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.

arXiv comment26 pages, 13 figures; figure 12 updated

References in corpus (20)

• 2D Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
• Fluctuations of eigenvalues of random normal matrices
• Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
• Large N expansion for the 2D Dyson gas
• FQHE on curved backgrounds, free fields and large N
• The noise in the circular law and the Gaussian free field
• Hydrodynamics of Euler incompressible fluid and the Fractional Quantum Hall Effect
• The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem
• Entanglement entropy and Berezin-Toeplitz operators
• Internal energy of the classical two- and three-dimensional one-component-plasma
• Entanglement spectroscopy of chiral edge modes in the Quantum Hall effect
• Analogies between random matrix ensembles and the one-component plasma in two-dimensions
• Edge wave and boundary layer of vortex matter
• Singular Behavior At The Edge of Laughlin States
• Is the Two-Dimensional One-Component Plasma Exactly Solvable?
• Anomalous Hydrodynamics of Fractional Quantum Hall States
• Exact and asymptotic features of the edge density profile for the one component plasma in two dimensions
• Note: Melting criterion for soft particle systems in two dimensions
• Vortex flows on closed surfaces
• Universal optimality of the $E_8$ and Leech lattices and interpolation formulas

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