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Power-law distributions for the areas of the basins of attraction on a potential energy landscapeClaire P. Massen and Jonathan P. K. DoyePhys. Rev. E 71, 037101 (2007)AbstractDespite the popularity of energy landscape approaches for understanding a wide variety of chemical physics phenomena, relatively little is known about the universal properties of complex, high-dimensional potential energy landscapes. Here, we show that there is a deep analogy between the way the energy landscape is divided into basins of attractions surrounding the minima, and the way that space is packed in self-similar, space-filling hypersphere packings, such as the Apollonian packing. In particular, for some archetypal supercooled liquids, we find that the probability distribution for the basin areas is a power-law over a large number of decades, with an exponent that is in excellent agreement with that predicted from this analogy. These results suggest that the basins of attraction provide a fractal tiling of the energy landscape, and that a scale-free pattern of connections between the minima is a general property of energy landscapes.The full paper is available from Physical Review E Online and arXiv.org. |