Phase transitions in persistent and run-and-tumble walks

• DOI: 10.1016/j.physa.2019.121934
• ArXiv number: 1808.09715

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.

• Full paper

Related research projects

PACSS (UIB)

Physics approach to complexity in sociotechnical systems

P.I.: Raúl Toral

This project, Physics approach to complexity in sociotechnical systems (PACSS), wants to contribute to the understanding of sociotechnical phenomena from the perspective provided by the application of the modern field of complex …

MdM-IFISC-AccSp

Ayuda Solicitud Maria de Maeztu

P.I.: Maxi San Miguel

Acción Especial Govern