TY - JOUR

T1 - Trace of anomalous diffusion in a biased quenched trap model

AU - Akimoto, Takuma

AU - Saito, Keiji

N1 - Funding Information:
T.A. was supported by a JSPS Grant-in-Aid for Scientific Research (Grant No. JP18K03468) and K.S. was supported by JSPS Grants-inAid for Scientific Research (Grant No. JP17K05587).
Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/4

Y1 - 2020/4

N2 - Diffusion in a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We show several transition points at which sample-to-sample fluctuations of the drifts or the diffusion coefficients remain large even when the system size becomes large, i.e., non-self-averaging. Moreover, we find that the disorder average of the diffusion coefficient diverges or becomes 0 when the corresponding annealed model generates superdiffusion or subdiffusion, respectively. This result implies that anomalous diffusion in an annealed model is traced by anomaly of the diffusion coefficients in the corresponding quenched model.

AB - Diffusion in a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We show several transition points at which sample-to-sample fluctuations of the drifts or the diffusion coefficients remain large even when the system size becomes large, i.e., non-self-averaging. Moreover, we find that the disorder average of the diffusion coefficient diverges or becomes 0 when the corresponding annealed model generates superdiffusion or subdiffusion, respectively. This result implies that anomalous diffusion in an annealed model is traced by anomaly of the diffusion coefficients in the corresponding quenched model.

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U2 - 10.1103/PhysRevE.101.042133

DO - 10.1103/PhysRevE.101.042133

M3 - Article

C2 - 32422836

AN - SCOPUS:85084539127

SN - 1063-651X

VL - 101

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

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

IS - 4

M1 - 042133

ER -