纳米尺度上的限制性三体问题
Restricted three body problems at the nanoscale
摘要：
本文研究了纳米尺度下经典的限制性三体问题，如三个C60富勒烯的圆平面限制性问题，以及一个碳原子和两个C60富勒烯的圆平面限制性问题.我们用Lennard-Jones势来模拟富勒烯之间的范德华力。特别是，富勒烯上的碳原子之间的成对势能近似的连续的方法，使两个富勒烯之间的总分子能量可以解析地确定。由于我们假设分子之间的这种相互作用发生在足够大的距离，经典的三体问题分析是合理的，以确定集体角速度的两个和三个C60富勒烯在纳米级。我们发现两个和三个富勒烯系统的最大角频率达到太赫兹范围，我们确定了碳原子和两个富勒烯系统的稳定点和碳原子具有最大速度的点。
英文摘要：
In this paper, we investigate some of the classical restricted three body problems at the nanoscale, such as the circular planar restricted problem for three C60 fullerenes, and a carbon atom and two C60 fullerenes. We model the van der Waals forces between the fullerenes by the Lennard-Jones potential. In particular, the pairwise potential energies between the carbon atoms on the fullerenes are approximated by the continuous approach, so that the total molecular energy between two fullerenes can be determined analytically. Since we assume that such interactions between the molecules occur at sufficiently large distance, the classical three body problems analysis is legitimate to determine the collective angular velocity of the two and three C60 fullerenes at the nanoscale. We find that the maximum angular frequency of the two and three fullerenes systems reach the terahertz range and we determine the stationary points and the points which have maximum velocity for the carbon atom for the carbon atom and the two fullerenes system.
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