コロキウム

The Vlasov equation is a partial differential equation describing temporal evolution of a long-range Hamiltonian system in the limit of large population. In a spatially periodic system, we consider a stable stationary state and inject two spatially periodic pulses at time t=0 and τ successively. The pulse responses can appear not only at t=0 and τ but also at time T(>τ). This phenomenon is called echo. If the stationary state is spatially homogeneous, the two pulses should have different spatial Fourier modes to create the echo. However, in the case of the inhomogeneous stationary states, echo occurs even if the two pulses consist of one Fourier mode. This theoretical prediction is numerically examined. We also discuss on the echo time T with comparing the homogeneous and inhomogeneous cases.