Colored non-Gaussian noise driven open systems: Generalization of Kramers’ theory with a unified approach

Baura, Alendu; Sen, Monoj Kumar; Goswami, Gurupada; Bag, Bidhan Chandra

doi:10.1063/1.3521394

Cited by 34 publications

(11 citation statements)

References 61 publications

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“…Before elaborating further on our own ideas, we point out that there is currently a large interest in non-Gaussian noises among the physics community. Baura et al studied the escape rate of a particle from a metastable state subject to non-Gaussian noises defined by a type of Langevin equation [6]. Milotti has shown that non-Gaussianity arises very easily when analyzing data collected from relatively small samples using statistical estimators that are asymptotically Gaussian [7].…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussian stochastic dynamics of spins and oscillators: A continuous-time random walk approach

Packwood

Tanimura

2011

Phys. Rev. E

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We consider separately a spin and an oscillator that are coupled to their environment. After a finite interval of random length, the state of the environment changes, and each change causes a random change in the resonance frequency of the spin or vibrational frequency of the oscillator. Mathematically, the evolution of these frequencies is described by a continuous-time random walk. Physically, the stochastic dynamics can be understood as non-Gaussian because the frequency of the system and state of the environment change on comparable time scales. These dynamics are also nonstationary, and so might apply to a nonequilibrium environment. The resonance and vibrational spectra of the spin and oscillator, as well as the ensemble-averaged displacement of the oscillator, are investigated in detail. We observe some distinct non-Gaussian features of the dynamics, such as the narrow, leptokurtic shape of the resonance spectrum of the spin and beating of the average oscillator displacement. The convergence to Gaussian dynamics as changes in the environment occur with increasing frequency is also considered. Among other results, we observe narrowing of the resonance and vibrational lines in the Gaussian limit due to a weakening of the system-environment interaction.

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Section: Introductionmentioning

confidence: 99%

Non-Gaussian stochastic dynamics of spins and oscillators: A continuous-time random walk approach

Packwood

Tanimura

2011

Phys. Rev. E

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“…representing the motion of the point P (see (12)) under forces (15) and (16). In this regard, let the initial position be x (0) ∈ (−1, 1) and let it be any initial velocity v (0) ∈ (−∞, ∞).…”

Section: Average Exit Timementioning

confidence: 99%

“…Namely, the Tsallis q-statistics is obtained in the case of quadratic V (x). For such quadratic potentials, the resulting non-Gaussian bounded process (as well as the case q > 1) has been investigated in a series of influential papers [7][8][9][10][11][12] showing that the departure from the Gaussian PDF in the noise induces remarkable effects in noise-induced transitions and in stochastic resonance [7][8][9]11,13]. This process is sometimes called Tsallis-Borland process [1], although it should be more precisely called the Tsallis-Stariolo-Borland (TSB) process, as we will do in the following.…”

Section: Introductionmentioning

confidence: 99%

Boundedness vs unboundedness of a noise linked to Tsallis q-statistics: The role of the overdamped approximation

Domingo

d’Onofrio

Flandoli

2017

Journal of Mathematical Physics

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An apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well, under overdamped approximation. Here, however, we show that the aforementioned procedure can be fallacious and lead to incorrect results. We indeed provide a counter-example concerning one of the most employed bounded noises, hereafter called Tsallis-Stariolo-Borland (TSB) noise, which admits the well known Tsallis q-statistics as stationary density. In fact, we show that for negative values of the Tsallis parameter q (corresponding to sufficiently large diffusion coefficient of the stochastic force), the motion resulting from the overdamped approximation is unbounded. We then investigate the cause of the failure of Kramers first type approximation, and we formally show that the solutions of the full Newtonian non-approximated model are bounded, following the physical intuition. Finally, we provide a new family of bounded noises extending the TSB noise, the boundedness of whose solutions we formally show.

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“…Another point to be noted here is that, keeping in mind the Ornstein-Uhlenbeck (OU) noise process [30], the above form of differential equation is very illuminating about non-Gaussian behavior of noise and to attend the Gaussian limit. This form was considered in different contexts in the recent past [31][32][33][34][35][36][37][38][39][40].…”

Section: The Modelmentioning

confidence: 99%

Synchronization of Nonidentical Coupled Phase Oscillators in the Presence of Time Delay and Noise

Ray

Sen

Baura

et al. 2013

Journal of Complex Systems

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We have studied in this paper the dynamics of globally coupled phase oscillators having the Lorentzian frequency distribution with zero mean in the presence of both time delay and noise. Noise may be Gaussian or non-Gaussian in characteristics. In the limit of zero noise strength, we find that the critical coupling strength (CCS) increases linearly as a function of time delay. Thus the role of time delay in the dynamics for the deterministic system is qualitatively equivalent to the effect of frequency fluctuations of the phase oscillators by additive white noise in absence of time delay. But for the stochastic model, the critical coupling strength grows nonlinearly with the increase of the time delay. The linear dependence of the critical coupling strength on the noise intensity also changes to become nonlinear due to creation of additional phase difference among the oscillators by the time delay. We find that the creation of phase difference plays an important role in the dynamics of the system when the intrinsic correlation induced by the finite correlation time of the noise is small. We also find that the critical coupling is higher for the non-Gaussian noise compared to the Gaussian one due to higher effective noise strength.

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Colored non-Gaussian noise driven open systems: Generalization of Kramers’ theory with a unified approach

Cited by 34 publications

References 61 publications

Non-Gaussian stochastic dynamics of spins and oscillators: A continuous-time random walk approach

Non-Gaussian stochastic dynamics of spins and oscillators: A continuous-time random walk approach

Boundedness vs unboundedness of a noise linked to Tsallis q-statistics: The role of the overdamped approximation

Synchronization of Nonidentical Coupled Phase Oscillators in the Presence of Time Delay and Noise

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