolar coupling between a pair of selected nuclei is beset with problems that require special solutions. In this article the use of cross polarization for measuring dipolar couplings in liquid crystals is illustrated. Transient oscillations observed during cross polarization provide the dipolar couplings between essentially isolated nearest neighbour spins which can be extracted for several sites simultaneously by employing two-dimensional NMR techniques. The use of the method for obtaining heteronuclear dipolar couplings and hence the order parameters of liquid crystals is presented. Several modifications to the basic experiment are considered and their utility illustrated. A method for obtaining proton-proton dipolar couplings, by utilizing cross polarization from the dipolar reservoir, is also presented.     

Amplitude death induced by mixed attractive and repulsive coupling in the relay system

The amplitude death (AD) phenomenon is found in the relay system in the presence of the mixed couplings composed of attractive coupling and repulsive coupling. The generation mechanism of AD is revealed and shows that the middle oscillator achieving AD is a prerequisite to further suppress oscillation of the outermost oscillators for the paradigmatic Stuart-Landau and Rössler models. Moreover, regarding the Stuart-Landau relay system as a small motif of star network, we also observe that the mixed couplings can facilitate AD state of the whole network system. Particularly, the threshold of coupling strength is invariable with the change of network size. Our findings may shed a new insight to explore the effects of hybrid coupling on complex systems, also provide a new strategy to control dynamic behaviors in engineering science and neuroscience fields.     

Bifurcation, amplitude death and oscillation patterns in a system of three coupled van der Pol oscillators with diffusively delayed velocity coupling

In this paper, we study a system of three coupled van der Pol oscillators that are coupled through the damping terms. Hopf bifurcations and amplitude death induced by the coupling time delay are first investigated by analyzing the related characteristic equation. Then the oscillation patterns of these bifurcating periodic oscillations are determined and we find that there are two kinds of critical values of the coupling time delay: one is related to the synchronous periodic oscillations, the other is related to eight branches of asynchronous periodic solutions bifurcating simultaneously from the zero solution. The stability of these bifurcating periodic solutions are also explicitly determined by calculating the normal forms on center manifolds, and the stable synchronous and stable phase-locked periodic solutions are found. Finally, some numerical simulations are employed to illustrate and extend our obtained theoretical results and numerical studies also describe the switches of stable synchronous and phase-locked periodic oscillations.     

Effect of Cherenkov dissipation on vortex velocity in a waveguide-coupled Josephson junction

A motion of slow and fast vortices in a waveguide-coupled Josephson junction induced by a transport current flowing through the entire structure is studied; the coupling is not assumed to be weak. For a fast vortex, conditions are established under which current oscillations due to energy dissipation via Cherenkov radiation of Swihart waves become comparable to the current compensating for ohmic losses in the Josephson junction, waveguide, and adjacent superconductors. For a slow vortex, it is proved that intermediate and strong couplings of the Josephson junction to the waveguide shift current oscillations to the velocity range below the Swihart velocity of the Josephson junction.     

Light propagation and oscillations in two-dimensional graded square photonic lattices

We have studied the optical oscillations and transitions in two-dimensional graded square photonic lattices (GSPL) formed by evanescently coupled optical waveguide arrays with parabolic confinements in all transverse directions. When we retain only the orthogonal couplings, decoupled one-dimensional models can be used to obtain the various normal modes, which correspond to a variety of optical oscillations. Six different combinations of Bloch oscillation (BO), dipole oscillation (DO), and reflections from the boundaries of finite lattice are classified on the phase diagram. If we include the diagonal couplings, transitions among various oscillations are obtained with the Hamiltonian optics approach and confirmed by the field-evolution analysis. We studied in detail a typical example in which a switching occurs from the constituent BO and DO to both DOs in the two orthogonal directions. The method to analyze the complex field evolution in GSPL can be extended to similar systems with different types of lattices and/or confinements.     

Synchronization in a multiplex network of gene oscillators

Study of the synchronization in the network of gene oscillator network has vital importance in understanding of rhythmicity of molecular and cellular activities. In this paper, we analyze a network of linearly coupled genetic oscillators in a multiplex structure. The coupling strength values are changed and the coupling range is considered to be fixed, but different in the two layers. The analyses are done in two cases of periodic and chaotic oscillations. By computing the statistical measures, the interlayer and intralayer synchronization states are studied. The results show that the layer with higher coupling range has more enhanced synchrony and is less affected by the turbulent behavior of the other layer. On the other hand, the layer with lower coupling range approaches synchronization by strengthening the interlayer and intralayer couplings. The interlayer synchronization is also achieved in high coupling strength values.     

Measurements of the Drift Current Oscillations in Thrusters with Closed Electron Drift

An induction method used to measure the drift current in thrusters with anode layer (TAL) has been applied for measuring the integral distortion of the magnetic field in the channel of a low-power stationary plasma thruster (SPT). Experiments are described in which the integral level of magnetic field oscillations in the narrow channel of a thruster with closed electron drift was determined. Experimental data show that when a discharge is ignited in an SPT, the drift current completely demagnetizes the discharge gap (the ratio between the self-magnetic and external fields reaches 90%). The same effect has been observed in TALs. In thrusters of both types, the total discharge current is one and a half order of magnitude higher than that typical of the stationary discharge and the plasma glow is observed not only inside but also outside the discharge channel. Drift current oscillations have been measured under steady-state conditions. It has been shown, in particular, that when the oscillations are intense (in weak magnetic fields on the order of 100 G), the drift-current-induced distortion of the magnetic field may reach 33%. Under rated operating conditions (200 G), the distortion does not exceed 8%. Beyond optimal operating conditions, the type of oscillation in SPTs and TALs and their performances differ. For example, in SPTs, a critical magnetic field at which the “turbulent” regime sets in is absent. In general, the discharge current is weakly dependent on the magnetic field.     

Multiphoton dynamics of qutrits in the ultrastrong coupling regime with a quantized photonic field

Multiphoton resonant excitation of a three-state quantum system (a qutrit) with a single-mode photonic field is considered in the ultrastrong coupling regime, when the qutrit–photonic field coupling rate is comparable to appreciable fractions of the photon frequency. For ultrastrong couplings, the obtained solutions of the Schrödinger equation that reveal multiphoton Rabi oscillations in qutrits with the interference effects leading to the collapse and revival of atomic excitation probabilities at the direct multiphoton resonant transitions.     

Moving and Interaction of Compact-like Pulses in Klein-Gordon Lattice System

We study the moving and interaction of the compact-like pulses in the system of an anharmonic lattice with a double well on-site potential by a direct algebraic method and numerical experiments. It is found that the localization of the compact-like pulse is related to the nonlinear coupling parameter Cnl and the potential barrier height V0 of the double well potential. The velocity of the moving compact-like pulse is determined by the linear coupling parameter Cl, the localization parameter q (the nonlinear coupling parameter Cnl) and the potential barrier height Vo.Numerical experiments demonstrate that appropriate Cl is not detrimental to a stable moving of the compact-like pulse.However, the head on interaction of two compact-like pulses in the lattice system with comparatively small Cl leads to the appearance of a discrete stationary localized mode and small amplitude nonlinear oscillation background, while moderate Cl results in the emergence of two moving deformed pulses with damping amplitude and decay velocity and radiating oscillations, and biggish Cl brings on the appearing of four deformed kinks with radiating oscillations and different moving velocities.     

Chaos dynamics in semiconductor lasers with polarization-rotated optical feedback

By using polarization-rotated optical feedback from the transverse-electric (TE) mode to the transverse-magnetic (TM) mode, chaotic oscillations for both polarization modes are excited in a semiconductor laser. We find different correlations between these chaotic oscillations than those found in previous studies. In this study, the dynamics are strongly dependent on their radio-frequency (RF) components and they are divided into three RF regions. For low-pass filtered signals lower than the laser relaxation oscillation, there is an antiphase correlation between the two polarization modes. On the other hand, the two polarization modes have an in-phase correlation for the RF components of the high-pass filtered signals, which are higher than the relaxation oscillation. However, no correlations were observed between the two modes for the intermediate RF components that include the relaxation oscillation frequency. We also perform numerical calculations for the model and obtain good agreement between the theoretical and experimental results.     

Hydrodynamics and heat transfer for large amplitude pulsating laminar flow in channels

The heat transfer at superposition of high-frequency oscillations on a laminar flow of a liquid in flat and rectan-gular channels at a distance from an inlet of a heated site is investigated under boundary conditions on channel walls of the first and second kind. For the flat channel, the obtained analytical expressions for the amplitude and phase profiles of the longitudinal velocity oscillations are used as a function of the dimensionless oscillation frequency in the form of functions of a real variable. It is shown that the mean value taken for the perimeter of the channel and also the period of oscillations, the Nusselt number for large amplitudes of mean velocity oscillations over the cross section can signifi-cantly exceed its stationary value. The limiting value of the ratio of Nusselt numbers for a pulsating and steady flow in the region of high pulsation frequencies is found.     

Periodic and chaotic oscillations of the electrochemical potential of p-Si in contact with an aqueous (CuSO4+HF) solution, caused by electroless Cu deposition

Periodic and chaotic oscillations were observed for the potential of p-type Si(111) immersed in an aqueous (HF+CuSO(4)) solution, accompanied by electroless Cu deposition on p-Si. They were, to our knowledge, the first examples of open-circuit potential oscillations observed for semiconductor electrodes. The oscillations appeared only when the Cu deposit formed a continuous porous film composed of mutually connected submicrometer-sized particles. Besides, the Si surface was kept flat within the size less than 50 nm even after the prolonged oscillation for a few hours, though the Si surface should be etched considerably with HF for this time. A plausible model is proposed for the periodic oscillation, in which interestingly coupling of autocatalytic shift in the flat-band potential of Si (U(fb)) caused by the change in the coverage of the Si oxide and the connection and disconnection of the Cu film with the Si surface plays the key role. The appearance of the chaotic oscillation is also explained by taking into account an oscillation-coupled change in the HF or Cu(2+) concentration near the Si surface.     

High-frequency magneto-oscillations in GaAs/AlGaAs quantum wells

We have observed very high-frequency, highly reproducible magneto-oscillations in modulation doped GaAs/AlGaAs quantum well structures. The oscillations are periodic in an inverse magnetic field (1/B) and their amplitude increases with temperature up to T approximately 700 mK. Being initially most pronounced around the filling factor nu=1/2, they move towards lower nu with increasing T. Front and back-gating data imply that these oscillations require a coupling to a parallel conducting layer. A comparison with existing oscillation models renders no explanation.     

Resonance imaging of dynamical filamentary current structures in a semiconductor

The spatially resolved observation of the nonlinear dynamical behavior of spontaneous current oscillations obtained during low-temperature avalanche breakdown of homogeneously p-doped germanium is reported. Stationary current filaments developing in the breakdown regime through impurity impact ionization were observed two-dimensionally by means of a scanning electron microscope equipped with a liquid-helium cryostage. Further, spontaneous current oscillations showing typical transitions to chaos were localized two-dimensionally by means of a novel resonance imaging technique, which provides spatially resolved analysis of the nonlinear dynamical behavior. From these measurements different oscillation frequencies were clearly identified as spatially separated oscillation centers localized along the stationary current filaments. The electron beam was demonstrated to act as an exemplary control parameter, which can be manipulated both spatially and temporally.