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