Clustering in anomalous files of independent particles

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.

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