2007/06/20 by Claire P. Massen, Jonathan P. K. Doye, Mahmood S. Shivji +4 · 2 citations
Biochemistry, Genetics and Molecular Biology · Environmental Science · Physics and Astronomy · #Ichthyology and Marine Biology #Identification and Quantification in Food #Molecular Biology Techniques and Applications #Quantum many-body systems #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1063/1.2773721
published as J. Chem. Phys. 127, 114306 (2007) · 10 pages, 10 figures
arxiv created 2007/06/20 · openalex publication_date 2008/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
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, the aim is 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, the evolution of the potential energy landscape can be followed from one with just a single minimum to a complex landscape with many minima and a scale-free pattern of connections. It is found 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.