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Non-Gaussian normal diffusion in low dimensional systems

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Abstract

Brownian particles suspended in disordered crowded environments often exhibit non-Gaussian normal diffusion (NGND), whereby their displacements grow with mean square proportional to the observation time and non-Gaussian statistics. Their distributions appear to decay almost exponentially according to “universal” laws largely insensitive to the observation time. This effect is generically attributed to slow environmental fluctuations, which perturb the local configuration of the suspension medium. To investigate the microscopic mechanisms responsible for the NGND phenomenon, we study Brownian diffusion in low dimensional systems, like the free diffusion of ellipsoidal and active particles, the diffusion of colloidal particles in fluctuating corrugated channels and Brownian motion in arrays of planar convective rolls. NGND appears to be a transient effect related to the time modulation of the instantaneous particle’s diffusivity, which can occur even under equilibrium conditions. Consequently, we propose to generalize the definition of NGND to include transient displacement distributions which vary continuously with the observation time. To this purpose, we provide a heuristic one-parameter function, which fits all time-dependent transient displacement distributions corresponding to the same diffusion constant. Moreover, we reveal the existence of low dimensional systems where the NGND distributions are not leptokurtic (fat exponential tails), as often reported in the literature, but platykurtic (thin sub-Gaussian tails), i.e., with negative excess kurtosis. The actual nature of the NGND transients is related to the specific microscopic dynamics of the diffusing particle.

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Acknowledgements

Y.L. was supported by the NSF China under Grant Nos. 11875201 and 11935010. P.K.G. was supported by SERB Start-up Research Grant (Young Scientist) No. YSS/2014/000853, and the UGC-BSR Start-Up Grant No. F.30-92/2015.

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Authors and Affiliations

  1. Center for Phononics and Thermal Energy Science, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China

    Qingqing Yin, Yunyun Li & Fabio Marchesoni

  2. Dipartimento di Fisica, Università di Camerino, I-62032, Camerino, Italy

    Fabio Marchesoni

  3. Department of Chemistry, Presidency University, Kolkata, 700073, India

    Subhadip Nayak & Pulak K. Ghosh

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  1. Qingqing Yin
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  2. Yunyun Li
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  5. Pulak K. Ghosh
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Correspondence to Yunyun Li, Fabio Marchesoni or Pulak K. Ghosh.

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arXiv: 2101.06875. This article can also be found at https://doi.org/10.1007/s11467-020-1022-0.

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Yin, Q., Li, Y., Marchesoni, F. et al. Non-Gaussian normal diffusion in low dimensional systems. Front. Phys. 16, 33203 (2021). https://doi.org/10.1007/s11467-020-1022-0

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