Clustering in anomalous files of independent particles

Flomenbom-BPS - 19 Louis Marshal St., Tel Aviv, 62668 Israel

^a flomenbo@flomenbom.net

Received: 8 February 2011
Accepted: 7 April 2011

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 undescribed 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, , only for anomalous α, characterizing the criticality of a phase transition. The asymptotic mean square displacement per particle in the file is about, . We show numerically that this phenomenon of a dynamical phase transition is very stable, and relate it with the mysterious phenomenon of rafts in biological membranes, and with regulation of biological channels.