Long-lasting small traveling clusters are studied in the Hamiltonian
mean-field model by comparing between attractive and repulsive
interactions. Nonlinear Landau damping theory predicts that a gaussian
momentum distribution on a spatially homogeneous background permits
the existence of traveling clusters in the repulsive case, as in
plasma systems, but not in the attractive case. Nevertheless,
extending the analysis to a two-parameter family of momentum
distributions of Fermi-Dirac type, we theoretically predict the
existence of traveling clusters in the attractive case; these findings
are confirmed by direct $N$-body numerical simulations. The parameter
region with the traveling clusters is much reduced in the attractive
case with respect to the repulsive case.

参考文献: Phys.Rev.E 79, 036208 (2009