Coherent transport in a periodically driven bistable system

The quantum dynamics of a quartic double well, subjected to a harmonically oscillating field, is studied in the framework of the Floquet formalism. The modifications of the familiar tunneling process due to the driving are investigated numerically and explained in terms of the structure of the corresponding local quasienergy spectrum. In particular, there is a one-dimensional manifold in the parameter space spanned by the amplitude and frequency of the driving force, where tunneling is almost completely suppressed by the coherent driving. The quantal dynamics in the semiclassical regime as well as the influence of weak incoherent processes are briefly discussed.     

Time-varying coupling-induced logical stochastic resonance in a periodically driven coupled bistable system

Coupling-induced logical stochastic resonance(LSR) can be observed in a noise-driven coupled bistable system where the behaviors of system can be interpreted consistently as a specific logic gate in an appropriate noise level. Here constant coupling is extended to time-varying coupling, and then we investigate the effect of time-varying coupling on LSR in a periodically driven coupled bistable system. When coupling intensity oscillates periodically with the same frequency with periodic force or relatively high frequency, the system successfully yields the desired logic output. When coupling intensity oscillates irregularly with phase disturbance, large phase disturbance reduces the area of optimal parameter region of coupling intensity and response speed of logic devices. Although the system behaves as a desired logic gate when the frequency of time-periodic coupling intensity is precisely equal to that of periodic force, the desired logic gate is not robust against tiny frequency difference and phase disturbance. Therefore, periodic coupling intensity with high frequency ratio is an optimal option to obtain a reliable and robust logic operation.     

A theoretical study of the non-linear response of a periodically driven bistable system

Summary In this paper, a comprehensive theory for the non-linear response of a periodically driven bistable system is presented. Analytic results for the full spectral response, including the signal-to-noise ratio (SNR), are obtained. In addition, the whole hierarchy of escape time distributions is calculated. Theoretical connection between these distributions and the SNR is made, enabling the SNR to be calculated from the knowledge of a single escape time distribution. The theoretical calculations are compared with the results of analogue simulation. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

Hopping and phase shifts in noisy periodically driven bistable systems

We consider a periodically driven bistable system in the presence of fluctuations. In a number of recent papers it has been shown that the amplitude of the response of the noisy system to periodic modulations exhibits stochastic resonance, i.e. a resonance-like behavior as a function of the noise intensity. In this paper, we consider the phase shift between the response and the periodic driving. For weak periodic driving, the phase shift also shows a resonance like behaviour as a function of the noise strength, but this effect is shown to be of different origin than the one responsible for stochastic resonance. Furthermore, the phase shift is demonstrated to exhibit a resonance-like behavior as a function of the driving frequency.     

Phase transitions in a bistable system driven by two colored noises

The colored noise problem is studied from the point of view of consistent Markovian approximations through extending unified colored-noise approximation to the case of two-colored-noise driving systems. A bistable system simultaneously driven by multiplicative and additive colored noise is investigated by means of the extended unified colored-noise approximation. It is found that, for weak strength and color of the additive noise, the form of the stationary probability distribution changes from a unimodal to a bimodal structure via a three modal one as the correlation time of the multiplicative colored noise increases, showing the system undergoes a first order phase transition from a monostable to a bistable state. Numerical simulations support our results. Received 10 August 1998 and Received in final form 23 April 1999     

Distribution of escape times for a deterministically driven bistable system

In this paper, we analyze the sequence of escape times for a particle in a symmetric double-well potential coupled to a chain of monodimensional oscillators and we find that, in some range of energies, the probability of escape exhibits the multimodal form that is characteristic of bistable systems driven by a periodic signal embedded in noise. We identify two different modes contributing to the overall hopping dynamics of the particle, each one having a definite dependence on the energy of the chain. Those findings suggest a model for internal fluctuations that could be useful in the study of some problems of interest in physics and biology.     

Fluctuation-induced transitions of a bistable driven polariton system in the presence of damping

Fluctuation-induced transitions from the lower energy state of a bistable nonlinear driven microcavity oscillator are analyzed beyond the Fluctuation–Dissipation theorem. The sources of noise are: both fluctuations of the external pumping and inevitable interaction with the exciton reservoir in the cavity. We show that finite polariton lifetime strongly modifies the phase portrait and influences the temporal parameters of the transition within the bistable regime. To investigate the transient dynamics of the driven polariton system, three different approaches are realized: numerical experiment (1), i.e. direct solution of the quasiclassical dynamic equation for polariton amplitude driven by an external pump, (2) solution of two dimensional Fokker–Planck-equation and (3) effective one dimensional Fokker–Planck-equation, obtained within a low-damping approximation. We show that the escape times obtained within the numerical experiment and the 2D-Fokker–Planck-equation coincide. In contrast, the one dimensional Fokker–Planck-approximation fails for large damping parameters due to strong deviation of the phase trajectories from those obtained within the low-damping approximation. The range of the ratio between damping and detuning for which the 1d approximation is valid, is shown to be smaller than 0.04. Finally, we determine the impact of the fluctuations on experiments illustrated by the narrowing of the hysteresis cycle.     

Tunnelling in periodically driven systems

Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.     

Superfluid-insulator transition in a periodically driven optical lattice

We demonstrate that the transition from a superfluid to a Mott insulator in the Bose-Hubbard model can be induced by an oscillating force through an effective renormalization of the tunneling matrix element. The mechanism involves adiabatic following of Floquet states, and can be tested experimentally with Bose-Einstein condensates in periodically driven optical lattices. Its extension from small to very large systems yields nontrivial information on the condensate dynamics.     

Routes to bursting in a periodically driven oscillator

The dynamical behaviors of a periodic excited oscillator with multiple time scales in the form that order gap exists between the frequency of the excitation and the natural frequency, are investigated in this Letter. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamics. Different types of bursting phenomena, such as fold/Hopf bursting, fold/Hopf/homoclinic bursting and Hopf/homoclinic bursting, are presented, the mechanism of which is obtained based on the bifurcations of the generalized autonomous system as well as the introduction of the so-called transformed phase portraits. Furthermore, the evolution of the bursting is discussed in details, in which one may find that when the two limit cycles caused by the Hopf bifurcations of the two related equilibrium points interact with each other, homoclinic bifurcation may occur, leading to the merge of the two cycles to form a large amplitude cycle. The homoclinic bifurcation may cause the two asymmetric bursters to merge into a symmetric enlarged burster, in which the large amplitude of the spiking state agrees well with the amplitude of the cycle caused by the homoclinic bifurcation.     

关联噪声驱动的非对称双稳系统的随机共振

运用统一色噪声近似理论和两态模型理论,研究了周期矩形信号和关联的乘性色噪声和加性白噪声驱动的非对称双稳系统的随机共振现象,得到了适合信号任意幅值的信噪比表达式.信噪比是乘性噪声强度、加性噪声强度、乘性噪声自关联时间、噪声耦合强度的非单调函数,所以该双稳系统中出现了随机共振.同时,调节加性噪声强度比调节乘性噪声强度更容易产生随机共振.势阱静态非对称性和噪声之间的耦合强度对信噪比的影响是不同的. 关键词： 非对称双稳系统 随机共振 信噪比 周期矩形信号     

Stochastic resonance in an asymmetric bistable system driven by coloured noises

The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises.The approximate Fokker-Planck equation is derived based on the Novikov theorem and the Fox approach.By applying the two-state theory,the expression of the signal-to-noise ratio is obtained in the adiabatic limit.The effects of the noise parameters on signal-to-ratio are discussed.It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.     

“Escape” of a periodically driven particle from a metastable state in a noisy system

We consider the statistical properties of the escape time of a particle initially sitting in a potential well subject to a combination of white noise and a periodic forcing term. As one finds in the case of the much-studied bistable potential, different kinds of resonant effects can occur, as measured by the survival probability and the average residence time. When this time is considered as a function of the noise strength, then we show that for small amplitudes of the forcing term there are no resonant effects, while for large amplitudes such effects can appear. We also show that a resonant phenomenon is possible in terms of the amplitude of a periodic forcing term.     

Periodic renewal processes: application to periodically driven FitzHugh-Nagumo system

Stimulation with periodic force is a standard method to study response properties of a system. Here we examine a special type of systems which generate a sequence of events with uncorrelated time intervals. We review analytical tools to calculate the gain and the signal-to-noise ratio for such systems when perturbed by sinusoidal signal and then apply these tools to the stochastic FitzHugh-Nagumo model.     

Asymmetry-induced spectral peaks in periodically forced noisy bistable systems

The occurrence of finite-width peaks in the spectral background of a time-sinusoidally forced overdamped bistable Duffing oscillator, subject to a noise-floor, is reported. The peaks, which only occur in the presence of a symmetry-breaking dc signal, are located at approximately the odd integer multiples of the forcing frequency. An analytic expression for the height of the peaks is derived and validated via computer simulations. The peak heights display a non-monotonic dependence on the system asymmetry.     

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.