Electrons on the Sphere
Electrons on the Sphere
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球体上的电子
DOI：
10.1142/9789814533232_0022
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发表时间：
1995
影响因子：
2.1
通讯作者：
Y. M. Zhou
中科院分区：
文献类型：
--
作者：
E. Rakhmanov;E. Saff;Y. M. Zhou
研究了单位球面上n点（带电粒子）通过幂律电位v (r) =rα,−2 <α< 2，α≠0和当α= 0时v (r) = log（1/r）相互作用的排列能量。给出了α= 0，±1,n = 2，…，200三种经典情况下的数值实验结果。我们还研究了平衡点的几何结构及其群性质。在α= 0的情况下，我们证明了最小能量点必须是很好地分开的，即任何两个不同的点之间至少有（3/5）个单位距离。
We investigate the energy of arrangements ofNpoints (charged particles) on the surface of the unit sphere in ℝ3, interacting through a power law potentialV(r) =rα, − 2 <α< 2,α≠ 0 andV(r) = log(1/r) forα= 0. Results of numerical experiments are presented for the three classical casesα= 0, ± 1, forN= 2, …, 200. We also investigate the geometric structures of the equilibrium points and their group properties. In the caseα= 0, we prove that theNpoints of minimal energy must be well-separated in the sense that any two distinct points are at least (3/5)units distance apart.