Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
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DOI：
10.1016/j.physa.2004.01.041
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发表时间：
2004-06-01
影响因子：
3.3
通讯作者：
Ruffo, S
中科院分区：
文献类型：
--
作者：
Yamaguchi, YY;Barré, J;Ruffo, S
我们详细研究了N粒子动力学中长程相互作用的原型--哈密顿平均场模型中向平衡的驰豫。特别地，我们指出了与之相关的N-->；无穷大Vlasov动力学定态的无穷大所起的作用。在此背景下，我们导出了一个新的空间均匀分布稳定性的一般判据，并将其解析预测与哈密顿有限N动力学的数值模拟进行了比较。然后，我们根据Vlasov方程提出并数值验证了松弛过程的一个方案。当系统从非定常或Vlasov不稳定定态出发时，系统首先通过非定常状态快速收敛到Vlasov方程的稳定定态：我们通过引入适当的指示符在有限N系统中数值地刻画了这种动态不稳定性。向Boltzmann-Gibbs平衡演化的第一步是一个缓慢的准稳定过程，这个过程通过Vlasov方程的不同稳定定态进行。如果有限的N系统被初始化为Vlasov稳定的齐次状态，它将保持在准稳定状态中囚禁一段时间，该时间随着平凡的幂定律N-1.7而增加。在这种准静态区域中的单粒子动量分布不具有幂函数尾部，因此不能用由Tsallis统计量导出的q指数分布来拟合。(C)2004爱思唯尔B.V.保留所有权利。
We perform a detailed study of the relaxation towards equilibrium in the Hamiltonian Mean-Field model, a prototype for long-range interactions in N-particle dynamics. In particular, we point out the role played by the infinity of stationary states of the associated N --> infinity Vlasov dynamics. In this context, we derive a new general criterion for the stability of any spatially homogeneous distribution, and compare its analytical predictions with numerical simulations of the Hamiltonian, finite N, dynamics. We then propose, and verify numerically, a scenario for the relaxation process, relying on the Vlasov equation. When starting from a nonstationary or a Vlasov unstable stationary state, the system shows initially a rapid convergence towards a stable stationary state of the Vlasov equation via nonstationary states: we characterize numerically this dynamical instability in the finite N system by introducing appropriate indicators. This first step of the evolution towards Boltzmann-Gibbs equilibrium is followed by a slow quasi-stationary process, that proceeds through different stable stationary states of the Vlasov equation. If the finite N system is initialized in a Vlasov stable homogeneous state, it remains trapped in a quasi-stationary state for times that increase with the tiontrivial power law N-1.7. Single particle momentum distributions in such a quasi-stationary regime do not have power-law tails, and hence cannot be fitted by the q-exponential distributions derived from Tsallis statistics. (C) 2004 Elsevier B.V. All rights reserved.