The boundary density profile of a Coulomb droplet. Freezing at the edge

TL;DR

This paper investigates the boundary density oscillations of a 2D one-component plasma droplet at low temperatures, combining Monte Carlo simulations with a Wigner crystallization model to explain edge behavior.

Contribution

It provides a numerical analysis of boundary density oscillations and introduces a Wigner crystallization framework to interpret these phenomena.

Findings

Density oscillations decay with distance from the boundary.

Oscillation period correlates with Wigner crystal structure.

Wigner crystallization explains the edge density profile.

Abstract

We revisit the problem of computing the boundary density profile of a droplet of two-dimensional one-component plasma (2D OCP) with logarithmic interaction between particles in a confining harmonic potential. At a sufficiently low temperature but still in the liquid phase, the density exhibits oscillations as a function of the distance to the boundary of the droplet. We obtain the density profile numerically using Monte-Carlo simulations of the 2D OCP. We argue that the decay and period of those oscillations can be explained within a picture of the Wigner crystallization near the boundary, where the crystal is gradually melted with the increasing distance to the boundary.