Stochastic resonance in multi-stable system driven by Lévy noise

In this paper, the stochastic resonance (SR) of a multi-stable system driven by Lévy noise is investigated by the mean signal-to-noise ratio gain (SNR-GM). The characteristics for resonant output of multi-stable system, governed by the system parameters (a and c), the noise amplification factor D of Lévy noise are investigated under different values of stability index α and asymmetry parameter β of Lévy noise. The results reveal that the parameter α is closer to 1, the amplitude of SNR-GM versus system parameter a (or c) is larger. The interval of SR presents a trend that the curve of SNR-GM shifts to the right with the increase of α especially when α > 1. In addition, the SNR-GM for different values of system parameter a (or c) exhibits a tendency to move to the left with the increase of system parameter c (or a). Finally, the simulation results prove that the proposed multi-stable model has better advantage than bistable system and monostable system in signal enhancement and SNR-GM performance.     

A multi-stable energy harvester: Dynamic modeling and bifurcation analysis

A theoretical investigation is conducted on the dynamic and energetic characteristics of a multi-stable bimorph cantilever energy harvester that uses magnetic attraction effect. The multi-stable energy harvester under study is composed of a bimorph cantilever beam with soft magnetic tip and two externally fixed permanent magnets that are arranged in series. With this configuration, the magnetic force and the moment that are exerted on the cantilever tip tend to be highly dependent on the magnetic field induced by the external magnets. Such an energy harvester can possess multi-stable potential functions, ranging from mono-stable to penta-stable. The mechanism that governs the formation of this multi-stability is thoroughly identified and examined thorough a bifurcation analysis performed on the system?s equilibrium solutions. From this analysis, it is found that the transitions between these multi-stable states occur through very complicated bifurcation scenarios that include degenerate pitchfork bifurcations and mergers of pitchfork bifurcations or saddle-node bifurcations. Bifurcation set diagram is obtained, which is composed of five separate parametric regions, from mono- to penta-stability. The resulting stability map satisfactorily describes the multi-stable characteristics of the present energy harvester. In addition, the dynamic and energetic characteristics of the present multi-stable energy harvester are more thoroughly examined using its potential energy diagrams and a series of numerical simulations, and the obtained results are compared with those for the equivalent bi-stable cases.     

Second-order solutions for the dynamics of a semi-infinite cable on a unilateral substrate

We present an asymptotic solution of a moving-boundary problem which describes the nonlinear oscillations of semi-infinite cables resting on an elastic substrate reacting in compression only, and subjected to a constant distributed load and to a small harmonic displacement applied to the finite boundary. Our solution is correct through the second-order terms in a smallness parameter, which we identify with the amplitude of the harmonic oscillation at the boundary, and it complements the first-order solution presented in an earlier work. The second-order analysis confirms the existence of two different regimes in the behaviour of the system, one below (called subcritical) and one above (called supercritical) a certain critical (cutoff) excitation frequency. In the latter, energy is lost by radiation at infinity, while in the former this phenomenon does not occur and various resonances are observed instead. We show that these two regimes exist at all orders in the expansion parameter, and that the cutoff frequency decreases at each order. We also perform a limited comparison of our asymptotic results with a numerical solution. The two approaches show very good agreement.     

Effect of non-Markovianity on synchronization

We investigate the transient spontaneous quantum synchronization between two qubits interacting with a common non-Markovian environment based on a collision model. We are mainly interested in the effect of non-Markovianity on the synchronization between two qubits. We find that the non-Markovianity always delay the anti-synchronization and decrease the parameter region where the qubits get anti-synchronized. Meanwhile, we define V to characterize the visibility of synchronization and show that there is an apparent link among V, entanglement and quantum mutual information whether in the Markovian or non-Markovian regimes when the environment is in the vacuum state. Moreover, with the increase of temperature, the parameter region of the emergence of anti-synchronization and the time to get anti-synchronized in the non-Markovian regime gradually approaches that in the Markovian regime. The high temperature decreases the parameter region of the emergence of anti-synchronization in both Markovian and non-Markovian regimes, and breaks the connection among V, entanglement and quantum mutual information.     

光学多稳系统的相变及临界点分类

参照朗道相变理的基本精神,确定光学多稳性系统的相变与临床界现象,揭示了相变的多样性,以及多稳系统通向完全单稳状态态的不同路径。多稳性的级次愈高,相变的式样也就愈多。     

Two types of ground-state bright solitons in a coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate

We study two types of bright solitons in an attractive Bose-Einstein condensate with a spin-orbit interaction. By solving the coupled nonlinear Schr odinger equations with the variational method and the imaginary time evolution method,fundamental properties of solitons are carefully investigated in different parameter regimes. It is shown that the detuning between the Raman beam and energy states of the atoms dominates the ground state type and spin polarization strength.The soliton dynamics is also studied for various moving velocities for zero and nonzero detuning cases. We find that the shape of individual component solitons can be maintained when the moving speed of solitons is low and the detuning is small in the coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate.     

Mesoscopic Fluctuations for the Thinned Circular Unitary Ensemble

In this paper we study the asymptotic behavior of mesoscopic fluctuations for the thinned Circular Unitary Ensemble. The effect of thinning is that the eigenvalues start to decorrelate. The decorrelation is stronger on the larger scales than on the smaller scales. We investigate this behavior by studying mesoscopic linear statistics. There are two regimes depending on the scale parameter and the thinning parameter. In one regime we obtain a CLT of a classical type and in the other regime we retrieve the CLT for CUE. The two regimes are separated by a critical line. On the critical line the limiting fluctuations are no longer Gaussian, but described by infinitely divisible laws. We argue that this transition phenomenon is universal by showing that the same transition and their laws appear for fluctuations of the thinned sine process in a growing box. The proofs are based on a Riemann-Hilbert problem for integrable operators.     

A model for layered high-temperature superconductors with two CuO2 layers per unit cell

We extend a model for layered high-temperature superconductors to systems with two CuO₂ layers per unit cell and two interlayer spacings with different physical properties. The carriers are assumed to occupy Fermi liquid states, forming narrow tight-binding bands. The layers are coupled by weak interlayer-hopping matrix elements between adjacent sheets, as well as by an attractive interaction between carriers in neighboring layers in addition to an on-site intralayer coupling. We solve the Gorkov equations for this model to obtain the critical temperature and the density of states of the oneparticle excitations from the superconducting condensate, and discuss various parameter regimes concerning the coupling between the two layers. We compare our results with current experimental findings for high-temperature superconductors. The presence of two CuO₂ layers leads to multi-peak features in the superconducting density of states, as has been observed in recent tunneling measurements.     

Two-collective Mode Entanglement in a Four-level Atomic Ensemble

We propose a theoretical method to obtain two-collective mode entanglement in a four-level atomic ensemble. One collective mode is produced due to the Raman atomic coherence, the acquisition of another collective mode is ascribed to the quantum interference in two four-wave mixing processes. We show that two-collective mode and two original single modes are also in the entangled state in experimentally accessible parameter regimes.     

Study of the Nonlinear Dynamics of a Traveling-Wave-Tube Oscillator with Delayed Feedback

We present the results of numerical simulations of the nonlinear dynamics of a traveling-wave-tube (TWT) oscillator with delayed feedback. Basic properties of stationary single-frequency oscillation regimes are considered, and the onset of self-modulation is studied in detail. Various route-to-chaos scenarios corresponding to successively increasing values of the beam current are simulated numerically. It is shown that the basic scenario is a quasi-periodic route to chaos, while the beam deceleration in strongly nonlinear regimes causes transitions via intermittency to regimes based on modes with higher frequencies. Competition between these two scenarios leads to a complex picture of regular and chaotic self-modulation regimes in the parameter space. Such a behavior is typical of distributed electron–wave self-excited oscillators with delayed feedback.     

Study on the mean first-passage time and stochastic resonance of a multi-stable system with colored correlated noises

The mean first-passage time (MFPT) and the weak signal detection method of stochastic resonance (SR) on multi-stable nonlinear system under color correlated noise are studied. Using the uniform color noise approximation method, the Fokker-Planck equation of the system is obtained, and the steady-state probability density function of the multi-stable system driven by the multiplicative noise and additive noise is derived. On the basis of this, the formula of MFPT is derived, and the influence of parameters on the MFPT is analyzed. The problem of weak signal detection under color noise background is studied based on multi-stable SR. The results of simulation and experiment show that the method can effectively extract the frequency feature of weak signal in the background of color noise.     

Pattern formation during deformation of a confined viscoelastic layer: from a viscous liquid to a soft elastic solid

We study pattern formation during tensile deformation of confined viscoelastic layers. The use of a model system [poly(dimethylsiloxane) with different degrees of cross-linking] allows us to go continuously from a viscous liquid to an elastic solid. We observe two distinct regimes of fingering instabilities: a regime called "elastic" with interfacial crack propagation, where the fingering wavelength scales only with the film thickness, and a bulk regime called "viscoelastic," where the fingering instability shows a Saffman-Taylor-like behavior. We find good quantitative agreement with theory in both cases and present a reduced parameter describing the transition between the two regimes and allowing us to predict the observed patterns over the whole range of viscoelastic properties.     

Spectroscopy of a driven solid-state qubit coupled to a structured environment

We study the asymptotic dynamics of a driven spin-boson system where the environment is formed by a broadened localized mode. Upon exploiting an exact mapping, an equivalent formulation of the problem in terms of a quantum two-state system (qubit) coupled to a harmonic oscillator which is itself Ohmically damped, is found. We calculate the asymptotic population difference of the two states in two complementary parameter regimes. For weak damping and low temperature, a perturbative Floquet-Born-Markovian master equation for the qubit-oscillator system can be solved. We find multi-photon resonances corresponding to transitions in the coupled quantum system and calculate their line-shape analytically. In the complementary parameter regime of strong damping and/or high temperatures, non-perturbative real-time path integral techniques yield analytic results for the resonance line shape. In both regimes, we find very good agreement with exact results obtained from a numerical real-time path-integral approach. Finally, we show for the case of strong detuning between qubit and oscillator that the width of the n-photon resonance scales with the nth Bessel function of the driving strength in the weak-damping regime.     

Optical conductivity of the one-dimensional dimerized Hubbard model at quarter filling

We investigate the optical conductivity in the Mott insulating phase of the one-dimensional extended Hubbard model with alternating hopping terms (dimerization) at quarter band filling. Optical spectra are calculated for the various parameter regimes using the dynamical density-matrix renormalization group method. The study of limiting cases allows us to explain the various structures found numerically in the optical conductivity of this model. Our calculations show that the dimerization and the nearest-neighbor repulsion determine the main features of the spectrum. The on-site repulsion plays only a secondary role. We discuss the consequences of our results for the theory of the optical conductivity in the Bechgaard salts.     

Hartman effect and nonlocality in quantum networks

We study the phase time for various quantum mechanical networks having potential barriers in their arms to find the generic presence of Hartman effect. In such systems it is possible to control the ‘super arrival’ time in one of the arms by changing parameters on another, spatially separated from it. This is yet another quantum nonlocal effect. Negative time delays (time advancement) and ‘ultra Hartman effect’ with negative saturation times have been observed in some parameter regimes.     

Nonequilibrium tensile deformation of amorphous polymers in the rubbery state: Temperature,strain rate,and strain effects. I

We analyze nonequilibrium tensile deformational behavior of an amorphous uncrosslinked random copolymer of styrene and acrylonitrile stretched above its Tg at various temperatures and constant strain rates. The variable investigated is the force required to pull the specimen to a certain strain level. Our results suggest the deformational behavior in the rubbery state can be incorporated in a universal scheme where strain, strain rate, and temperature effects are all superposed, e.g., the effect of strain is identical to the effect of temperature and strain rate. This unexpected result is true within two contiguous but distinct regimes of strain, on both sides of ca. 40% strain, suggesting that non-equilibrium extension at constant pulling speed in the rubbery state occurs by at least two successive mechanisms. Our results also reveal that the physical parameter which should be used to achieve a true superposition of strain rate and temperature data is not as simple as has long been commonly proposed. For instance, we cannot use force alone nor the true stress, nor even the stress divided by strain. The best results are obtained when the function used is a complex function of force and strain. We introduce and explore in depth in this paper and future ones a new method to analyze the data. This method does not impose the choice of the functions which yield superposition and it provides an empirical mean for finding these functions. We have applied our method to other classical elastomers (PIB and SBR) stretched under similar conditions: we find the same conclusions, in particular the same small strain-middle strain transition separating two regimes of deformational behavior in the rubbery state.     

Persistent clusters in lattices of coupled nonidentical chaotic systems

Two-dimensional (2D) lattices of diffusively coupled chaotic oscillators are studied. In previous work, it was shown that various cluster synchronization regimes exist when the oscillators are identical. Here, analytical and numerical studies allow us to conclude that these cluster synchronization regimes persist when the chaotic oscillators have slightly different parameters. In the analytical approach, the stability of almost-perfect synchronization regimes is proved via the Lyapunov function method for a wide class of systems, and the synchronization error is estimated. Examples include a 2D lattice of nonidentical Lorenz systems with scalar diffusive coupling. In the numerical study, it is shown that in lattices of Lorenz and Rossler systems the cluster synchronization regimes are stable and robust against up to 10%-15% parameter mismatch and against small noise.     

Propagating characters of Gaussian laser beam in plasmas with non-homogeneous radial temperature distribution

We investigate the propagation regimes of laser beam in plasmas with radial distribution of electron temperature, characterized by ratio parameter of radial Gaussian distribution. By following the WKB method and paraxial approximation, the propagation equations of laser beam are derived and discussed for two nonlinearity mechanisms respectively. Both the critical curves for different ratio parameters are plotted, and it is proved that the self-focusing or self-trapping mode could be realized only when the ratio parameter excesses 1. The variations of laser beam-width are calculated, which indicates the feasibly effective modification of propagation characters by radial distribution of electron temperature.     

Bifurcations in excised larynx experiments

Bifurcation analysis was applied to vocal fold vibration in excised larynx experiments. Phonation onset and vocal instabilities were studied in a parameter plane spanned by subglottal pressure and asymmetry of either vocal fold adduction or elongation. Various phonatory regimes were observed, including single vocal fold oscillations. Selected spectra demonstrated correspondence between these regimes and vocal registers noted in the literature. To illustrate the regions spanned by the various phonatory regimes, two-dimensional bifurcation diagrams were generated. Many instabilities or bifurcations were noted in the regions of coexistence, i.e., regions in which the phonatory regimes overlap. Bifurcations were illustrated with spectrograms and fundamental frequency contours. Where possible, results from these studies were related to clinical observations.