TY - JOUR

T1 - Distributional behaviors of time-averaged observables in the Langevin equation with fluctuating diffusivity

T2 - Normal diffusion but anomalous fluctuations

AU - Akimoto, Takuma

AU - Yamamoto, Eiji

N1 - Funding Information:
T.A. was partially supported by a Grant-in-Aid for Young Scientists (B) (Grant No. 26800204). E.Y. was funded by MEXT Grant-in-Aid for the Program for Leading Graduate Schools.
Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/6/6

Y1 - 2016/6/6

N2 - 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.

AB - 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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U2 - 10.1103/PhysRevE.93.062109

DO - 10.1103/PhysRevE.93.062109

M3 - Article

AN - SCOPUS:85004098372

VL - 93

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 6

M1 - 062109

ER -