Pulse solutions of the fractional effective models of the Fermi-Pasta-Ulam lattice with long-range interactions
Autor: | Ramaz Khomeriki, Thierry Dauxois, Andrea Trombettoni, Jean Pierre Nguenang, Gervais Nazaire Beukam Chendjou, Stefano Ruffo |
---|---|
Přispěvatelé: | Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies (SISSA / ISAS), Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Department of Physics, Tbilis State University, École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Chendjou, G. N. B., Nguenang, J. P., Trombettoni, A., Dauxois, T., Khomeriki, R., Ruffo, S. |
Jazyk: | angličtina |
Rok vydání: | 2019 |
Předmět: |
Statistics and Probability
non-Galilean invariance Fractional Boussinesq Equation (FBE) Long-Range Interactions (LRI) FOS: Physical sciences Constant field Birkhoff Normal Form 01 natural sciences 010305 fluids & plasmas Settore FIS/03 - Fisica della Materia [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS] Lattice (order) Toda Lattice 0103 physical sciences [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] 010306 general physics Pulse solutions Condensed Matter - Statistical Mechanics Mathematical physics Ansatz Physics Spacetime Statistical Mechanics (cond-mat.stat-mech) fractional Boussinesq equation (FBE) Long-range interactions nonlinear oscillators Fermi-Pasta-Ulam model fractional differential equations Fermi-Pasta-Ulam model Statistical and Nonlinear Physics fractional differential equations Fermi-Pasta-Ulam (FPU) model Non-Galilean invariance Settore FIS/02 - Fisica Teorica Modelli e Metodi Matematici Long-range interactions Ordinary differential equation long-range interactions (LRI) Equipartition Energy density Exponent Statistics Probability and Uncertainty nonlinear oscillators Fermi Gamma-ray Space Telescope |
Zdroj: | Journal of statistical mechanics 2019 (2019). doi:10.1088/1742-5468/ab47fd info:cnr-pdr/source/autori:Chendjou G.N.B.; Pierre Nguenang J.; Trombettoni A.; Dauxois T.; Khomeriki R.; Ruffo S./titolo:Pulse solutions of the fractional effective models of the Fermi-Pasta-Ulam lattice with long-range interactions/doi:10.1088%2F1742-5468%2Fab47fd/rivista:Journal of statistical mechanics/anno:2019/pagina_da:/pagina_a:/intervallo_pagine:/volume:2019 Journal of Statistical Mechanics: Theory and Experiment Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2019, 2019 (10), pp.104015. ⟨10.1088/1742-5468/ab47fd⟩ Journal of Statistical Mechanics: Theory and Experiment, 2019, 2019 (10), pp.104015. ⟨10.1088/1742-5468/ab47fd⟩ |
ISSN: | 1742-5468 |
DOI: | 10.1088/1742-5468/ab47fd |
Popis: | We study analytical solutions of the Fractional Boussinesq Equation (FBE), which is an effective model for the Fermi-Pasta-Ulam (FPU) one-dimensional lattice with long-range couplings. The couplings decay as a power-law with exponent s, with 1 < s < 3, so that the energy density is finite, but s is small enough to observe genuine long-range effects. The analytic solutions are obtained by introducing an ansatz for the dependence of the field on space and time. This allows to reduce the FBE to an ordinary differential equation, which can be explicitly solved. The solutions are initially localized and they delocalize progressively as time evolves. Depending on the value of s the solution is either a pulse (meaning a bump) or an anti-pulse (i.e., a hole) on a constant field for 1 < s < 2 and 2 < s < 3, respectively. 10 pages, 2 figures. The paper is accepted in JSTAT, the special issue "New Trends in Nonequilibrium Statistical Mechanics: Classical and Quantum Systems (nesmcq18)" |
Databáze: | OpenAIRE |
Externí odkaz: |