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Article

Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking

1
Department of Mechanical and Physical Engineering, Tottori University, Tottori 680-8552, Japan
2
Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(8), 565; https://doi.org/10.3390/e20080565
Received: 7 June 2018 / Revised: 16 July 2018 / Accepted: 16 July 2018 / Published: 2 August 2018
(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)
Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as the particles are constantly pushed back by their neighbors. Since this “cage effect” emerges from many-body dynamics involving spatiotemporally correlated motions, the slow diffusion should be understood not simply as a one-body problem but as a part of collective dynamics, described in terms of space–time correlations. Such collective dynamics are illustrated here by calculations of the two-particle displacement correlation in a system of repulsive Brownian particles confined in a (quasi-)one-dimensional channel, whose subdiffusive behavior is known as the single-file diffusion (SFD). The analytical calculation is formulated in terms of the Lagrangian correlation of density fluctuations. In addition, numerical solutions to the Langevin equation with large but finite interaction potential are studied to clarify the effect of overtaking. In the limiting case of the ideal SFD without overtaking, correlated motion with a diffusively growing length scale is observed. By allowing the particles to overtake each other, the short-range correlation is destroyed, but the long-range weak correlation remains almost intact. These results describe nested space–time structure of cages, whereby smaller cages are enclosed in larger cages with longer lifetimes. View Full-Text
Keywords: caged dynamics; stochastic processes; collective motion; single-file diffusion; normal and anomalous diffusion; displacement correlation; overtaking; hopping rate; label variable; Dean–Kawasaki equation caged dynamics; stochastic processes; collective motion; single-file diffusion; normal and anomalous diffusion; displacement correlation; overtaking; hopping rate; label variable; Dean–Kawasaki equation
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MDPI and ACS Style

Ooshida, T.; Goto, S.; Otsuki, M. Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking. Entropy 2018, 20, 565. https://doi.org/10.3390/e20080565

AMA Style

Ooshida T, Goto S, Otsuki M. Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking. Entropy. 2018; 20(8):565. https://doi.org/10.3390/e20080565

Chicago/Turabian Style

Ooshida, Takeshi, Susumu Goto, and Michio Otsuki. 2018. "Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking" Entropy 20, no. 8: 565. https://doi.org/10.3390/e20080565

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