『Linear Response Theory based on the Vlasov Equation』
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
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