Configurational entropy of Wigner crystals

TL;DR

This paper investigates the configurational entropy of classical Wigner crystals in traps, providing a robust measure of structural uncertainty due to multiple stable configurations, applicable to systems with up to 100 particles.

Contribution

It introduces the concept of configurational entropy as a reliable measure of uncertainty in the structural arrangements of Wigner crystals, surpassing the limitations of counting metastable states.

Findings

Total metastable configurations are not well-defined.

Configurational entropy effectively quantifies structural uncertainty.

Method is reliable even with limited simulation time.

Abstract

We present a theoretical study of classical Wigner crystals in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable configurations. Strongly interacting systems of classical charged particles confined in traps are known to form regular structures. The number of distinct arrangements grows very rapidly with the number of particles, many of these arrangements have quite low occurrence probabilities and often the lowest-energy structure is not the most probable one. We perform numerical simulations on systems containing up to 100 particles interacting through Coulomb and Yukawa forces, and show that the total number of metastable configurations is not a well defined and representative quantity. Instead, we propose to rely on the configurational entropy as a robust and objective measure of uncertainty. The configurational entropy can be understood as the logarithm of the effective number of states; it is insensitive to the presence of overlooked low-probability states and can be reliably determined even within a limited time of a simulation or an experiment.