京大文学部東館１階演習室３(155号室)

小川駿(京都大学)

『Linear Response Theory based on the Vlasov Equation』

(山口義幸氏(京大情報)との共同研究)

Hamiltonian systems with long-range interactions are trapped in long-lasting non-equilibrium states called quasi-stationary states. a way to analyze a Hamiltonian system with long-range interaction is to use the Vlasov equation. Quasi-stationary states are recognized as stable stationary solutions to the Vlasov equation. In this talk, we look into response to the external forces in quasi-stationary states. For sufficiently small external forces, we propose the linear response theory based on the Vlasov equation, where the theory is applicable to general one dimensional systems in both homogeneous and inhomogeneous quasi-stationary states. The theory is applied to the Hamiltonian mean-field model, a zero-field susceptibility obtained explicitly and the Curie-Weiss law is derived in a disordered phase as well as in the equilibrium statistical mechanics. The linear response to an external field and a zero-field susceptibility is also derived in an ordered phase, and resonance absorption is observed.

Last modified: Fri Jan 20 18:47:33 JST 2012