Dec 3 – 4, 2020
Europe/Warsaw timezone

Packets of diffusing particles exhibit universal exponential tails

Dec 3, 2020, 12:00 PM
30 minute lecture S2


Eli Barkai (Bar Ilan Univeristy)


Brownian motion is a Gaussian process described by the central limit theorem. How- ever, exponential decays of the positional probability density function $P(X, t)$ of packets of spreading random walkers, were observed in numerous situations that include glasses, live cells, and bacteria suspensions. We show that such exponential behavior is generally valid in a large class of problems of transport in random media. By extending the large deviations approach for a continuous time random walk, we uncover a general universal behavior for the decay of the density [1]. It is found that fluctuations in the number of steps of the random walker, performed at finite time, lead to exponential decay (with logarithmic corrections) of $P(X, t)$. This universal behavior also holds for short times, a fact that makes experimental observations readily achievable. Time permitting we then formulate the hitchhiker model where interacting molecules form aggregates, that lead to fluctuations in the diffusion field, and a many body mechanism for the exponential tails [2].

[1] E. Barkai and Stas Burov, Packets of diffusing particles exhibit universal exponential tails, Phys. Rev. Lett. 124, 060603 (2020).
[2] M. Hidalgo-Soria, and E. Barkai, The Hitchhiker model for Laplace diffusion processes in the cell environment, Phys. Rev. E 102, 012109 (2020).

Primary author

Eli Barkai (Bar Ilan Univeristy)

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