Nonequilibrium first-order phase transition in semiconductor system driven by colored noise

We examine the mechanisms of action of colored multiplicative noise in a positionally disordered semiconductor with Moss–Burstein shift. It is shown that the action of multiplicative noise causes nonequilibrium first-order phase transition of the disorder–order-type in electron subsystem of semiconductor. There are relatively little changes in a condensed matter at such phase transitions, but the electron subsystem undergoes a strong reorganization. The steady photocarriers concentration distribution is studied within a unified colored-noise approximation.     

Stochastic resonance in periodic potentials driven by colored noise

We studied the motion of an underdamped Brownian particle in a periodic potential subject to a harmonic excitation and a colored noise. The average input energy per period and the phase lag are calculated to quantify the phenomenon of stochastic resonance (SR). The numerical results show that most of the out-of-phase trajectories make a transition to the in-phase state as the temperature increases. And the colored noise delays the transitions between these two dynamical states. The each curve of the average input energy per period and the phase lag versus the temperature exist a mono peak and SR appears in this system. Moreover, the optimal temperature where the SR occurs becomes larger and the region of SR grows wider as the correlation time of colored noise increases.     

Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics

Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit–environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution.     

A semi-analytic method for computing the long-time order parameter dynamics in mean-field coupled overdamped oscillators with colored noises

The order parameter dynamics of a mean-field model is frequently investigated in macroscopic cumulant dynamics, from which a bifurcation can be predicted qualitatively. In this Letter, for quantitatively investigating the long-time order parameter dynamics, a semi-analytic method is proposed based on approximate nonlinear Fokker-Planck equations. Applying the new method to the mean-field model of periodically driven overdamped bistable oscillators with colored noise, we exhibit the bifurcation behavior and the nonlinear stochastic resonance of the order parameter by tuning noise intensity or coupling coefficient, and the accuracy of the new method are verified by direct simulation. Our observations disclose some new properties about the order parameter dynamics of the mean-field model. For example, the periodic signal shifts the critical coupling coefficient to a larger value, while the nonzero correlation time of the colored noise shifts it to a lower value. Our observation also discloses that there is no quantitatively corresponding relation between the resonant peak and the critical bifurcation parameter of the Gaussian moment system.     

Effect of colored noise on chains of chaotic oscillators

Equations that describe a ring system consisting of a closed circuit of n (n = 2, 3, 4, ...) unidirectionally coupled self-oscillation systems that exhibit chaotic dynamics are analyzed in the presence of external colored noise. For simplicity, detailed results of numerical calculations are presented for three oscillators. It is demonstrated that the external colored noise that is exerted upon partial oscillators of the ring system may facilitate the development of synchronous oscillations and reduce transient processes related to stabilization of chaotic synchronization. The effect is qualitatively interpreted. For comparison, numerical methods are employed to analyze the effect of external colored noise on an open circuit consisting of three oscillators.     

Metastable systems driven by colored noise: The stationary state

The influence of the Bardeen-Herring back-jump correlations on the Fermi-Dirac statistics of the one-dimensional nonhomogeneous fermionic lattice gas is studied by the Monte Carlo simulation technique and semianalytically. The resulting distribution is obtained, exhibiting increased population of the lower levels in comparison to the Fermi-Dirac statistics.     

Inversion in harmonic noise driven bistable oscillators

We consider the dynamics in a asymmetrical bistable oscillator driven externally by a noisy harmonic oscillator. The basic for our approach is the energy dynamics in each well of the oscillator in the low friction limit. We discuss the possibility of energy inversion states generated by harmonic noise and show this effect by simulations.     

Measurements of two-dimensional densities for a bistable device driven by colored noise

We have constructed an electronic circuit which accurately mimics the dynamics of a nonequilibrium, bistable flow driven by additive, exponentially correlated, Gaussian noise. The noise voltage and voltages representing the velocity and displacement were measured, digitized and then assembled into the stationary, statistical densitiesW(V _n ,X) andW for several noise intensities and correlation times. Our measurements are in good agreement with the theoretical results of Jung and Risken described in the preceeding paper.     

Uncertainty principle for control of ensembles of oscillators driven by common noise

We discuss control techniques for noisy self-sustained oscillators with a focus on reliability, stability of the response to noisy driving, and oscillation coherence understood in the sense of constancy of oscillation frequency. For any kind of linear feedback control — single and recursive delay feedback, linear frequency filter, etc. — the phase diffusion constant, quantifying coherence, and the Lyapunov exponent, quantifying reliability, can be efficiently controlled but their ratio remains constant. Thus, an “uncertainty principle” can be formulated: the loss of reliability occurs when coherence is enhanced and, vice versa, coherence is weakened when reliability is enhanced. Treatment of this principle for ensembles of oscillators synchronized by common noise or global coupling reveals a substantial difference between the cases of slightly non-identical oscillators and identical ones with intrinsic noise.     

Effective potential and weak noise transitions

We review the notion of effective potential for stochastic processes and discuss its possible applications. We calculate this function up to first order in a parameter measuring the intensity of the noise for a general nonlinear system. The result is applied exhibiting a transition induced by weak noise.     

色关联噪声驱动下非线性神经元模型的相干共振

研究了关联的加性离子通道噪声和乘性突触噪声共同作用下非线性积分发放神经元模型中的相干共振现象.运用绝热近似理论和统一色噪声近似方法,得到了神经元首次点火概率分布和神经元放电峰峰间隔的变差系数的近似表达式.研究表明,首次点火概率分布和变差系数是突触噪声强度、离子通道噪声强度、乘性色噪声自相关时间和噪声关联强度的函数,适当的噪声强度、噪声自相关时间和噪声关联强度可以减小神经元发放峰峰间隔的变差系数,使系统的相干性达到最大值,从而引起神经元出现相干共振现象.同时讨论了离子通道噪声强度、突触噪声强度、乘性色噪声自相关时间和噪声关联强度对系统相干共振的影响.     

Enhancement of density divergence in an insect outbreak model driven by colored noise

The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper.According to the Fokker-Planck equation in the unified colored-noise approximation,we analyse the stationary probability distribution and the mean first-passage time of this model.By numerical analysis,the effects of the self-correlation time of insect birth rate and predation rate respectively reveal a manifest population divergence on the insect density.The decrease of the mean first-passage time indicates an enhancement dynamic on the density divergency with colored noise of a large self-correlation time based on the insect outbreak model.     

Unstable state dynamics: Treatment of colored noise

The diffusion of a particle set near an unstable point in a bistable potential is considered. The scaling theory of fluctuations proposed originally for onedimensional systems driven by Gaussian white noise is extended to arbitrary dimensions. The merits and drawbacks of the scaling theory are discussed by taking a model problem in one dimension. It is shown in passing that the saddle point approximation enables one to get analytic expressions for various moments of the stochastic process. The two different methods to include asymptotic fluctuations-which are absent in the usual scaling solution-are shown to be equivalent. An alternate way of including asymptotic fluctuations is attempted by solving the associated Fokker-Planck equation using the Fer formula. The reason for the failure of this method is traced. After this, it is argued that the unified scaling theory should be applicable for treatment of colored noise as well, for the scaling assumption is independent of the statistical property of the driving noise. Explicit Monte Carlo simulation of a model onedimensional system driven by exponentially correlated Gaussian noise is performed and compared with the scaling solution to bolster this point. The agreement is very good.     

色噪声背景下微弱正弦信号的混沌检测

提出一种利用混沌在特定状态下对参数的敏感性来实现微弱正弦信号检测的新方案-该方案可以有效地将深陷在色噪声背景中的微弱正弦信号检测出来-给出了混沌检测的方法,分析了混沌检测中噪声对系统状态的影响-仿真实验表明该混沌检测系统对小信号非常敏感，对任何零均值色噪声均具有极强的抑制能力- 关键词： 微弱正弦信号 混沌检测 色噪声 信噪比     

Soluble models for dynamics driven by a super-diffusive noise

We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given.     

Amplitude death in an array of limit-cycle oscillators

We analyze a large system of limit-cycle oscillators with mean-field coupling and randomly distributed natural frequencies. We prove that when the coupling is sufficiently strong and the distribution of frequencies has sufficiently large variance, the system undergoes amplitude death-the oscillators pull each other off their limit cycles and into the origin, which in this case is astable equilibrium point for the coupled system. We determine the region in couplingvariance space for which amplitude death is stable, and present the first proof that the infinite system provides an accurate picture of amplitude death in the large but finite system.     

Interfacial growth in driven Ginzburg-Landau models: Short and long-time dynamics

Interfacial growth in driven systems is studied from the initial stage to the longtime regime. Numerical integrations of a Ginzburg-Landan type equation with a new flux term introduced by an external field are presented. The interfacial instabilities are induced by the external field. From the numerical results, we obtain the dispersion relation for the initial growth. During the intermediate temporal regime, fingers of a characteristic triangular shape could grow. Depending on the boundary conditions, the final state corresponds to strips, multifinger states, or a one-finger state. The results for the initial growth are interpreted by means of surface-driven and Mullins-Sekerka instabilities. The shape of the one-finger state is explained in terms of the characteristic length introduced by the external field.     

Holes in the probability density of strongly colored noise driven systems

A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value ₀, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >₀, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >₀, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax ²/2+bx ⁴/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve ₀(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of ₀ for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.