Exploring the origins of the power-law properties of energy landscapes: An egg-box model

Claire P. Massen, Jonathan P.K. Doye and Rupert W. Nash

Physica A: Statistical Mechanics and its Applications, 2007, vol. 382, issue 2, 683-692

Abstract: Multidimensional potential energy landscapes (PELs) have a Gaussian distribution for the energies of the minima, but at the same time the distribution of the hyperareas for the basins of attraction surrounding the minima follows a power-law. To explore how both these features can simultaneously be true, we introduce an “egg-box” model. In these model landscapes, the Gaussian energy distribution is used as a starting point and we examine whether a power-law basin area distribution can arise as a natural consequence through the swallowing up of higher-energy minima by larger low-energy basins when the variance of this Gaussian is increased sufficiently. Although the basin area distribution is substantially broadened by this process, it is insufficient to generate power-laws, highlighting the role played by the inhomogeneous distribution of basins in configuration space for actual PELs.

Keywords: Energy landscapes; Power-laws; Scale-free networks (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:382:y:2007:i:2:p:683-692

DOI: 10.1016/j.physa.2007.04.054

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