Phase transitions in persistent and run-and-tumble walks
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 . In the corresponding force-versus-extension relation, the extension becomes independent of the force beyond a critical value. The transition is anticipated in dimensions and , 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 and above, preceding the usual stiffening appearing beyond a critical value of the force.
Cite
@article{arxiv.1808.09715,
title = {Phase transitions in persistent and run-and-tumble walks},
author = {Karel Proesmans and Raul Toral and Christian Van den Broeck},
journal= {arXiv preprint arXiv:1808.09715},
year = {2019}
}