Phase transitions in persistent and run-and-tumble walks

Karel Proesmans; Raul Toral; Christian Van den Broeck

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arXiv · 1808.09715

Phase transitions in persistent and run-and-tumble walks

Karel Proesmans·Raul Toral·Christian Van den Broeck

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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.

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Karel Proesmans, Raul Toral, Christian Van den Broeck. 2018-08-29. Phase transitions in persistent and run-and-tumble walks. https://arxiv.org/abs/1808.09715

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