Metastable configurations of Wigner crystals in a circular trap

Abstract

We model the formation of ordered structures in systems consisting of up to 52 identical particles interacting by Coulomb repulsion forces and confined within a two-dimensional parabolic trap. Our algorithm consists of a number of Metropolis steps followed by the steepest-descent minimization of the total potential energy of the system. The role of the first (Metropolis) stage is to create a random canonically distributed configuration, while the subsequent minimization locates the closest local minimum starting from this random configuration. In most cases we find that more than one stable configuration may be formed, and often the lowest-energy configuration is not the most probable one. The concept of configurational entropy isintroduced to quantify the uncertainty due to the availability of several alternative structures. Keywords: Wigner crystallization, Monte Carlo simulation, entropy