Resonances while surmounting a fluctuating barrier

Abstract

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.

Resonant activation in the presence of nonequilibrated baths

“…The effect is due to higher probabilities of the extreme events (large fluctuations) allowed by the Lévy statistics. Similarly to the Gaussian-bath case, a typical asymptotic behavior of the MFPT has been recovered for large and small frequencies of the dichotomous noise: for small γ MFPT tends to the average MFPTs for the both barrier configurations, while for large γ it becomes equal to the MFPT over the average potential barrier [29,31,32].…”

“…2 (lower panel). By comparison to the results obtained for a motion of a particle subject to the additive white Gaussian noise [29,30,31,32,33], the value of the MFPT is smaller and resonant activation is observed at lower frequencies γ. Moreover, for H ± = ±8, asymptotic values of MFPT estimated for γ → ∞ and γ → 0 are higher (lower) than in the corresponding white Gaussian noise case [29,30,33].…”

“…The main difference between the model considered here is a form of driving, additive fluctuations. Whereas in the previous papers mainly white Gaussian noises have been considered [29,31,32,33,34], here additive noises are assumed to be α-stable [21], that might arise from the contact with not fully equilibrated bath.…”

Scaling properties for a classical particle in a time-dependent potential well

“…20 For the classical case, in particular for systems in which a classical particle interacts with a time-dependent potential, different formalisms were developed, including treatments of the problem of a time-modulated barrier 5,21,22 and of a classical particle in a time-dependent oscillating well. 23,24 Consideration of the dynamics of these problems in the presence of noise has recently led to exact descriptions of diffusion within static single and double-square well potentials, 25,26 the introduction of an external field for twolevel systems in a classical potential, 27 a general solution of the problem of activated escape in periodically driven systems, 28 analytic solutions for the problem of a piecewise bistable potential in the limit of weak external perturbation, 29 calculation of the escape flux from a multiwell metastable potential at times preceding the formation of quasiequilibrium, 30 activation over a randomly fluctuating barrier, 31,32 and diffusion across a randomly fluctuating barrier. 33 In this paper we revisit the problem of a classical particle interacting with an infinitely deep potential well containing a periodically oscillating square well, with the aim of describing some of its scaling properties.…”

Kinetic models for stochastically modified ionic channels

“…The motivation for this study lies in our interest in noise-induced resonance-like phenomena, a subject that has been extensively investigated by physicists for some twenty years. It was found that under some conditions, potential fluctuations can lead to resonant activation [5][6][7], an effect in which the mean time to overcome a potential barrier may significantly decrease, provided the barrier height changes randomly with a characteristic time scale of the same order as the characteristic time scale t r of the intrawell processes [8]. Although resonant activation is investigated mostly as a generalization of the standard Kramers' problem [9] of Brownian diffusion, its simplest presentation by means of a discrete kinetic scheme is possible [6,10].…”