Multi-Resonant-Activation for a System Only Driven by Multi-State Noise

We consider the escape of the particles multi-state noise. It is shown that, the noise can make over fluctuating potential barrier for a system only driven by a the particles escape over the fluctuating potential barrier in some circumstances; but in other circumstances, it can not. If the noise can make the particle escape over the fluctuating potential barrier, the mean first passage time （MFPT） can display the phenomenon of multi-resonant-activation. For this phenomenon, there are two kinds of resonant activation to appear. One is resonant activation for the MFPTs as the function of the flipping rates of the fluctuating potential barrier; the other is that for the MFPTs as the functions of the transition rates of the multi-state noise.     

Escape for System with Non-Fluctuating Potential Barrier Only Driven by Three-State Noise

We study the escape for the mean first passage time （MFPT） over a potential barrier for a system with non- fluctuating potential barrier and only driven by a three-state noise. It is shown that in some circumstances, the three-state noise can induce the resonant activation for the MFPT over the potential barrier; but in other circumstances, it can not. There are three resonant activations for the MFPT over the potential barrier, which are respectively as the functions of the transition rates of the three-state noise.     

Mean First Passage Time for System with Fluctuating Potential Barrier and Coupled Noise

In this paper we study the mean first passage time (MFPT) over a fluctuation potential barrier driven by a coupled noise. It is shown that the MFPT over the fluctuation potential barrier displays resonant activations as the function of the flipping rate of the fluctuation potential barrier, and as the function of the dichotomous noise transition rate.     

Escape over Fluctuating Barrier for a Stochastic Model of Motor Proteins in the Case of Environmental Perturbation

We study the mean first passage time (MFPT) over the fluctuatingpotential barrier for a stochastic model of motor proteins in the case of environmental perturbation proposed by J.H. LI et al. [Phys. Rev. E57 (1998) 39171. The MFPT is derived for a particle over the fluctuating potential barrier. It is shown that (i) there is resonant activation for the MFPT as a function of the flipping rate of the fluctuating potential barrier; (ii) the additive and multiplicative noises can weaken the resonant activation, but the correlations between them enhance the resonant activation; (iii) the susceptibility of the resonant activation to the multiplicative noise is far larger than that to the additive noise.     

Could one single dichotomous noise cause resonant activation for exit time over potential barrier？

This paper studies the mean first passage time （or exit time, or escape time） over the non-fluctuating potential harrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make the particles escape over the potential barrier, in some circumstances; but in other circumstances, it can not. In the case that the particles escape over the potential harrier, a resonant activation phenomenon for the mean first passage time over the potential barrier is obtained.     

Stochastic resonance, reverse-resonance, and resonant activation induced by a multi-state noise

In this paper, we investigate the periodic response for a linear system driven by a multiplicative multi-state noise (which is composed of the multiplication of two dichotomous noises) to an input temporal oscillatory signal, and the escape of Brownian particles over the fluctuating potential barrier for a system with a piece-wise linear potential and driven by an additive multi-state noise (which is also composed of the multiplication of two dichotomous noises). For the first system, we get the stochastic resonance phenomenon for the amplitude of the periodic response vs. the two dichotomous noise strengths, and the phenomenon of reverse-resonance for the amplitude of the periodic response vs. k, which represents the asymmetry degree of the dichotomous noises. For the second system, we obtain the resonant activation phenomenon, for which the mean first passage time of the Brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi-state noise.     

Enhancement of stability in randomly switching potential with metastable state

The overdamped motion of a Brownian particle in randomly switching piece-wise metastable linear potential shows noise enhanced stability (NES): the noise stabilizes the metastable system and the system remains in this state for a longer time than in the absence of white noise. The mean first passage time (MFPT) has a maximum at a finite value of white noise intensity. The analytical expression of MFPT in terms of the white noise intensity, the parameters of the potential barrier, and of the dichotomous noise is derived. The conditions for the NES phenomenon and the parameter region where the effect can be observed are obtained. The mean first passage time behaviors as a function of the mean flipping rate of the potential for unstable and metastable initial configurations are also analyzed. We observe the resonant activation phenomenon for initial metastable configuration of the potential profile.Received: 16 June 2004, Published online: 31 August 2004PACS: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 02.50.-r Probability theory, stochastic processes, and statistics - 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)     

Flux of a Ratchet Model and Applications to Processive Motor Proteins

In this paper, we investigate the stationary probability current (or flux) of a Brownian ratchet model as a function of the flipping rate of the fluctuating potential barrier. It is shown that, with suitably selecting the parameters' values of the ratchet system, we can get the negative resonant activation, the positive resonant activation, the double resonant activation, and the current reversal, for the stationary probability current versus the flipping rate. The appearance of these phenomena is the result of the cooperative effects of the potential's dichotomous fluctuations and the internal thermal fluctuations on the evolution of the flux versus the flipping rate of the fluctuating potential barrier. In addition, some applications of our results to the motor proteins are discussed.     

Flux of a Ratchet Model and Applications to Processive Motor Proteins

In this paper, we investigate the stationary probability current(or flux) of a Brownian ratchet model as a function of the flipping rate of the fluctuating potential barrier. It is shown that, with suitably selecting the parameters' values of the ratchet system, we can get the negative resonant activation, the positive resonant activation,the double resonant activation, and the current reversal, for the stationary probability current versus the flipping rate.The appearance of these phenomena is the result of the cooperative effects of the potential's dichotomous fluctuations and the internal thermal fluctuations on the evolution of the flux versus the flipping rate of the fluctuating potential barrier. In addition, some applications of our results to the motor proteins are discussed.     

Resonances while surmounting a fluctuating barrier

Electronic analog experiments on escape over a fluctuating potential barrier are performed for the case when the fluctuations are caused by Ornstein-Uhlenbeck noise (OUN). In its dependence on the relation between the two OUN parameters (the correlation time tau and noise strength Q) the nonmonotonic variation of the mean escape time T as a function of tau can exhibit either a minimum (resonant activation), or a maximum (inhibition of activation), or both these effects. The possible resonant nature of these features is discussed. We claim that T is not a good quantity to describe the resonancelike character of the problem. Independently of the specific relation between the OUN parameters, the resonance manifests itself as a maximal lowering of the potential barrier during the escape event, and it appears for tau of the order of the relaxation time toward the metastable state.     

Energy diffusion controlled reaction rate of reacting particle driven by broad-band noise

The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic averaging method. The averaged It? stochastic differential equation describing the energy diffusion and the Pontryagin equation governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as the inverse of the MFPT by solving the Pontryagin equation. The results of two special cases of broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that the reaction rate can be well predicted using the stochastic averaging method.     

Escape process and stochastic resonance under noise intensity fluctuation

We study the effects of noise intensity fluctuations on the stationary and dynamical properties of an overdamped Langevin model with a bistable potential and external periodical driving force. We calculated the stationary distributions, mean-first passage time (MFPT) and the spectral amplification factor using a complete set expansion (CSE) technique. We found resonant activation (RA) and stochastic resonance (SR) phenomena in the system under investigation. Moreover, the strength of RA and SR phenomena exhibit non-monotonic behavior and their trade-off relation as a function of the squared variation coefficient of the noise intensity process. The reliability of CSE is verified with Monte Carlo simulations.     

色关联噪声驱动的非对称双稳系统中平均首次穿越时间的研究

研究了由色关联的乘性白噪声和加性白噪声驱动的非对称双稳系统中，色关联及非对称性对平均首次穿越时间的影响.数值结果表明乘性噪声强度α和加性噪声强度D及互相关时间τ对首次穿越时间T的影响是一致的，加性和乘性噪声间的互关联强度λ及势阱的非对称性r对T的影响是一致的.τ的增加能提高粒子的逃逸率，λ的增加则减小逃逸率.     

Discrete dynamics and metastability: Mean first passage times and escape rates

The problem of escape from a domain of attraction is applied to the case of discrete dynamical systems possessing stable and unstable fixed points. In the presence of noise, the otherwise stable fixed point of a nonlinear map becomes metastable, due to noise-induced hopping events, which eventually pass the unstable fixed point. Exact integral equations for the moments of the first passage time variable are derived, as well as an upper bound for the first moment. In the limit of weak noise, the integral equation for the first moment, i.e., the mean first passage time (MFPT), is treated, both numerically and analytically. The exponential leading part of the MFPT is given by the ratio of the noise-induced invariant probability at the stable fixed point and unstable fixed point, respectively. The evaluation of the prefactor is more subtle: It is characterized by a jump at the exit boundaries, which is the result of a discontinuous boundary layer function obeying an inhomogeneous integral equation. The jump at the boundary is shown to be always less than one-half of the maximum value of the MFPT. On the basis of a clear-cut separation of time scales, the MFPT is related to the escape rate to leave the domain of attraction and other transport coefficients, such as the diffusion coefficient. Alternatively, the rate can also be obtained if one evaluates the current-carrying flux that results if particles are continuously injected into the domain of attraction and captured beyond the exit boundaries. The two methods are shown to yield identical results for the escape rate of the weak noise result for the MFPT, respectively. As a byproduct of this study, we obtain general analytic expressions for the invariant probability of noisy maps with a small amount of nonlinearity.     

Colored multiplicative and additive non-Gaussian noise-driven dynamical system: Mean first passage time

We have studied the barrier crossing dynamics in presence of non-Gaussian noises. It has been observed that multiplicative colored non-Gaussian noise can induce resonant activation (RA). The conspicuous dependence of mean first passage time (MFPT) on correlation time (_τ2${\tau }_2$) of additive colored noise having fixed variance have been analyzed. Beyond a critical value of _τ2${\tau }_2$ the MFPT increases for a given rate of increase of noise strength with _τ2${\tau }_2$ if the additive colored noise is non-Gaussian. The MFPT first decreases with increase of the non-Gaussian parameter (measures deviation from Gaussian character) of multiplicative colored noise followed by an increase exhibiting a minimum. The appearance of the minimum critically depends on the additive noise.     

Escape from a fluctuating system: a master equation and trapping approach

We present a general solution for the mean exit time in a system with on-site fluctuations between two configurations described by a master equation. The coupled configurations represent a spatially discretized version of an escape over a fluctuating barrier [C. R. Doering and J. C. Gadoua, Phys. Rev. Lett. 69, 2318 (1992)], and passage through modulating channels. Based on the general properties of the mean exit time, we obtain a simple solution for a coupled "birth" and "death" case that exhibits resonant activation. Within this exactly solvable model we derive analytically the optimal fluctuating rate, which is sensitive to the initial condition and scales as 1/n, where n is the system size. Our approach unifies a number of escape problems and points towards the generality of resonant activation.     

Effect of two asymmetries on current of a Brownian particle

A Brownian particle in an asymmetric periodic potential and subjected to an asymmetric dichotomous noise was investigated. In the frame of Fokker-Planck equation, exact expression of current of the system was derived. By means of numerical calculations, the results indicate that: (i) as the symmetry of either potential or noise is broken, a steady current will form; (ii) as the two symmetries are broken simultaneously, the current does not always appear, dependent on values of symmetric parameters of the potential and the noise; (iii) the current exhibits non-monotonic behavior as a function of symmetric parameter of the potential, while monotonic behavior as a function of symmetric parameter of the noise; (iv) in the case the potential symmetry is not broken seriously, the current is greatly influenced on by the noise symmetric parameter; (v) absolute values of the current as a function of height of potential barrier first increase then approach to saturation as the spatial potential is symmetric, while varies monotonically as the dichotomous noise is symmetric. In addition, the planes of the two symmetric parameters, which determine directions of the current, are drawn.     

Macroscopic resonant tunneling in an rf-SQUID flux qubit

We have observed the macroscopic resonant tunneling of magnetic flux between macroscopically distinct quantum states in a superconducting flux qubit.The dependences of the macroscopic resonant tunneling on the barrier height of the potential well,the flux bias and the initial state are investigated.Detailed measurements of the tunneling rate as a function of the flux bias reveal the feature of the quantum noise in the superconducting flux qubit.     

Stochastic resonance in a monostable system driven by square-wave signal and dichotomous noise

<正>This paper investigates the stochastic resonance in a monostable system driven by square-wave signal,asymmetric dichotomous noise as well as by multiplicative and additive white noise.By the use of the properties of the dichotomous noise,it obtains the expressions of the signal-to-noise ratio under the adiabatic approximation condition.It finds that the signal-to-noise ratio is a non-monotonic function of the asymmetry of the dichotomous noise,and which varies non-monotonously with the intensity of the multiplicative and additive noise as well as the system parameters.Moreover, the signal-to-noise ratio depends on the correlation rate and intensity of the dichotomous noise.     

Microscopic model of critical current noise in Josephson junctions

We present a simple microscopic model to show how fluctuating two-level systems in a Josephson junction tunnel barrier of thickness L can modify the potential energy of the barrier and produce critical current noise spectra. We find low frequency 1/f noise that goes as L5. Our values are in good agreement with recent experimental measurements of critical current noise in Al/AlOx/Al Josephson junctions. We also investigate the sensitivity of the noise on the nonuniformity of the tunnel barrier.