摘要翻译：
我们发展了具有弱长程相互作用的哈密顿系统的动力学理论。从Klimontovich方程出发，利用拟线性理论，得到了一个适用于空间非均匀系统的、考虑记忆效应的一般动力学方程。在适当的热力学极限下，该方程在1/n阶是有效的，它与BBGKY体系中得到的动力学方程是一致的。对于N趋于无穷大，它归结为描述无碰撞系统的Vlasov方程。我们描述了在粗晶尺度上相混合和剧烈弛豫导致准稳态(QSS)形成的过程。我们用Lynden-Bell的统计理论解释了QSS的物理本质，并讨论了不完全弛豫问题。在论文的第二部分，我们考虑了被测粒子在热浴中的弛豫。从Klimontovich方程出发，直接计算扩散张量和摩擦力，导出了一个Fokker-Planck方程。我们给出了这些量的一般表达式，这些表达式适用于可能具有长相关时间的空间非均匀系统。我们证明了扩散项和摩擦项具有非常相似的结构，由一种广义Kubo公式给出。当力的自相关函数随时间缓慢减小时，我们还得到了相应的非马尔可夫动力学方程。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。
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英文标题：
《Hamiltonian and Brownian systems with long-range interactions: IV.
  General kinetic equations from the quasilinear theory》
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作者：
Pierre-Henri Chavanis
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最新提交年份：
2009
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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 develop the kinetic theory of Hamiltonian systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a general kinetic equation that can be applied to spatially inhomogeneous systems and that takes into account memory effects. This equation is valid at order 1/N in a proper thermodynamic limit and it coincides with the kinetic equation obtained from the BBGKY hierarchy. For N tending to infinity, it reduces to the Vlasov equation describing collisionless systems. We describe the process of phase mixing and violent relaxation leading to the formation of a quasi stationary state (QSS) on the coarse-grained scale. We interprete the physical nature of the QSS in relation to Lynden-Bell's statistical theory and discuss the problem of incomplete relaxation. In the second part of the paper, we consider the relaxation of a test particle in a thermal bath. We derive a Fokker-Planck equation by directly calculating the diffusion tensor and the friction force from the Klimontovich equation. We give general expressions of these quantities that are valid for possibly spatially inhomogeneous systems with long correlation time. We show that the diffusion and friction terms have a very similar structure given by a sort of generalized Kubo formula. We also obtain non-markovian kinetic equations that can be relevant when the auto-correlation function of the force decreases slowly with time. 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.
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PDF链接：
https://arxiv.org/pdf/705.4579