Vlasov stability of the Hamiltonian mean field model

Celia Anteneodo and Raúl O. Vallejos

Physica A: Statistical Mechanics and its Applications, 2004, vol. 344, issue 3, 383-392

Abstract: We investigate the dynamical stability of a fully coupled system of N inertial rotators, the so-called Hamiltonian Mean Field model. In the limit N→∞, and after proper scaling of the interactions, the μ-space dynamics is governed by a Vlasov equation. We apply a nonlinear stability test to (i) a selected set of spatially homogeneous solutions of Vlasov equation, qualitatively similar to those observed in the quasi-stationary states arising from fully magnetized initial conditions, and (ii) numerical coarse-grained distributions of the finite-N dynamics. Our results are consistent with previous numerical evidence of the disappearance of the homogeneous quasi-stationary family below a certain energy.

Keywords: Long-range interactions; Nonextensivity; Vlasov equation (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:344:y:2004:i:3:p:383-392

DOI: 10.1016/j.physa.2004.06.006

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