具有长程相互作用的哈密顿和布朗系统：III。的 空间非均匀系统的BBGKY族

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摘要翻译：
我们研究了弱长程相互作用系统中关联的增长。从BBGKY族出发，在适当的热力学极限$n~+infty$范围内，用1/n次方展开BBGKY族的解，确定了两体关联函数的演化。由于有限的n$效应，这些关联导致了系统在Vlasov区之外的碰撞演化。我们得到了一个可应用于空间非均匀系统并考虑记忆效应的一般动力学方程。这些特性是具有非屏蔽远程交互作用的系统所特有的。对于像等离子体这样具有短记忆时间的空间均匀系统，我们恢复了经典的Landau（或Lenard-Balescu）方程。我们的方法的一个有趣之处是发展一种保留在物理空间（而不是傅立叶空间）中的形式主义，它可以处理空间上的非均匀系统。这启发了基础物理学，并提供了具有明确物理解释的新的动力学方程。然而，除非我们把自己限制在空间均匀系统中，否则只有忽略粒子之间的某些集体效应，才能得到封闭的动力学方程。还给出了考虑集体效应的一般精确耦合方程。我们用这一动力学理论讨论了弱长程相互作用体系中的剧烈无碰撞弛豫和慢碰撞弛豫过程。特别地，我们研究了弛豫时间与系统尺寸的关系，并对这些系统的所有数值结果进行了相干讨论。
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英文标题：
《Hamiltonian and Brownian systems with long-range interactions: III. The
  BBGKY hierarchy for spatially inhomogeneous systems》
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作者：
Pierre-Henri Chavanis
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We study the growth of correlations in systems with weak long-range interactions. Starting from the BBGKY hierarchy, we determine the evolution of the two-body correlation function by using an expansion of the solutions of the hierarchy in powers of 1/N in a proper thermodynamic limit $N\to +\infty$. These correlations are responsible for the ``collisional'' evolution of the system beyond the Vlasov regime due to finite $N$ effects. We obtain a general kinetic equation that can be applied to spatially inhomogeneous systems and that takes into account memory effects. These peculiarities are specific to systems with unshielded long-range interactions. For spatially homogeneous systems with short memory time like plasmas, we recover the classical Landau (or Lenard-Balescu) equations. An interest of our approach is to develop a formalism that remains in physical space (instead of Fourier space) and that can deal with spatially inhomogeneous systems. This enlightens the basic physics and provides novel kinetic equations with a clear physical interpretation. However, unless we restrict ourselves to spatially homogeneous systems, closed kinetic equations can be obtained only if we ignore some collective effects between particles. General exact coupled equations taking into account collective effects are also given. We use this kinetic theory to discuss the processes of violent collisionless relaxation and slow collisional relaxation in systems with weak long-range interactions. In particular, we investigate the dependence of the relaxation time with the system size and provide a coherent discussion of all the numerical results obtained for these systems.
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PDF链接：
https://arxiv.org/pdf/705.4405

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关键词：相互作用 哈密顿 III BBG interactions interactions 具有 动力学 方程 效应