Length Scales in Brownian yet Non-Gaussian Dynamics
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American Physical Society
Miotto, J. M... [et al.] (2021). Length scales in Brownian yet non-Gaussian dynamics. Physical Review X, 11(3), 031002. DOI: [10.1103/PhysRevX.11.031002]
SponsorshipGerman Research Foundation (DFG) ME 1535/7-1; European Commission through the Marie Sklodowska-Curie Individual Fellowship 840195
According to the classical theory of Brownian motion, the mean-squared displacement of diffusing particles evolves linearly with time, whereas the distribution of their displacements is Gaussian. However, recent experiments on mesoscopic particle systems have discovered Brownian yet non-Gaussian regimes where diffusion coexists with an exponential tail in the distribution of displacements. Here we show that, contrary to the present theoretical understanding, the length scale λ associated with this exponential distribution does not necessarily scale in a diffusive way. Simulations of Lennard-Jones systems reveal a behavior λ ∼ t1=3 in three dimensions and λ ∼ t1=2 in two dimensions. We propose a scaling theory based on the idea of hopping motion to explain this result. In contrast, simulations of a tetrahedral gelling system, where particles interact by a nonisotropic potential, yield a temperature-dependent scaling of λ. We interpret this behavior in terms of an intermittent hopping motion. Our findings link the Brownian yet non-Gaussian phenomenon with generic features of glassy dynamics and open new experimental perspectives on the class of molecular and supramolecular systems whose dynamics is ruled by rare events.