作为牛顿N体系统大N极限的Schr $\ddot{o}$ dinger-Poisson方程：在大尺度暗物质动力学中的应用
The Schr$\ddot{o}$dinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics
摘要：
本文讨论了在大$N$极限下，如何用Schr $\ddot{o}$ dinger-Poisson方程描述经典牛顿N体系统的动力学.这个结果是基于随机量子化介绍纳尔逊，并在Calogero猜想。根据Calogero猜想，新出现的有效普朗克常数是根据N体系统的参数计算的$\hbar \sim M^{5/3} G^{1/2} (N/<ρ>)^{1/6}$，其中$G$是引力常量，$N$和$M$是物体的数量和质量，$<ρ>$是它们的平均密度。讨论了这一结果在大尺度结构形成背景下的相关性。特别是，这一发现提供了进一步的论据，在支持的有效性的Schr $\ddot{o}$丁格方法的数值倍的N体模拟的暗物质动力学在大宇宙尺度。
英文摘要：
In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schr$\ddot{o}$dinger-Poisson equations in the large $N$ limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as $\hbar \sim M^{5/3} G^{1/2} (N/<ρ>)^{1/6}$, where is $G$ the gravitational constant, $N$ and $M$ are the number and the mass of the bodies, and $<ρ>$ is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schr$\ddot{o}$dinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales.
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