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

Motivated by Laughlin’s plasma analogy, 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. The 2D OCP appears in connection to many different problems: the electron density of Laughlin’s wave function, certain random matrix ensembles, and chiral vortex fluids. Reference: arXiv:2009.02359