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Physical Review E, Statistical, Nonlinear and Soft Matter Physics

Publication date: 2011-01
Volume: 84
ISSN: 2470-0045, 1539-3755 PMID: 22304084
DOI: 10.1103/PhysRevE.84.061151
Publisher: Published by the American Physical Society through the American Institute of Physics


de Buyl, Pierre
Mukamel, David ; Ruffo, Stefano


Science & Technology, Physical Sciences, Physics, Fluids & Plasmas, Physics, Mathematical, Physics, LONG-RANGE INTERACTIONS, STATISTICAL-MECHANICS, RELAXATION, SYSTEMS, EQUATION, MODEL, cond-mat.stat-mech


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(γ) for large N, with γ1.7 for some initial conditions with homogeneously distributed particles. We propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analyzing 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 γ ~/= 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.