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Brownian particles in a periodic potential corrugated by disorder: Anomalous diffusion and ergodicity breaking

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  • Guo, Wei
  • Liu, Ying-Zhou
  • Huang, Fei-Jie
  • Shi, Hong-Da
  • Du, Lu-Chun

Abstract

We present the anomalous diffusion and ergodicity breaking surviving in a finite time scale, as an overdamped Brownian particle in one-dimensional potentials, consisting of periodic and random components. By virtue of numerical simulations, we demonstrate the non-ergodic superdiffusion, non-ergodic subdiffusion, and non-ergodic uncertain diffusion, which are identified by the observable quantities (the mean squared displacement and ergodicity breaking parameter) averaged over quenched disorder and noise realizations in this system. Moreover, the analytical expression of ergodicity recovery time below and above which the system, respectively, exhibits non-ergodic and ergodic behaviors approximatively, is obtained. These results may be beneficial in further understanding the biological processes, such as an ergodic and a non-ergodic process coexisting in the plasma membrane and the subdivision of larger molecules or tracers in living cells.

Suggested Citation

  • Guo, Wei & Liu, Ying-Zhou & Huang, Fei-Jie & Shi, Hong-Da & Du, Lu-Chun, 2023. "Brownian particles in a periodic potential corrugated by disorder: Anomalous diffusion and ergodicity breaking," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923008044
    DOI: 10.1016/j.chaos.2023.113903
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    References listed on IDEAS

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    1. Gorka Muñoz-Gil & Giovanni Volpe & Miguel Angel Garcia-March & Erez Aghion & Aykut Argun & Chang Beom Hong & Tom Bland & Stefano Bo & J. Alberto Conejero & Nicolás Firbas & Òscar Garibo i Orts & Aless, 2021. "Objective comparison of methods to decode anomalous diffusion," Nature Communications, Nature, vol. 12(1), pages 1-16, December.
    2. Viktor Stojkoski & Trifce Sandev & Ljupco Kocarev & Arnab Pal, 2021. "Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process," Papers 2104.01571, arXiv.org, revised Aug 2021.
    3. D. Kulikov & N. Agudov & B. Spagnolo, 2011. "Gaussian models for the distribution of Brownian particles in tilted periodic potentials," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 83(2), pages 263-269, September.
    4. Sandev, Trifce & Kocarev, Ljupco & Metzler, Ralf & Chechkin, Aleksei, 2022. "Stochastic dynamics with multiplicative dichotomic noise: Heterogeneous telegrapher’s equation, anomalous crossovers and resetting," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    5. Sandev, Trifce & Schulz, Alexander & Kantz, Holger & Iomin, Alexander, 2018. "Heterogeneous diffusion in comb and fractal grid structures," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 551-555.
    6. Shi, Hong-Da & Du, Lu-Chun & Huang, Fei-Jie & Guo, Wei, 2022. "Collective topological active particles: Non-ergodic superdiffusion and ageing in complex environments," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Henrik Seckler & Ralf Metzler, 2022. "Bayesian deep learning for error estimation in the analysis of anomalous diffusion," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
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