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

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.

26 pages, 13 figures; figure 12 updated

References in corpus (4)

• 2D Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
• Large N expansion for the 2D Dyson gas
• FQHE on curved backgrounds, free fields and large N
• Entanglement spectroscopy of chiral edge modes in the Quantum Hall effect

Cited by in corpus (8)

• Cornering the universal shape of fluctuations
• Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $\beta$
• W-infinity Symmetry in the Quantum Hall Effect Beyond the Edge
• Scaling Limits of Planar Symplectic Ensembles
• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• Adiabatic Deformations of Quantum Hall Droplets
• Complex symmetric, self-dual, and Ginibre random matrices: Analytical results for three classes of bulk and edge statistics
• Quantum Hall edges beyond the plasma analogy