Phase transitions in persistent and run-and-tumble walks

Karel Proesmans, Raul Toral and Christian Van den Broeck

Physica A: Statistical Mechanics and its Applications, 2020, vol. 552, issue C

Abstract: We calculate the large deviation function of the end-to-end distance and the corresponding extension-versus-force relation for (isotropic) random walks, on and off-lattice, with and without persistence, and in any spatial dimension. For off-lattice random walks with persistence, the large deviation function undergoes a first order phase transition in dimension d>5. In the corresponding force-versus-extension relation, the extension becomes independent of the force beyond a critical value. The transition is anticipated in dimensions d=4 and d=5, where full extension is reached at a finite value of the applied stretching force. Full analytic details are revealed in the run-and-tumble limit. Finally, on-lattice random walks with persistence display a softening phase in dimension d=3 and above, preceding the usual stiffening appearing beyond a critical value of the force.

Keywords: Persistent random walk; Phase transitions; Large deviation theory (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:552:y:2020:i:c:s0378437119311367

DOI: 10.1016/j.physa.2019.121934

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