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Floating Wigner crystal with no boundary charge fluctuations

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1905.09138.pdf (238.4Kb)
Date
2019-07
Dewey
Sciences connexes (physique, astrophysique)
Sujet
floating crystal; Jellium
Journal issue
Physical Review B : Condensed matter and materials physics
Volume
100
Number
035127
Publication date
07-2019
DOI
http://dx.doi.org/10.1103/PhysRevB.100.035127
URI
https://basepub.dauphine.fr/handle/123456789/20132
Collections
  • CEREMADE : Publications
Metadata
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Author
Lewin, Mathieu
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lieb, Elliott H.
95369 Department of Physics
Seiringer, Robert
224226 Institute of Science and Technology Austria
Type
Article accepté pour publication ou publié
Abstract (EN)
We modify the “floating crystal” trial state for the classical homogeneous electron gas (also known as jellium), in order to suppress the boundary charge fluctuations that are known to lead to a macroscopic increase of the energy. The argument is to melt a thin layer of the crystal close to the boundary and consequently replace it by an incompressible fluid. With the aid of this trial state we show that three different definitions of the ground-state energy of jellium coincide. In the first point of view the electrons are placed in a neutralizing uniform background. In the second definition there is no background but the electrons are submitted to the constraint that their density is constant, as is appropriate in density functional theory. Finally, in the third system each electron interacts with a periodic image of itself; that is, periodic boundary conditions are imposed on the interaction potential.

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