Colloquium

Colloquium
準定常状態にあるハミルトン平均場モデルの外力に対する線形応答小川駿 7月1日(金)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, “Statistical physics II. Nonequilibrium statistical mechanics,” (Springer, 1985). [3] S. Ogawa and Y.Y.Yamaguchi, submitted.

準定常状態にあるハミルトン平均場モデルの外力に対する線形応答

小川駿

7月1日(金)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, “Statistical physics II. Nonequilibrium statistical mechanics,” (Springer, 1985).
[3] S. Ogawa and Y.Y.Yamaguchi, submitted.