Fast collective oscillations and clustering phenomena in an antiferromagnetic mean-field model

Autor: Xavier Leoncini, Arthur Vesperini, Roberto Franzosi, Stefano Ruffo, Andrea Trombettoni
Přispěvatelé: Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), CPT - E7 Systèmes dynamiques : théories et applications, Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Scienze Fisiche, della Terra e dell'Ambiente., Università degli Studi di Siena = University of Siena (UNISI)
Rok vydání: 2021
Předmět:
General Mathematics
General Physics and Astronomy
FOS: Physical sciences
Ergodicity-breaking
Physics - Classical Physics
Kinetic energy
Collective structure
Hamitonian mean-field model
Long-range interaction
Out-ofequilibrium
Quasi-stationary state
Settore FIS/03 - Fisica della Materia
symbols.namesake
Magnetization
Statistical physics
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
ComputingMilieux_MISCELLANEOUS
Condensed Matter - Statistical Mechanics
Physics
Hamiltonian mechanics
Statistical Mechanics (cond-mat.stat-mech)
Applied Mathematics
Classical Physics (physics.class-ph)
Statistical and Nonlinear Physics
Statistical mechanics
Nonlinear Sciences - Chaotic Dynamics
Physics - Plasma Physics
Settore FIS/02 - Fisica Teorica
Modelli e Metodi Matematici
Plasma Physics (physics.plasm-ph)
Microcanonical ensemble
Mean field theory
symbols
Probability distribution
Chaotic Dynamics (nlin.CD)
Hamiltonian (quantum mechanics)
Zdroj: Chaos, solitons and fractals 153 (2021): 111487-1–111487-7. doi:10.1016/j.chaos.2021.111487
info:cnr-pdr/source/autori:Vesperini A., Franzosi R.,Ruffo S., Trombettoni A.,Leoncini/titolo:Fast collective oscillations and clustering phenomena in an antiferromagnetic mean-field model/doi:10.1016%2Fj.chaos.2021.111487/rivista:Chaos, solitons and fractals/anno:2021/pagina_da:111487-1/pagina_a:111487-7/intervallo_pagine:111487-1–111487-7/volume:153
Chaos, Solitons & Fractals
Chaos, Solitons & Fractals, 2021, 153 (2), pp.111487. ⟨10.1016/j.chaos.2021.111487⟩
ISSN: 0960-0779
1873-2887
DOI: 10.48550/arxiv.2106.07392
Popis: We study the out-of-equilibrium properties of the antiferromagnetic Hamiltonian Mean-Field model at low energy. In this regime, the Hamiltonian dynamics exhibits the presence of a long-lived metastable state where the rotators are gathered in a bicluster. This state is not predicted by equilibrium statistical mechanics in the microcanonical ensemble. Performing a low kinetic energy approximation, we derive the explicit expression of the magnetization vector as a function of time. We find that the latter displays coherent oscillations, and we show numerically that the probability distribution for its phase is bimodal or quadrimodal. We then look at the individual rotator dynamics as a motion in an external time-dependent potential, given by the magnetization. This dynamics exhibits two distinct time scales, with the fast one associated to the oscillations of the global magnetization vector. Performing an average over the fast oscillations, we derive an expression for the effective force acting on the individual rotator. This force is always bimodal, and determines a low frequency oscillation of the rotators. Our approach leads to a self-consistent theory linking the time-dependence of the magnetization to the motion of the rotators, providing a heuristic explanation for the formation of the bicluster.
Databáze: OpenAIRE
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