Rocha Filho T M, Amato M A, Santana A E, Figueiredo A, Steiner J R
Instituto de Física and International Center for Condensed Matter Physics Universidade de Brasília, CP 04455, 70919-970 Brasília, Brazil.
Instituto de Física, Universidade de Brasília, CP 04455, 70919-970 Brasília, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):032116. doi: 10.1103/PhysRevE.89.032116. Epub 2014 Mar 13.
The time evolution of the one-particle distribution function of an N-particle classical Hamiltonian system with long-range interactions satisfies the Vlasov equation in the limit of infinite N. In this paper we present a new derivation of this result using a different approach allowing a discussion of the role of interparticle correlations on the system dynamics. Otherwise for finite N collisional corrections must be introduced. This has allowed a quite comprehensive study of the quasistationary states (QSSs) though many aspects of the physical interpretations of these states still remain unclear. In this paper a proper definition of time scale for long time evolution is discussed, and several numerical results are presented for different values of N. Previous reports indicate that the lifetimes of the QSS scale as N1.7 or even the system properties scale with exp(N). However, preliminary results presented here indicates that time scale goes as N2 for a different type of initial condition. We also discuss how the form of the interparticle potential determines the convergence of the N-particle dynamics to the Vlasov equation. The results are obtained in the context of the following models: the Hamiltonian mean field, the Self-gravitating ring model, and one- and two-dimensional systems of gravitating particles. We have also provided information of the validity of the Vlasov equation for finite N.
具有长程相互作用的N粒子经典哈密顿系统的单粒子分布函数的时间演化在N趋于无穷大的极限下满足弗拉索夫方程。在本文中，我们使用一种不同的方法给出了这一结果的新推导，这种方法允许讨论粒子间关联对系统动力学的作用。否则，对于有限的N，必须引入碰撞修正。这使得对准稳态（QSSs）进行了相当全面的研究，尽管这些状态的物理解释的许多方面仍不清楚。本文讨论了长时间演化的时间尺度的恰当定义，并给出了不同N值的几个数值结果。先前的报告表明，QSS的寿命按N^1.7缩放，甚至系统性质按exp(N)缩放。然而，这里给出的初步结果表明，对于不同类型的初始条件，时间尺度按N^2变化。我们还讨论了粒子间势的形式如何决定N粒子动力学向弗拉索夫方程的收敛。结果是在以下模型的背景下获得的：哈密顿平均场、自引力环模型以及一维和二维引力粒子系统。我们还提供了有限N时弗拉索夫方程有效性的信息。
