First passage times for a tracer particle in single file diffusion and fractional Brownian motion

The Journal of Chemical Physics
Lloyd P Sanders, Tobias Ambjörnsson

Abstract

We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm-defined by the Hurst parameter, H ∈ (0, 1)] is studied, of interest here as fBm and SFD systems belong to the same universality class. Extensive stochastic (non-Markovian) SFD and fBm simulations are performed and compared to two analytical Markovian techniques: the method of images approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that the MIA cannot approximate well any temporal scale of the SFD FPTD. Our exact inversion of the Willemski-Fixman integral equation captures the long-time power-law exponent, when H ≥ 1/3, as predicted by Molchan [Commun. Math. Phys. 205, 97 (1999)] for fBm. When H < 1/3, which includes homogeneous SFD (H = 1/4), and heterogeneous SFD (H < 1/4), the WFA fails to agree with any temporal scale of the simulations and Molchan's long-time result. SFD systems are compared to their fBm count...Continue Reading

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Citations

Mar 15, 2013·The Journal of Chemical Physics·T GuérinR Voituriez
Apr 26, 2013·The Journal of Chemical Physics·Artem Ryabov
Dec 2, 2017·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Shivangi Sharma, Parbati Biswas
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Jul 7, 2019·Nature Communications·N LevernierT Guérin
Nov 28, 2019·Physical Review. E·Thomas VojtaRalf Metzler
May 20, 2020·Physical Review. E·Benjamin Walter, Kay Jörg Wiese
Dec 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel CamposVicenç Méndez
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Artem Ryabov, Petr Chvosta
Oct 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Leibovich, E Barkai

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