Length Scales in Brownian yet Non-Gaussian Dynamics
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 reg...
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| Main Authors: | , , , |
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| Format: | article |
| Language: | EN |
| Published: |
American Physical Society
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/39e94b29a290409788c79ef30545653c |
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| Summary: | 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∼t^{1/3} in three dimensions and λ∼t^{1/2} 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. |
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