Braids in classical gravity
Braids in classical gravity
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发表时间：
1993
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通讯作者：
Cristopher Moore
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作者：
Cristopher Moore
在2+1维中移动的点质量在时空中绘制出辫子。如果它们在某些成对势能的影响下运动，可能会有什么类型的辫子？通过从所希望的拓扑的虚构路径开始，并通过最小化作用量来放松它们，我们探索了形式V ex：rc<；的势能的辫子类型，从所有辫子类型都出现的Q‘：：；-2到系统可积的0’=2。我们还讨论了对称性和稳定性问题，包括动力学问题和算法问题。我们提出了这种拓扑分类作为多体动力学的工具。
Point masses moving in 2+1 dimensions draw out braids in spacetime. If they move under the influence of some pairwise potential, what braid types are possible? By starting with fictional paths of the desired topology and 'relaxing' them by minimizing the action, we explore the braid types of potentials of the form V ex: rC< from Q' ::; -2, where all braid types occur, to 0' = 2 where the system is integrable. We also discuss issues of symmetry and stability, both of the dynamics and of the algorithm. We propose this kind of topological classification as a tool for many-body dynamics.