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

Cardoso, Gabriel; Stéphan, Jean-Marie; Abanov, Alexander G.

doi:10.1088/1751-8121/abcab9

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

Journal Article · Thu Dec 03 00:00:00 EST 2020 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8121/abcab9· OSTI ID:1805175

^[1]; ^[2]; ^[3]

Stony Brook Univ., NY (United States); Stony Brook University
Univ. of Lyon (France)
Stony Brook Univ., NY (United States)

In this paper, we revisit the problem of computing the boundary density profile of a droplet of two-dimensional one-component plasma (2D OCP) with logarithmic inter- action 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.

View Accepted Manuscript (DOE)

Research Organization:: Stony Brook Univ., NY (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0017662

OSTI ID:: 1805175

Alternate ID(s):: OSTI ID: 23130922

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 1 Vol. 54; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (51)

Classical coulomb systems near a plane wall. I Jancovici, B. Journal of Statistical Physics, Vol. 28, Issue 1 https://doi.org/10.1007/bf01011622	journal	May 1982
Statistical mechanics of two-dimensional Coulomb systems de Leeuw, S. W.; Perram, J. W. Physica A: Statistical Mechanics and its Applications, Vol. 113, Issue 3 https://doi.org/10.1016/0378-4371(82)90156-x	journal	July 1982
Analogies between random matrix ensembles and the one-component plasma in two-dimensions Forrester, Peter J. Nuclear Physics B, Vol. 904 https://doi.org/10.1016/j.nuclphysb.2016.01.014	journal	March 2016
On the classical two-dimensional one-component Coulomb plasma Alastuey, A.; Jancovici, B. Journal de Physique, Vol. 42, Issue 1 https://doi.org/10.1051/jphys:019810042010100	journal	January 1981
Surface density profile of the one-component plasma Badiali, J. P.; Rosinberg, M. L.; Levesque, D. Journal of Physics C: Solid State Physics, Vol. 16, Issue 11 https://doi.org/10.1088/0022-3719/16/11/021	journal	April 1983
Vortex flows on closed surfaces Bogatskiy, A. Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 47 https://doi.org/10.1088/1751-8121/ab4e6a	journal	October 2019
Monte Carlo evaluation of trial wave functions for the fractional quantized Hall effect: Disk geometry Morf, R.; Halperin, B. I. Physical Review B, Vol. 33, Issue 4 https://doi.org/10.1103/physrevb.33.2221	journal	February 1986
Edge of the Laughlin droplet Datta, Nilanjana; Morf, Rudolf; Ferrari, Ruggero Physical Review B, Vol. 53, Issue 16 https://doi.org/10.1103/physrevb.53.10906	journal	April 1996
Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response Can, T.; Laskin, M.; Wiegmann, P. Physical Review Letters, Vol. 113, Issue 4 https://doi.org/10.1103/physrevlett.113.046803	journal	July 2014
Edge Wave and Boundary Layer of Vortex Matter Bogatskiy, A.; Wiegmann, P. Physical Review Letters, Vol. 122, Issue 21 https://doi.org/10.1103/physrevlett.122.214505	journal	May 2019
Temperature Dependence of the Shear Modulus and Melting of the Two-Dimensional Electron Solid Morf, R. H. Physical Review Letters, Vol. 43, Issue 13 https://doi.org/10.1103/physrevlett.43.931	journal	September 1979
Entanglement spectroscopy of chiral edge modes in the Quantum Hall effect Estienne, Benoit; Stéphan, Jean-Marie arXiv https://doi.org/10.48550/arxiv.1911.10125	text	January 2019
On a periodic boundary value problem with exponential nonlinearities Ricciardi, Tonia; Tarantello, Gabriella Differential and Integral Equations, Vol. 11, Issue 5 https://doi.org/10.57262/die/1367329668	journal	January 1998
Internal Energy of the Classical Two- and Three-Dimensional One-Component-Plasma: Internal Energy of the Classical Two- and Three-Dimensional One-Component-Plasma Khrapak, S. A.; Khrapak, A. G. Contributions to Plasma Physics, Vol. 56, Issue 3-4 https://doi.org/10.1002/ctpp.201500104	journal	April 2016
A Monte Carlo study of the classical two-dimensional one-component plasma Caillol, J. M.; Levesque, D.; Weis, J. J. Journal of Statistical Physics, Vol. 28, Issue 2 https://doi.org/10.1007/bf01012609	journal	June 1982
Classical Coulomb systems near a plane wall. II Jancovici, B. Journal of Statistical Physics, Vol. 29, Issue 2 https://doi.org/10.1007/bf01020786	journal	October 1982
FQHE on curved backgrounds, free fields and large N Ferrari, Frank; Klevtsov, Semyon Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/jhep12(2014)086	journal	December 2014
Fluctuations of Two Dimensional Coulomb Gases Leblé, Thomas; Serfaty, Sylvia Geometric and Functional Analysis, Vol. 28, Issue 2 https://doi.org/10.1007/s00039-018-0443-1	journal	April 2018
Uniqueness of Solutions to the Mean Field Equations for the Spherical Onsager Vortex Lin, Chang-Shou Archive for Rational Mechanics and Analysis, Vol. 153, Issue 2 https://doi.org/10.1007/s002050000085	journal	June 2000
Entanglement Entropy and Berezin–Toeplitz Operators Charles, Laurent; Estienne, Benoit Communications in Mathematical Physics, Vol. 376, Issue 1 https://doi.org/10.1007/s00220-019-03625-y	journal	November 2019
Exact and Asymptotic Features of the Edge Density Profile for the One Component Plasma in Two Dimensions Can, T.; Forrester, P. J.; Téllez, G. Journal of Statistical Physics, Vol. 158, Issue 5 https://doi.org/10.1007/s10955-014-1152-2	journal	December 2014
Statistical mechanics of simple coulomb systems Baus, M. Physics Reports, Vol. 59, Issue 1 https://doi.org/10.1016/0370-1573(80)90022-8	journal	March 1980
Uniqueness of solutions for a mean field equation on torus Lin, Chang-Shou; Lucia, Marcello Journal of Differential Equations, Vol. 229, Issue 1 https://doi.org/10.1016/j.jde.2005.11.003	journal	October 2006
Is the Two-Dimensional One-Component Plasma Exactly Solvable? Šamaj, L. Journal of Statistical Physics, Vol. 117, Issue 1/2 https://doi.org/10.1023/B:JOSS.0000044056.19438.2c	journal	October 2004
Charge Fluctuations in the Two-Dimensional One-Component Plasma Levesque, D.; Weis, J. -J.; Lebowitz, J. L. Journal of Statistical Physics, Vol. 100, Issue 1/2, p. 209-222 https://doi.org/10.1023/a:1018643829340	journal	January 2000
The Sixth-Moment Sum Rule for the Pair Correlations of the Two-Dimensional One-Component Plasma: Exact Result Kalinay, P.; Markoš, P.; Šamaj, L. Journal of Statistical Physics, Vol. 98, Issue 3/4, p. 639-666 https://doi.org/10.1023/a:1018667207145	journal	February 2000
Statistical Ensembles of Complex, Quaternion, and Real Matrices Ginibre, Jean Journal of Mathematical Physics, Vol. 6, Issue 3 https://doi.org/10.1063/1.1704292	journal	March 1965
Freezing of the classical two‐dimensional, one‐component plasma Radloff, Patricia L.; Bagchi, Biman; Cerjan, Charles The Journal of Chemical Physics, Vol. 81, Issue 3 https://doi.org/10.1063/1.447775	journal	August 1984
Note: Melting criterion for soft particle systems in two dimensions Khrapak, Sergey The Journal of Chemical Physics, Vol. 148, Issue 14 https://doi.org/10.1063/1.5027201	journal	April 2018
Ordering, metastability and phase transitions in two-dimensional systems Kosterlitz, J M; Thouless, D J Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203 https://doi.org/10.1088/0022-3719/6/7/010	journal	April 1973
Large- N expansion for the 2D Dyson gas Zabrodin, A.; Wiegmann, P. Journal of Physics A: Mathematical and General, Vol. 39, Issue 28 https://doi.org/10.1088/0305-4470/39/28/S10	journal	June 2006
Large- N expansion for the 2D Dyson gas Zabrodin, A.; Wiegmann, P. Journal of Physics A: Mathematical and General, Vol. 39, Issue 28 https://doi.org/10.1088/0305-4470/39/28/s10	journal	June 2006
Crystallization for Coulomb and Riesz interactions as a consequence of the Cohn-Kumar conjecture Petrache, Mircea; Serfaty, Sylvia Proceedings of the American Mathematical Society, Vol. 148, Issue 7 https://doi.org/10.1090/proc/15003	journal	March 2020
The Noise in the Circular Law and the Gaussian Free Field Rider, B.; Virag, B. International Mathematics Research Notices https://doi.org/10.1093/imrn/rnm006	journal	July 2010
Entanglement spectroscopy of chiral edge modes in the quantum Hall effect Estienne, Benoit; Stéphan, Jean-Marie Physical Review B, Vol. 101, Issue 11 https://doi.org/10.1103/physrevb.101.115136	journal	March 2020
Melting and the vector Coulomb gas in two dimensions Young, A. P. Physical Review B, Vol. 19, Issue 4 https://doi.org/10.1103/physrevb.19.1855	journal	February 1979
Dislocation-mediated melting in two dimensions Nelson, David R.; Halperin, B. I. Physical Review B, Vol. 19, Issue 5 https://doi.org/10.1103/physrevb.19.2457	journal	March 1979
Hydrodynamics of Euler incompressible fluid and the fractional quantum Hall effect Wiegmann, P. B. Physical Review B, Vol. 88, Issue 24 https://doi.org/10.1103/physrevb.88.241305	journal	December 2013
Singular behavior at the edge of Laughlin states Can, T.; Forrester, P. J.; Téllez, G. Physical Review B, Vol. 89, Issue 23 https://doi.org/10.1103/physrevb.89.235137	journal	June 2014
Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions Kapfer, Sebastian C.; Krauth, Werner Physical Review Letters, Vol. 114, Issue 3 https://doi.org/10.1103/physrevlett.114.035702	journal	January 2015
Theory of Two-Dimensional Melting Halperin, B. I.; Nelson, David R. Physical Review Letters, Vol. 41, Issue 2 https://doi.org/10.1103/physrevlett.41.121	journal	July 1978
Exact Results for the Two-Dimensional One-Component Plasma Jancovici, B. Physical Review Letters, Vol. 46, Issue 6 https://doi.org/10.1103/physrevlett.46.386	journal	February 1981
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations Laughlin, R. B. Physical Review Letters, Vol. 50, Issue 18 https://doi.org/10.1103/physrevlett.50.1395	journal	May 1983
Cooperative Phenomena below Melting of the One-Component Two-Dimensional Plasma Choquard, Ph.; Clerouin, J. Physical Review Letters, Vol. 50, Issue 26 https://doi.org/10.1103/physrevlett.50.2086	journal	June 1983
Sum rules in charged fluids Martin, Ph. A. Reviews of Modern Physics, Vol. 60, Issue 4 https://doi.org/10.1103/revmodphys.60.1075	journal	October 1988
Anomalous hydrodynamics of fractional quantum Hall states Wiegmann, P. Journal of Experimental and Theoretical Physics, Vol. 117, Issue 3 https://doi.org/10.1134/s1063776113110162	journal	September 2013
Gauge Fields in Condensed Matter Kleinert, H. World Scientific https://doi.org/10.1142/0356	book	November 1989
2D Coulomb gases and the renormalized energy Sandier, Etienne; Serfaty, Sylvia The Annals of Probability, Vol. 43, Issue 4 https://doi.org/10.1214/14-aop927	journal	July 2015
Fluctuations of eigenvalues of random normal matrices Ameur, Yacin; Hedenmalm, Håkan; Makarov, Nikolai Duke Mathematical Journal, Vol. 159, Issue 1 https://doi.org/10.1215/00127094-1384782	journal	July 2011
Log-Gases and Random Matrices (LMS-34) Forrester, Peter J. London Mathematical Society Monographs, Vol. 34 https://doi.org/10.1515/9781400835416	book	December 2010
The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem Bauerschmidt, Roland; Bourgade, Paul; Nikula, Miika Advances in Theoretical and Mathematical Physics, Vol. 23, Issue 4 https://doi.org/10.4310/atmp.2019.v23.n4.a1	journal	January 2019

Similar Records

Matrix model for a quantum Hall droplet with manifest particle-hole symmetry

Journal Article · Fri Apr 15 00:00:00 EDT 2005 · Physical Review. D, Particles Fields · OSTI ID:20709105

Numerical simulation of Coulombic freezing

Conference · Fri Jan 31 23:00:00 EST 1992 · OSTI ID:5732217

Numerical simulation of Coulombic freezing

Conference · Fri Jan 31 23:00:00 EST 1992 · OSTI ID:10132386

Related Subjects

2D OCP
2D melting
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Coulomb plasma
Monte-Carlo method
Wigner crystal
boundary density
freezing

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

Citation Formats

References (51)

Similar Records

Related Subjects