长程相互作用系统的无碰撞弛豫动力学理论
Kinetic theory of collisionless relaxation for systems with long-range interactions
摘要：
我们发展了与林登-贝尔统计理论有关的长程相互作用系统的无碰撞弛豫动力学理论。我们处理多层次的情况。我们从Vlasov方程的准线性理论得到的动力学方程和从最大熵产生原理得到的松弛方程之间的连接。我们提出了一种方法来封闭相级矩的动力学方程的无限层次，并获得与广义熵形式相关联的广义Landau、Lenard-Balescu或Kramers方程形式的粗粒度分布函数的动力学方程[P.H. Chavanis，Physica A { \bf 332}，89（2004）]。这使我们能够超越与费米-狄拉克型熵相关的两能级情形。我们讨论了与二维湍流的许多类比。我们还提到了可能的应用程序，目前的形式主义的费米子和玻色子暗物质晕。
英文摘要：
We develop the kinetic theory of collisionless relaxation for systems with long-range interactions in relation to the statistical theory of Lynden-Bell. We treat the multi-level case. We make the connection between the kinetic equation obtained from the quasilinear theory of the Vlasov equation and the relaxation equation obtained from a maximum entropy production principle. We propose a method to close the infinite hierarchy of kinetic equations for the phase level moments and obtain a kinetic equation for the coarse-grained distribution function in the form of a generalized Landau, Lenard-Balescu or Kramers equation associated with a generalized form of entropy [P.H. Chavanis, Physica A {\bf 332}, 89 (2004)]. This allows us to go beyond the two-level case associated with a Fermi-Dirac-type entropy. We discuss the numerous analogies with two-dimensional turbulence. We also mention possible applications of the present formalism to fermionic and bosonic dark matter halos.
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