Vlasov stability of the Hamiltonian Mean Field model
arXiv:cond-mat/0401179 · doi:10.1016/j.physa.2004.06.006
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 $N \to \infty$, 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 homogenous quasi-stationary family below a certain energy.
11 pages, 5 figures. Submitted as a contribution to the proceedings of the International Workshop on Trends and Perspectives on Extensive and Non-Extensive Statistical Mechanics, November, 19-21, 2003, Angra dos Reis, Brazil