par de Buyl, Pierre 
;Mukamel, David;Ruffo, Stefano
Référence Physical review. E, Statistical, nonlinear, and soft matter physics, 84, 6, page (061151)
Publication Publié, 2011-12-28
;Mukamel, David;Ruffo, StefanoRéférence Physical review. E, Statistical, nonlinear, and soft matter physics, 84, 6, page (061151)
Publication Publié, 2011-12-28
Article révisé par les pairs
| Résumé : | Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of N globally coupled particles moving on a ring, the Hamiltonian Mean Field model (HMF), have shown that it diverges as N^gamma for large N, with gamma ~ 1.7 for some initial conditions with homogeneously distributed particles. We propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analysing models of uncoupled particles moving in an external field. For the HMF model, we show numerically that the relaxation time of these states diverges with N with the exponent gamma ~ 1. The method, applicable to other models with globally coupled particles, also allows an exact evaluation of the stability limit of homogeneous steady states. In some cases it provides a good approximation for the correspondence between the initial condition and the final steady state. |
