Clustering in anomalous files of independent particles

Abstract

The dynamics of classical hard particles in a quasi one-dimensional channel were studied since the 1960s and used for explaining processes in chemistry, physics and biology and in applications. Here we show that in a previously un-described file made of anomalous, independent, particles (with jumping times taken from, ψ_α (t) t^(-1-α), 0<α<1), particles form clusters. At steady state, the percentage of particles in clusters is about, \surd(1-α^3), only for anomalous α, characterizing the criticality of a phase transition. The asymptotic mean square displacement per particle in the file is about, log^2(t). We show numerically that this exciting phenomenon of a phase transition is very stable, and relate it with the mysterious phenomenon of rafts in biological membranes, and with regulation of biological channels.

main text (13 pages, 4 figures), plus supplementary material (15 pages, 6 figures)

References in corpus (5)

• Bias- and bath-mediated pairing of particles driven through a quiescent medium
• Dynamics of heterogeneous hard spheres in a file
• Renewal-anomalous-heterogeneous files
• Dissimilar bouncy walkers
• Current and density fluctuations for interacting particle systems with anomalous diffusive behavior

Cited by in corpus (5)

• Excluded-volume effects in the diffusion of hard spheres
• Aging dynamics in interacting many-body systems
• Interacting single-file system: Fractional Langevin formulation versus diffusion-noise approach
• Insights from Single-File Diffusion into Cooperativity in Higher Dimensions
• Walks of bubbles on a hot wire in a liquid bath