Phase transitions in persistent and run-and-tumble walks
| Autor: | Raúl Toral, Christian Van den Broeck, Karel Proesmans |
|---|---|
| Přispěvatelé: | Research Foundation - Flanders, Ministerio de Ciencia, Innovación y Universidades (España), Agencia Estatal de Investigación (España), European Commission, PROESMANS, Karel, Toral, Raul, VAN DEN BROECK, Christian |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Physics Phase transition Statistical Mechanics (cond-mat.stat-mech) Isotropy Phase (waves) FOS: Physical sciences Condensed Matter Physics Critical value Random walk 01 natural sciences 010305 fluids & plasmas Dimension (vector space) Phase transitions 0103 physical sciences Large deviation theory Large deviations theory Limit (mathematics) Statistical physics 010306 general physics Condensed Matter - Statistical Mechanics Persistent random walk |
| Zdroj: | Digital.CSIC. Repositorio Institucional del CSIC instname |
| DOI: | 10.48550/arxiv.1808.09715 |
| Popis: | 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. KP is a postdoctoral fellow of the Research Foundation-Flanders (FWO). RT acknowledges financial support from Agencia Estatal de Investigación (AEI, Spain) and Fondo Europeo de Desarrollo Regional under Grant No. RTI2018-093732-B-C21 (AEI/FEDER,UE) and the María de Maeztu Program for Units of Excellence in R&D (MDM-2017-0711). |
| Databáze: | OpenAIRE |
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