Floating Wigner crystal and periodic jellium configurations

Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 62(8), 083305.

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Journal Article | Published | English
Abstract
Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)], we present a modified “floating crystal” trial state for jellium (also known as the classical homogeneous electron gas) with density equal to a characteristic function. This allows us to show that three definitions of the jellium energy coincide in dimensions d ≥ 2, thus extending the result of Cotar and Petrache [“Equality of the Jellium and uniform electron gas next-order asymptotic terms for Coulomb and Riesz potentials,” arXiv: 1707.07664 (2019)] and Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)] that the three definitions coincide in dimension d ≥ 3. We show that the jellium energy is also equivalent to a “renormalized energy” studied in a series of papers by Serfaty and others, and thus, by the work of Bétermin and Sandier [Constr. Approximation 47, 39–74 (2018)], we relate the jellium energy to the order n term in the logarithmic energy of n points on the unit 2-sphere. We improve upon known lower bounds for this renormalized energy. Additionally, we derive formulas for the jellium energy of periodic configurations.
Publishing Year
Date Published
2021-08-11
Journal Title
Journal of Mathematical Physics
Volume
62
Issue
8
Article Number
083305
ISSN
eISSN
IST-REx-ID

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Lauritsen AB. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 2021;62(8). doi:10.1063/5.0053494
Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/5.0053494
Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” Journal of Mathematical Physics. American Institute of Physics, 2021. https://doi.org/10.1063/5.0053494.
A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,” Journal of Mathematical Physics, vol. 62, no. 8. American Institute of Physics, 2021.
Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 62(8), 083305.
Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” Journal of Mathematical Physics, vol. 62, no. 8, 083305, American Institute of Physics, 2021, doi:10.1063/5.0053494.
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