Distributional behaviors of time-averaged observables in the Langevin equation with fluctuating diffusivity

Normal diffusion but anomalous fluctuations

Takuma Akimoto, Eiji Yamamoto

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We consider the Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously over time, in order to study fluctuations of time-averaged observables in temporally heterogeneous diffusion processes. We find that the time-averaged mean-square displacement (TMSD) can be represented by the occupation time of a state in the asymptotic limit of the measurement time and hence occupation time statistics is a powerful tool for calculating the TMSD in the model. We show that the TMSD increases linearly with time (normal diffusion) but the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges, i.e., intrinsic nonequilibrium processes. Thus, we find that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.

Original languageEnglish
Article number062109
JournalPhysical Review E
Volume93
Issue number6
DOIs
Publication statusPublished - 2016 Jun 6

Fingerprint

Anomalous Diffusion
Langevin Equation
Diffusivity
diffusivity
Fluctuations
Mean Square
Diffusion Coefficient
Occupation Time
diffusion coefficient
occupation
Particle Tracking
Sojourn Time
Heterogeneous Environment
Asymptotic Limit
Diverge
Diffusion Process
Non-equilibrium
Anomalous
Linearly
Trajectory

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

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abstract = "We consider the Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously over time, in order to study fluctuations of time-averaged observables in temporally heterogeneous diffusion processes. We find that the time-averaged mean-square displacement (TMSD) can be represented by the occupation time of a state in the asymptotic limit of the measurement time and hence occupation time statistics is a powerful tool for calculating the TMSD in the model. We show that the TMSD increases linearly with time (normal diffusion) but the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges, i.e., intrinsic nonequilibrium processes. Thus, we find that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.",
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