摘要翻译：
以前已经表明，势能景观上的连通极小点网络是无标度的，这反映了围绕极小点的吸引盆地区域的幂律分布。在这里，我们通过研究一个13原子簇的势能景观是如何随着势的范围演化的，来更多地了解这些令人困惑的性质的物理起源。特别地，随着电位范围的减小，固定点的数量增加，从而景观变得粗糙，网络变得更大。因此，我们能够跟踪势能景观从一个只有一个最小值的景观到一个有许多最小值和无标度连接模式的复杂景观的演变。我们发现，在这个增长过程中，连通极小值网络中的新边优先附着在更高连通极小值上，从而导致无标度特征。此外，当电位范围较短和网络较大时出现的极小值具有较小的吸引盆地。由于网络呈指数增长，有许多较小的盆地，因此观察到的增长过程也产生了盆地超区域的幂律分布。
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英文标题：
《Preferential attachment during the evolution of a potential energy
  landscape》
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作者：
Claire P. Massen and Jonathan P.K. Doye
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  It has previously been shown that the network of connected minima on a potential energy landscape is scale-free, and that this reflects a power-law distribution for the areas of the basins of attraction surrounding the minima. Here, we set out to understand more about the physical origins of these puzzling properties by examining how the potential energy landscape of a 13-atom cluster evolves with the range of the potential. In particular, on decreasing the range of the potential the number of stationary points increases and thus the landscape becomes rougher and the network gets larger. Thus, we are able to follow the evolution of the potential energy landscape from one with just a single minimum to a complex landscape with many minima and a scale-free pattern of connections. We find that during this growth process, new edges in the network of connected minima preferentially attach to more highly-connected minima, thus leading to the scale-free character. Furthermore, minima that appear when the range of the potential is shorter and the network is larger have smaller basins of attraction. As there are many of these smaller basins because the network grows exponentially, the observed growth process thus also gives rise to a power-law distribution for the hyperareas of the basins.
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PDF链接：
https://arxiv.org/pdf/706.2935