paper

Remarks about the thermostatistical description of the HMF model Part II: Phenomenology of Relaxation Dynamics

arXiv:0910.2908

Abstract

After a general overview of some features of the relaxation dynamics of the Hamiltonian Mean Field model, its equilibrium thermodynamic properties are used to rephrase the out-of-equilibrium regime for energies below the critical point $u_{c} = 0.75$ in terms of an effective dynamical coexistence between a clustered and a gaseous phases, whose existence could be associated to the large relaxation times observed when $u_{1} < u < u_{c}$ , with $u_{1} = 0.5$ . Starting from the hypothesis that the \textit{parametric resonance} is the microscopic mechanism allowing the energetic interchange between the particles during the collisional regime, a phenomenological Fokker-Planck equation based on a Langevin equation with a multiplicative noise is proposed in order to describe the collisional relaxation of this system towards its final equilibrium, which supports the following dependence of the collisional relaxation timescale $I ¨ _{cr} = I ¨ _{0} N \equiv I N / g$ .

RevTex 4.0 style, 10 pages + 7 eps figures