京大工学部８号館３階南演習室

山口義幸(京大情報)

『Dynamics of perturbations around inhomogeneous backgrounds in the HMF model』

We investigate the dynamics of perturbation around inhomogeneous stationary states of the Vlasov equation corresponding to the Hamiltonian mean-field model. The inhomogeneous background induces a separatrix in the one-particle Hamiltonian system, and branch cuts generically appear in the analytic continuation of the dispersion relation in the complex frequency plane. We test the theory by direct comparisons with N-body simulations, using two families of distributions: inhomogeneous water-bags, and inhomogeneous thermal equilibria. In the water-bag case, which is not generic, no branch cut appears in the dispersion relation, whereas in the thermal equilibrium case, when looking for the root of the dispersion relation closest to the real axis, we have to consider several Riemann sheets. In both cases, we show that the roots of the continued dispersion relation give useful, although not complete, information to understand the dynamics of a perturbation. 備考： 本研究は Julien Barre', Alain Olivetti (Univ. Nice, France) との共同研究である。

Last modified: Fri May 21 15:56:20 2010