Phase transitions in persistent and run-and-tumble walks

Proesmans,Karel; Toral,Raul: Van den Broeck, Christian
Physica A (accepted) , 121934 (2020)

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 $d\geq 6$. This transition is both physically and mathematically similar to the Bose-Einstein condensation, with the condensed phase corresponding to a macroscopic fraction of the random walk oriented along the end-to-end distance. 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.

Esta web utiliza cookies para la recolección de datos con un propósito estadístico. Si continúas navegando, significa que aceptas la instalación de las cookies.

Más información De acuerdo