Thermal activation by power-limited coloured noise

2003

We present a study of the escape time from a metastable state in the presence of colored noise, generated by Ornstein-Uhlenbeck process. We analyze the role of the correlated noise and of unstable initial conditions of an overdamped Brownian particle on the enhancement of the average escape time as a function of the noise intensity. We observe the noise enhanced stability (NES) effect for all the initial unstable states and for all values of the correlation time τc investigated. We can distinguish two dynamical regimes characterized by: (a) a weak correlated noise and (b) a strong correlated noise, depending on the value of τc with respect to the relaxation time. With increasing τc we find : (i) a shift of the maximum of the average escape time towards higher values of noise intensity and an enhancement of the value of this maximum; (ii) a broadening of the NES region, which becomes very large in the strong colored noise regime; (iii) in this regime (b), the absence of the peculiar initial condition xc which separates the set of the initial unstable states lying into the divergency region from those which give only a nonmonotonic behavior of the average escape time. *

Physics Letters A, 1988

The brownian motion in a quartic double-well potential driven by coloured noise is investigated in the low-viscosity limit by means of analogue simulation. The dependence ofthe escape rate on the noise correlation-time~isdetermined for the conditions simulated: the escape rate decreases exponentially with increasing t 2. The relevant law is derived theoretically in the limit of vanishingly small viscosity and high potential barriers.

Physical Review E, 1993

An approach to compute the mean-first-passage time (MFPT) in bistable systems driven by colored noise is presented. The approach is valid in the limit of large but finite noise correlation time and finite noise strength, a case for which no satisfactory theory exists at present. Our approach is a modification of the fluctuating-potential theory proposed in Phys. Rev. Lett. 61, 7 (1988). Excellent agreement is found between our results for MFPT and that of the simulation results of Mannella, Palleschi, and Grigolini [Phys. Rev. A. 42, 5946 (1990)]. Interesting similarity between stochastic resonance and the colored-noise problem is brought out.

The European Physical Journal B, 2009

We have calculated the escape rate from a metastable of an open system driven by coloured non Gaussian and Gaussian thermal noise sources using the Fokker-Planck description of the stochastic process. We find that (i) the barrier crossing rate has a non-monotonic behaviour with the maximum as a function of the parameter of non-Gaussianity of the noise source; (ii) the crossing rate decreases rapidly for non Gaussian (NG) noise compared to Gaussian (G) with increasing noise correlation time; (iii) the crossing rate for NG noise reaches the limiting value before G noise. To check the validity of our approximate theoretical result we compared it with the numerical simulations and found a good agreement. Finally, we have checked that our general expression reduces to the standard Kramers' formula at an appropriate limit.

Fluctuation and Noise Letters, 2007

In this paper we have studied how barrier crossing dynamics is affected by colored additive non-Gaussian noise if the barrier fluctuates deterministically. Our investigation indicates that resonant activation(RA) is either enhanced or it becomes robust if noise characteristic is deviated from the Gaussian behavior. We find that additive colored non Gaussian noise can induce the RA-like phenomenon. Another interesting observation is that the turnover behavior persists even in presence of barrier fluctuations at finite rate. Finally, it is observed that mean first passage time(MFPT) decreases with increase of non-Gaussian characteristic of the additive colored noise for a given noise strength and noise correlation time and ultimately reaches to a limiting value. The limiting value remains almost the same if the barrier fluctuating frequency is zero or far from the resonant condition. But near the resonant condition the mean first passage time initially decreases and then increases pas...

We explore the problem of noise-enhanced stability occurring in an asymmetric double well potential when Brownian particles are driven by trichotomous noise and thermal noise in a dynamical regime where inertial effects can safely be neglected. In the stationary state, we exactly calculate the spatial density profile of the particles and the occupancy ratio between two potential wells. We show that, by conveniently choosing the system parameters, the occupancy of a metastable state is a double peaked function of thermal noise intensity. Thus, thermal noise may facilitate the occupation of the potential minima with an energy above the absolute minimum at certain finite values of temperature. The effect is more pronounced in case the kurtosis of the trichotomous noise tends to −2, i.e., in the case of dichotomous noise.

arXiv (Cornell University), 2015

Non-Gaussian noise influences many complex out-of-equilibrium systems on a wide range of scales such as quantum devices, active and living matter, and financial markets. Despite the ubiquitous nature of non-Gaussian noise, its effect on activated transitions between metastable states has so far not been understood in generality, notwithstanding prior work focusing on specific noise types and scaling regimes. Here, we present a unified framework for a general class of non-Gaussian noise, which we take as any finite-intensity noise with independent and stationary increments. Our framework identifies optimal escape paths as minima of a stochastic action, which enables us to derive analytical results for the dominant scaling of the escape rates in the weak-noise regime generalizing the conventional Arrhenius law. We show that non-Gaussian noise always induces a more efficient escape, by reducing the effective potential barrier compared to the Gaussian case with the same noise intensity. Surprisingly, for a broad class of amplitude distributions even noise of infinitesimally small intensity can induce an exponentially larger escape rate. As the underlying reason we identify the appearance of discontinuous minimal action paths, for which escape from the metastable state involves a finite jump. We confirm the existence of such paths by calculating the prefactor of the escape rate, as well as by numerical simulations. Our results highlight fundamental differences in the escape behaviour of systems subject to thermal and non-thermal fluctuations, which can be tuned to optimize switching behaviour in metastable systems.

http://www.sciencedirect.com/science/article/pii/S0378437106008168 . 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) of additive colored noise having fixed variance have been analyzed. Beyond a critical value of τ2 the MFPT increases for a given rate of increase of noise strength with τ2 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.

http://iopscience.iop.org/1742-5468/2008/02/P02014?fromSearchPage=true . We have studied the quantum stochastic dynamics of a system whose interaction with a reservoir is non-linear in system coordinates. In addition, the bath particles are driven by external noise with finite correlation. The effects of the space dependent friction and correlation of the external noise on the rate of decay of a particle from a metastable well have been examined. At a critical value of the correlation, the variation of the quantum decay rate versus the external noise strength exhibits a resonance

2000

Activated escape is investigated for systems that are driven by noise whose power spectrum peaks at a finite frequency. Analytic theory and analog and digital experiments show that the system dynamics during escape exhibit a symmetry-breaking transition as the width of the fluctuational spectral peak is varied. For double-well potentials, even a small asymmetry may result in a parametrically large difference of the activation energies for escape from different wells.

Physical review. A, 1987

The problem of the activation rate in overdamped (Smoluchowski) bistable oscillators subject to colored noise with correlation time w is discussed in detail. We show that a nontrivial prescription (the so-called Hanggi's ansatz) for truncating the~expansion of the Fokker-Planck equation describing this class of processes can reproduce the results of both analog and digital simulations in the regime of large activation energies. Such a prescription predicts a~dependence of the Arrhenius factor appearing in the determination of the relevant mean first-passage time but cannot be applied to reproduce the correct~dependence of the prefactor which may be dominant in the regime of rather small activation energies. An improved expression for the mean first-passage time in a double-well potential coupled to a time-correlated thermal bath is obtained on generalizing Kramer's theory of the activation rates accordingly. The new determination of the mean firstpassage time is meant to bridge previous approximations only valid in the regime of either large or small activation energies.

Lecture Notes in Physics, 2000

We present a quantum network approach to the treatment of thermal and quantum fluctuations in measurement devices. The measurement is described as a scattering process of input fluctuations towards output ones. We present the results obtained with this method for the treatment of a cold damped capacitive accelerometer.

The Journal of Chemical Physics, 2011

In this paper we have calculated escape rate from a meta stable state in the presence of both colored internal thermal and external nonthermal noises. For the internal noise we have considered usual Gaussian distribution but the external noise may be Gaussian or non-Gaussian in characteristic. The calculated rate is valid for low noise strength of non-Gaussian noise such that an effective Gaussian approximation of non-Gaussian noise wherein the higher order even cumulants of order "4" and higher are neglected. The rate expression we derived here reduces to the known results of the literature, as well as for purely external noise driven activated rate process. The latter exhibits how the rate changes if one switches from non-Gaussian to Gaussian character of the external noise.

Physical Review E, 2015

In this paper we present properties of an external colored cross-correlated noise-driven Brownian system which is coupled to a thermal bath. Multiplicative cross-correlated noises can stabilize the transition state. Thus by monitoring the interference between the noises one can understand the mechanism of a chemical reaction. At the same time, we have investigated how the interference affects the barrier-crossing dynamics. In its presence breakdown of the Arrhenius result occurs. The breakdown becomes prominent if the multiplicative noises become additive in nature. We have also investigated how the power law behavior of the rate constant as a function of damping strength is affected by the properties of external colored noises. Furthermore, we have observed that multiplicative colored cross-correlated noises can induce the resonant activation phenomenon.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2009

We present a study of the escape time from a metastable state of an overdamped Brownian particle, in the presence of colored noise generated by Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity. We observe the noise enhanced stability effect for all the initial unstable states used, and for all values of the correlation time τc investigated. We can distinguish two dynamical regimes characterized by weak and strong correlated noise respectively, depending on the value of τc with respect to the relaxation time of the system.