论文标题
具有任意相互作用潜力的一维均质远程相互作用系统的动力学理论
Kinetic theory of one-dimensional homogeneous long-range interacting systems with an arbitrary potential of interaction
论文作者
论文摘要
有限$ n $效果不可避免地推动了长期相互作用$ n $体系统的长期演变。 Balescu-Lenard动力学方程一般描述了此过程，该过程由$ {1/n} $效果提出，但这种动力学操作员完全通过对称性消失了一维同质系统：这种系统经历了动力学阻滞，并且无法以$ {1/n} $的整体放松。因此，只有通过三体相关来提出的较弱的$ {1/n^{2}} $效果，这些系统才能放松，从而导致进化速度较慢。在可以忽略集体效应的极限中，但是对于任意的成对相互作用潜力，我们得出了一个封闭而明确的动力学方程，描述了这种长期演变。我们展示了该动力学方程如何满足$ h $ - 理论，同时保存粒子数和能量，从而确保系统对玻尔兹曼平衡分布的不可避免的放松。只要互动是长期的，我们还展示了该方程如何无法通过进一步的动力学阻塞来折磨，即$ {1/n^{2}} $ dynamics始终是有效的。最后，我们说明该方程如何定量匹配直接$ n $ body模拟的测量值。
Finite-$N$ effects unavoidably drive the long-term evolution of long-range interacting $N$-body systems. The Balescu-Lenard kinetic equation generically describes this process sourced by ${1/N}$ effects but this kinetic operator exactly vanishes by symmetry for one-dimensional homogeneous systems: such systems undergo a kinetic blocking and cannot relax as a whole at this order in ${1/N}$. It is therefore only through the much weaker ${1/N^{2}}$ effects, sourced by three-body correlations, that these systems can relax, leading to a much slower evolution. In the limit where collective effects can be neglected, but for an arbitrary pairwise interaction potential, we derive a closed and explicit kinetic equation describing this very long-term evolution. We show how this kinetic equation satisfies an $H$-theorem while conserving particle number and energy, ensuring the unavoidable relaxation of the system towards the Boltzmann equilibrium distribution. Provided that the interaction is long-range, we also show how this equation cannot suffer from further kinetic blocking, i.e., the ${1/N^{2}}$ dynamics is always effective. Finally, we illustrate how this equation quantitatively matches measurements from direct $N$-body simulations.
