Resonant activation in the presence of nonequilibrated baths

Dybiec, Bartłomiej; Gudowska–Nowak, Ewa

doi:10.1103/physreve.69.016105

Cited by 68 publications

(67 citation statements)

References 51 publications

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“…In the following we shall omit cases when α = 1 with β = 0. In fact, this parameter set is known to induce instabilities in the numerical evaluation of corresponding trajectories [13,14,20,21,23].…”

Section: Escape In a Double Well: Survival Probability And Mean mentioning

confidence: 99%

“…The role of reflection, which in the case of a free diffusion [8] has been assured by wrapping the hitting (or crossing) trajectory around the boundary location, while preserving its assigned length, see in Ref. [8,23], is taken over naturally here by the confining potential walls of the symmetric double well. The details of our employed numerical scheme for stochastic differential equations driven by Lévy white noise has been detailed elsewhere [8].…”

Section: Escape In a Double Well: Survival Probability And Mean mentioning

confidence: 99%

“…using the standard techniques of integration of stochastic differential equation with respect to the Lévy stable PDFs [8,13,14,20,21,22,23]. The first passage time problem has been analyzed as τ = inf{t ≥ 0 | x(t) ≥ x b } with trajectories x(t) starting at x = x 0 and subject to corresponding boundary conditions.…”

Section: Escape In a Double Well: Survival Probability And Mean mentioning

confidence: 99%

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Escape driven byα-stable white noises

2007

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We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by white Lévy noise in a dynamical regime where inertial effects can safely be neglected. The behavior of escaping trajectories from one well to another is investigated by pointing to the special character that underpins the noise-induced discontinuity which is caused by the generalized Brownian paths that jump beyond the barrier location without actually hitting it. This fact implies that the boundary conditions for the mean first passage time (MFPT) are no longer determined by the well-known local boundary conditions that characterize the case with normal diffusion. By numerically implementing properly the set up boundary conditions, we investigate the survival probability and the average escape time as a function of the corresponding Lévy white noise parameters. Depending on the value of the skewness β of the Lévy noise, the escape can either become enhanced or suppressed: a negative asymmetry β causes typically a decrease for the escape rate while the rate itself depicts a non-monotonic behavior as a function of the stability index α which characterizes the jump length distribution of Lévy noise, with a marked discontinuity occurring at α = 1. We find that the typical factor of "two" that characterizes for normal diffusion the ratio between the MFPT for well-bottom-to-well-bottom and well-bottom-tobarrier-top no longer holds true. For sufficiently high barriers the survival probabilities assume an exponential behavior. Distinct non-exponential deviations occur, however, for low barrier heights.

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Section: Escape In a Double Well: Survival Probability And Mean mentioning

confidence: 99%

Section: Escape In a Double Well: Survival Probability And Mean mentioning

confidence: 99%

Section: Escape In a Double Well: Survival Probability And Mean mentioning

confidence: 99%

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Escape driven byα-stable white noises

2007

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“…The sample trajectories x(t) have been obtained by a direct integration of the Langevin equation (2) using the standard techniques of integration of stochastic differential equations with respect to the Lévy stable PDFs [16,17,25,26] …”

Section: Modelmentioning

confidence: 99%

“…The present work overviews properties of Lévy flights in external potentials with a focus on astonishing aspects of noise-induced phenomena [13,14,15] like resonant activation (RA), stochastic resonance (SR) and dynamic hysteresis [16,17,18,19,20]. In particular, the persistency of the SR occurrence is examined within a continuous and a two-state description of the generic system [18] composed of a test particle moving in the double well-potential and subject to the action of deterministic, periodic perturbations and α-stable Lévy type noises.…”

Section: Introductionmentioning

confidence: 99%

Lévy stable noise-induced transitions: stochastic resonance, resonant activation and dynamic hysteresis

Dybiec¹,

Gudowska–Nowak²

2009

J. Stat. Mech.

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A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the existence of timescale separation between the dynamics of the measured observable and the typical timescale of the noise allows external fluctuations to be modeled as temporally uncorrelated and therefore white. However, in many natural phenomena the assumptions concerning the abovementioned properties of "Gaussianity" and "whiteness" of the noise can be violated. In this context, in contrast to the spatiotemporal coupling characterizing general forms of non-Markovian or semi-Markovian Lévy walks, so called Lévy flights correspond to the class of Markov processes which still can be interpreted as white, but distributed according to a more general, infinitely divisible, stable and non-Gaussian law. Lévy noise-driven non-equilibrium systems are known to manifest interesting physical properties and have been addressed in various scenarios of physical transport exhibiting a superdiffusive behavior. Here we present a brief overview of our recent investigations aimed to understand features of stochastic dynamics under the influence of Lévy white noise perturbations. We find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by non-Gaussian, heavy-tailed fluctuations with infinite variance.

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