Algebraic damping in the one-dimensional Vlasov equation

Details Algebraic damping in the one-dimensional Vlasov equation Algebraic damping in the one-dimensional Vlasov equation

2011-04-11

arxiv.org/abs/1104.1890v2

J. Phys. A: Math. Theor. 44 (2011) 405502

Physics

Mathematical Physics

26 pages, 8 figures; text slightly modified, references added, typos corrected

Scientific paper

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation evolving according to the linearized Vlasov equation decays algebraically with the exponent -2 and a well defined frequency. The theoretical results are successfully tested against numerical $N$-body simulations, corresponding to the full Vlasov dynamics in the large $N$ limit, in the case of the Hamiltonian mean-field model. For this purpose, we use a weighted particles code, which allows us to reduce finite size fluctuations and to observe the asymptotic decay in the $N$-body simulations.

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