Floating Wigner crystal and periodic jellium configurations Lauritsen, Asbjørn Bækgaard ; https://orcid.org/0000-0003-4476-2288 Mathematical Physics Statistical and Nonlinear Physics ddc:530 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. AIP Publishing 2021 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/9891 https://research-explorer.ista.ac.at/download/9891/10188 Lauritsen AB. Floating Wigner crystal and periodic jellium configurations. <i>Journal of Mathematical Physics</i>. 2021;62(8). doi:<a href="https://doi.org/10.1063/5.0053494">10.1063/5.0053494</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0053494 info:eu-repo/semantics/altIdentifier/issn/0022-2488 info:eu-repo/semantics/altIdentifier/e-issn/1089-7658 info:eu-repo/semantics/altIdentifier/wos/000683960800003 info:eu-repo/semantics/altIdentifier/arxiv/2103.07975 https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess