The Linear Responce to the External Force for the Hamiltonian mean-field model in Quasi-stationary States

Ogawa Shun

July 1st 13:30

It is a common view that Hamiltonian systems with long-range interaction are trapped in non-equilibrium states called quasi-stationary states. A way to analyze such a Hamiltonian system is to use the Vlasov equation or collision-less Boltzmann equation, and quasi-stationary states are recognized as stable stationary solutions to the Vlasov equation[1].
In this talk, we use one of the simplest models with long-range interaction, the Hamiltonian mean-filed (HMF) model. We apply the linear response theory[2] to this system in spatially homogeneous quasi-stationary states. As a result, we can obtain the asymptotic forms of magnetization and susceptibility exactly. Moreover, it should be noted that the critical behavior of the susceptibility like the Curie-Weiss law is shown from this result straightforwardly by using the result exhibited in the article [3].

[1] A. Campa, T. Dauxois and S. Ruffo, Phys. Rep. 480, 57 (2009).
[2] D.J.Evans and P.J.Morriss, "Statistical mechanics of nonequilibrium liquids," (Cambridge University Press,2008) and R. Kubo, M. Toda and N. Hashitsume, ¡ÈStatistical physics II. Nonequilibrium statistical mechanics,¡É (Springer, 1985).
[3] S. Ogawa and Y.Y.Yamaguchi, submitted.