Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems

Spagnolo, Bernardo; Guarcello, Claudio; Magazzù, Luca; Carollo, Angelo; Adorno, Dominique Persano; Valenti, Davide

doi:10.3390/e19010020

Cited by 100 publications

(49 citation statements)

References 171 publications

(260 reference statements)

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“…The total amount of sand in the system is fixed similarly as the norm of the PDF Q(x, t) governed by Eq. (24). After a relatively short time (determined by the inverse gap, 1/(λ 0 − λ 1 ), between the two largest eigenvalues of the Fokker-Planck operator (21)), the timeindependent steady-state distribution of sand on the belts is established by balancing the sand (probability) currents caused by the three agents (i)-(iii) described above.…”

Section: B Qst(x) As a Steady-state Distribution Andmentioning

confidence: 99%

“…Quantum nonlinear effects in the unstable cubic potential are not only interesting for a fundamental comparison to their stochastic analogs, but they also open doors to quantum simulations and computation with continuous systems [7,8,83]. To derive dynamical equation (24) for the conditioned PDF Q(x, t) we first insert P (x, t) = Q(x, t)S(t) into the Fokker-Planck equation (20) for the unconditioned PDF P (x, t). After dividing the resulting equation by S(t) we obtain ∂ ∂t Q(x, t) + Q(x, t) S(t) dS dt = LQ(x, t).…”

Section: Concluding Remarks and Experimental Perspectivesmentioning

confidence: 99%

“…(20) by the second term on the left-hand side. To justify the equation (24) we need to identify the conditional probability current (25) in this second term, i.e., we need to show that 1 S(t) dS dt = J Q (a, t).…”

Section: Concluding Remarks and Experimental Perspectivesmentioning

confidence: 99%

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Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon

et al. 2018

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The trajectories of an overdamped particle in a highly unstable potential diverge so rapidly, that the variance of position grows much faster than its mean. A description of the dynamics by moments is therefore not informative. Instead, we propose and analyze local directly measurable characteristics, which overcome this limitation. We discuss the most probable particle position (position of the maximum of the probability density) and the local uncertainty in an unstable cubic potential, V(x)∼x^{3}, both in the transient regime and in the long-time limit. The maximum shifts against the acting force as a function of time and temperature. Simultaneously, the local uncertainty does not increase faster than the observable shift. In the long-time limit, the probability density naturally attains a quasistationary form. We interpret this process as a stabilization via the measurement-feedback mechanism, the Maxwell demon, which works as an entropy pump. The rules for measurement and feedback naturally arise from the basic properties of the unstable dynamics. All reported effects are inherent in any unstable system. Their detailed understanding will stimulate the development of stochastic engines and amplifiers and, later, their quantum counterparts.

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Section: B Qst(x) As a Steady-state Distribution Andmentioning

confidence: 99%

Section: Concluding Remarks and Experimental Perspectivesmentioning

confidence: 99%

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Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon

et al. 2018

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“…We plot the MFET as a function of noise intensity ε in Figure 18. Inspired by the literatures [50,51,52], we are interested in computing the MFET of the stochastic genetic model (3) starting from an unstable initial position, so we here set the exit domain is [0, 2]. We could see that the MFET has a monotonic behavior with the noise intensity ε.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

Wang

Cheng

Duan

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index β, causing a stochastic bifurcation at the non-Gaussianity index value α = 1 (i.e., it is a separating point or line for the likelihood for transcription), and achieving a turning point at the threshold value β≈-0.5 (i.e., beyond which the likelihood for transcription suddenly reversed for α values). The stochastic bifurcation and turning point phenomena do not occur in the symmetric noise case (β = 0). While in the multiplicative noise case, non-Gaussianity index value α = 1 is a separating point or line for both the MFET and the FEP. We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments in "regulating" the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes. This work offers insights for possible ways of achieving gene regulation in experimental research.

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“…Specifically, graphene stripe with anisotropically distributed on-site impurities shows Lévy flight transport in the stripe direction [6], and it has also been proposed that the particular electron-electron interaction of the graphene electronics can produce a Lévy flights distribution as a response to a laser source [5]. Moreover, it has been speculated that the anomalous premature switches affecting the switching currents in graphene-based JJs, that are likely to be unrelated to thermal fluctuations [7], could be ascribed to Lévy distributed phenomena, see Ref [8] where the nonsinusoidal potential appropriated for graphene JJs [9][10][11] has been investigated. Consequently, the response of any graphene-based device could be intrinsically affected by Lévy distributed fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Josephson-based Threshold Detector for Lévy-Distributed Current Fluctuations

et al. 2019

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We propose a threshold detector for Lévy distributed fluctuations based on a Josephson junction. The Lévy noise current added to a linearly ramped bias current results in clear changes in the distribution of switching currents out of the zero-voltage state of the junction. We observe that the analysis of the cumulative distribution function of the switching currents supplies information on both the characteristics shape parameter α of the Lévy statistics and the intensity of the fluctuations. Moreover, we discuss a theoretical model which allows to extract characteristic features of the Lévy fluctuations from a measured distribution of switching currents. In view of this results, this system can effectively find an application as a detector for a Lévy signal embedded in a noisy background. arXiv:1802.01095v3 [cond-mat.mes-hall]

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Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems

Cited by 100 publications

References 171 publications

Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon

Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

Josephson-based Threshold Detector for Lévy-Distributed Current Fluctuations

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