Anomalous Transport: A Deterministic Approach

Artuso, Roberto; Cristadoro, Giampaolo

doi:10.1103/physrevlett.90.244101

Cited by 43 publications

(54 citation statements)

References 31 publications

(41 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This violation of the factorization property seems to be a satisfactory explanation as to why the GDE [20] does not yield the proper Lévy diffusion in the asympotic limit. On the other hand, using the results of this section we recover the results of the numerical calculations and theoretical prediction of the fourth moments obtained by Allegrini et al [27] and, independently, by other groups [28]. To establish this latter point we integrate Eq.…”

Section: ͒͘ ͑24͒mentioning

confidence: 75%

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

et al. 2004

View full text Add to dashboard Cite

We study a two-state symmetric noise, with a given waiting time distribution ͑ ͒, and focus our attention on the connection between the four-time and two-time correlation functions. The transition of ͑ ͒ from the exponential to the nonexponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process.

show abstract

Section: ͒͘ ͑24͒mentioning

confidence: 75%

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

et al. 2004

View full text Add to dashboard Cite

show abstract

“…Surprisingly, in many cases the continuous spectrum qν(q) exhibits a bi-linear scaling (see details below). Examples for this piecewise linear behavior of qν(q) include nonlinear dynamical systems [2,[6][7][8][9], stochastic models with quenched and annealed disorder, in particular, the Lévy walk [16][17][18][19][20][21] and sand pile models [22]. Recent experiments on the active transport of polymers in the cell [15], theoretical investigation of the momentum [23] and the spatial [24] spreading of cold atoms in optical lattices and flows in porous media [25] further confirmed the generality of strong anomalous diffusion of the bi-linear type.…”

Section: Introductionmentioning

confidence: 99%

Infinite densities for Lévy walks

et al. 2014

View full text Add to dashboard Cite

Motion of particles in many systems exhibits a mixture between periods of random diffusive like events and ballistic like motion. In many cases, such systems exhibit strong anomalous diffusion, where low order moments |x(t)| q with q below a critical value qc exhibit diffusive scaling while for q > qc a ballistic scaling emerges. The mixed dynamics constitutes a theoretical challenge since it does not fall into a unique category of motion, e.g., the known diffusion equations and central limit theorems fail to describe both aspects. In this paper we resolve this problem by resorting to the concept of infinite density. Using the widely applicable Lévy walk model, we find a general expression for the corresponding non-normalized density which is fully determined by the particles velocity distribution, the anomalous diffusion exponent α and the diffusion coefficient Kα. We explain how infinite densities play a central role in the description of dynamics of a large class of physical processes and discuss how they can be evaluated from experimental or numerical data.

show abstract

“…It is also well known that a wide variety of deterministic dynamical systems exhibit anomalous diffusion [5,6,7,8]. Thus the question arises: Can deterministic dynamical systems exhibit weak ergodicity breaking?…”

Section: Introductionmentioning

confidence: 99%

Weak ergodicity breaking with deterministic dynamics

Bel¹,

Barkai²

2006

Europhys. Lett.

View full text Add to dashboard Cite

The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion deterministically. In the non-ergodic phase non-trivial distribution of the fraction of occupation times is obtained. The visitation fraction remains uniform even in the non-ergodic phase. In this sense the non-ergodicity is quantified, leading to a statistical mechanical description of the system even though it is not ergodic.

show abstract

Anomalous Transport: A Deterministic Approach

Cited by 43 publications

References 31 publications

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

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

Infinite densities for Lévy walks

Weak ergodicity breaking with deterministic dynamics

Contact Info

Product

Resources

About