Floating Wigner crystal and periodic jellium configurations

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

Download
OA 2021_JMathPhy_Lauritsen.pdf 4.35 MB [Published Version]

Journal Article | Published | English

Scopus indexed
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
2021-08-01
Journal Title
Journal of Mathematical Physics
Publisher
AIP Publishing
Acknowledgement
The author would like to thank Robert Seiringer for guidance and many helpful comments on this project. The author would also like to thank Mathieu Lewin for his comments on the manuscript and Lorenzo Portinale for providing his lecture notes for the course “Mathematics of quantum many-body systems” in spring 2020, taught by Robert Seiringer. The Proof of Theorem III.1 is inspired by these lecture notes.
Volume
62
Issue
8
Article Number
083305
ISSN
eISSN
IST-REx-ID

Cite this

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. AIP Publishing. https://doi.org/10.1063/5.0053494
Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” Journal of Mathematical Physics. AIP Publishing, 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. AIP Publishing, 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, AIP Publishing, 2021, doi:10.1063/5.0053494.
All files available under the following license(s):
Creative Commons Attribution 4.0 International Public License (CC-BY 4.0):
Main File(s)
Access Level
OA Open Access
Date Uploaded
2021-10-27
MD5 Checksum
d035be2b894c4d50d90ac5ce252e27cd


Export

Marked Publications

Open Data ISTA Research Explorer

Web of Science

View record in Web of Science®

Sources

arXiv 2103.07975

Search this title in

Google Scholar