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

Abstract

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.

A Novel & Stable Stochastic-Mean-Field-Game for Lossy Source-Coding Paradigms: A Many-Body-Theoretic Perspective

“…Step 1: Harmony of the Fluctuations 14 Cauchy-Kovalevskaya Theorem 15 principally indicates that if F(U(t, R(t))) is analytic in the vicinity of the point pair (t 0 , R 0 ), then, also U(t, R(t)) is analytic there. The analyticity of F(U(t, R(t))) is proven following the smoothness of the HJB.…”

“…Moreover, the Nash-equilibria may be far from Paretooptimal 19 sets [32]. Therefore, one may also require to 14 See e.g. [28] to understand that harmony of the fluctuations what it is.…”

Single-file transport in periodic potentials: The Brownian asymmetric simple exclusion process

“…Further direct observation was possible in colloidal experiments by optical imaging [16]. The aspect of subdiffusion was further elaborated in connection with general theories of anomalous transport [17], including descriptions in terms of fractional Brownian motion [18], effects of initial and boundary conditions [19,20], external force fields [21], time-varying potentials [22], first-passage time distributions [23][24][25], and partial overtaking of particles [26][27][28].…”

The effect of soft repulsive interactions on the diffusion of particles in quasi-one-dimensional channels: A hopping time approach

“…where F x is the mobility factor. 24,25 As the channel becomes wider, the particles are able to pass each other, and the system exhibits a dynamical transition or crossover from SFD to normal diffusion, 5,8,[26][27][28] where the MSD increases linearly in time in the long time limit. However, in the crossover regime, hopping events are rare because particles must overcome an entropic barrier caused by a restriction in configuration space as they attempt to pass.…”