Fractional kinetics emerging from ergodicity breaking in random media

Abstract

We present a modelling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments in living cells, such as ergodicity breaking, p-variation and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the length scale, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from non-fractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.

arXiv commentExtended version of arXiv:1508.01361: Gianni Pagnini, Daniel Molina-García, Tuan Minh Pham, Carlo Manzo, Paolo Paradisi, Ergodicity breaking in random media and the foundation of fractional kinetics

References in corpus (19)

• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
• Ergodic Properties of Fractional Brownian-Langevin Motion
• Memory and Chaos Effects in Spin Glasses
• Stochastic Ergodicity Breaking: a Random Walk Approach
• Non-diffusive transport in plasma turbulence: a fractional diffusion approach
• Nonergodic Subdiffusion from Brownian Motion in an Inhomogeneous Medium
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Aging dynamics in a colloidal glass of Laponite
• Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation
• Lévy flights of photons in hot atomic vapours
• Aging Correlation Functions for Blinking Nano-Crystals, and Other On - Off Stochastic Processes
• Characterizations and simulations of a class of stochastic processes to model anomalous diffusion
• Non-Markovian diffusion equations and processes: analysis and simulations
• Fluorescence intermittency in blinking quantum dots: renewal or slow modulation?
• Subordination Pathways to Fractional Diffusion
• Short note on the emergence of fractional kinetics

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