A generic feature of systems with long-range interactions is the presence of quasistationary states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian mean-field model, we demonstrate that a maximum entropy principle applied to the associated Vlasov equation explains known features of such states for a wide range of initial conditions. We are able to reproduce velocity distribution functions with an analytic expression which is derived from the theory with no adjustable parameters. A normal diffusion of angles is detected, which is consistent with Gaussian tails of velocity distributions. A dynamical effect, two oscillating clusters surrounded by a halo, is also found and theoretically justified.
Maximum entropy principle explains quasi-stationary states in systemswith long-range interactions: the example of the HMF model / A. ANTONIAZZI; D. FANELLI; J. BARRE; P. H. CHAVANIS; T. DAUXOIS; S. RUFFO. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - ELETTRONICO. - 75:(2007), pp. 011112-011112. [10.1103/PhysRevE.75.01112]
Maximum entropy principle explains quasi-stationary states in systemswith long-range interactions: the example of the HMF model
FANELLI, DUCCIO;RUFFO, STEFANO
2007
Abstract
A generic feature of systems with long-range interactions is the presence of quasistationary states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian mean-field model, we demonstrate that a maximum entropy principle applied to the associated Vlasov equation explains known features of such states for a wide range of initial conditions. We are able to reproduce velocity distribution functions with an analytic expression which is derived from the theory with no adjustable parameters. A normal diffusion of angles is detected, which is consistent with Gaussian tails of velocity distributions. A dynamical effect, two oscillating clusters surrounded by a halo, is also found and theoretically justified.File | Dimensione | Formato | |
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