Non-Poisson dichotomous noise: Higher-order correlation functions and aging

Allegrini, Paolo; Grigolini, Paolo; Palatella, Luigi; West, Bruce J.

doi:10.1103/physreve.70.046118

Cited by 23 publications

(34 citation statements)

References 37 publications

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“…The authors of Ref. [15] prove that in the renewal non-Poisson case, this factorization property is violated, thereby yielding the breakdown of the corresponding GME.…”

Section: Renewal Agingmentioning

confidence: 99%

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Absorption and emission in the non-poisson case: the theoretical challenge posed by renewal aging

Aquino

Palatella²,

Grigolini³

2005

Braz. J. Phys.

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This short paper aims at clarifying the physical meaning of a previous pubblication [G. Aquino, P. Grigolini, L. Palatella, Phys. Rev. Lett. 93 050601 (2004)], using later, although very recent, results. This has to do with the challenges posed to the Kubo-Anderson (KA) theory, and more in general to any form of Liouville-like approach, by the discovery of intermittent resonant fluorescence with a non-exponential distribution of waiting times. We show that to properly address the treatment of these problems the KA theory, valid in the case of aged systems, should be extended to aging systems, aging for a very extended time period or even forever, being a crucial consequence of non-Poisson statistics. This ambitious goal can be realized if we adopt the assumption that real wave-function collapses occur.

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“…The authors of Ref. [15] prove that in the renewal non-Poisson case, this factorization property is violated, thereby yielding the breakdown of the corresponding GME.…”

Section: Renewal Agingmentioning

confidence: 99%

“…The demonstration of Ref. [15] runs as follows. The construction of the Generalized Master Equation (GME) produced by dichotomous fluctuation is made possible by the factorization condition that, in the case with no bias, for the fourth-order correlation function reads:…”

Section: Renewal Agingmentioning

confidence: 99%

Absorption and emission in the non-poisson case: the theoretical challenge posed by renewal aging

Aquino

Palatella²,

Grigolini³

2005

Braz. J. Phys.

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“…Moreover, in a number of systems the kinetics is anomalously long time tailed which implies long time memory in them. The anomaly manifests itself in some interesting phenomena such as non-ergodicity [7,8,9], aging [10,11,12], slow relaxation [7,13,14,15], etc.…”

Section: Introductionmentioning

confidence: 99%

Non-Markovian stochastic Liouville equation and its Markovian representation: Extensions of the continuous-time random-walk approach

Shushin

2008

Phys. Rev. E

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Some specific features and extensions of the continuous time random walk (CTRW) approach are analyzed in detail within the Markovian representation (MR) and CTRW-based non-Markovian stochastic Liouville equation (SLE). In the MR CTRW processes are represented by multidimensional Markovian ones. In this representation the probability distribution function (PDF) W (t) of fluctuation renewals is associated with that of reoccurrences in a certain jump state of some Markovian controlling process. Within the MR the non-Markovian SLE, which describes the effect of CTRW-like noise on relaxation of dynamic and stochastic systems, is generalized to take into account the influence of relaxing systems on statistical properties of noise. The generalized nonMarkovian SLE is applied to study two modifications of the CTRW approach. One of them considers the cascaded CTRWs in which the controlling process is actually CTRW-like one controlled by another CTRW process, controlled in turn by the third one, etc. Within the MR simple expression for the PDF W (t) of total controlling process is obtained in terms of Markovian variants of controlling PDFs in the cascade. The expression is shown to be especially simple and instructive in the case of anomalous processes determined by long time tailed W (t). The cascaded CTRWs can model the effect of complexity of a system on relaxation kinetics (in glasses, fractals, branching media, ultrametric structures, etc.). Another CTRW-modification describes the kinetics of processes governed by fluctuating W (t). Within the MR the problem is analyzed in a general form without restrictive assumptions on correlations of PDFs of consecutive renewals. The analysis shows that W (t) can strongly affect the kinetics of the process. Possible manifestations of this effect are discussed.

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“…More recently, P. Allegrini et al studied non-Poisson dichotomous noise [10]. Their paper is particularly relevant here, as a particular case of non-Poisson dichotomous noise is studied below in some detail, namely a generalized RTS where waiting times between consecutive level changes follow a Mittag-Leffler distribution.…”

Section: Introductionmentioning

confidence: 99%

A random telegraph signal of Mittag-Leffler type

Ferraro¹,

Manzini²,

Masoero³

et al. 2009

Physica A: Statistical Mechanics and its Applications

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A general method is presented to explicitly compute autocovariance functions for non-Poisson dichotomous noise based on renewal theory. The method is specialized to a random telegraph signal of Mittag-Leffler type. Analytical predictions are compared to Monte Carlo simulations.Non-Poisson dichotomous noise is non-stationary and standard spectral methods fail to describe it properly as they assume stationarity.

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Non-Poisson dichotomous noise: Higher-order correlation functions and aging

Cited by 23 publications

References 37 publications

Absorption and emission in the non-poisson case: the theoretical challenge posed by renewal aging

Absorption and emission in the non-poisson case: the theoretical challenge posed by renewal aging

Non-Markovian stochastic Liouville equation and its Markovian representation: Extensions of the continuous-time random-walk approach

A random telegraph signal of Mittag-Leffler type

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