article published yes Asbjørn Bækgaard Lauritsen author e1a2682f-dc8d-11ea-abe3-81da9ac728f10000-0003-4476-2288 GradSch department RoSe department 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. https://research-explorer.ista.ac.at/download/9891/10188/2021_JMathPhy_Lauritsen.pdf application/pdfno AIP Publishing2021 eng Mathematical PhysicsStatistical and Nonlinear Physics 0022-2488 1089-7658 2103.07975 00068396080000310.1063/5.0053494 628 A.B. Lauritsen, Journal of Mathematical Physics 62 (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.” <i>Journal of Mathematical Physics</i>, vol. 62, no. 8, 083305, AIP Publishing, 2021, doi:<a href="https://doi.org/10.1063/5.0053494">10.1063/5.0053494</a>. Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2021. <a href="https://doi.org/10.1063/5.0053494">https://doi.org/10.1063/5.0053494</a>. 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> A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,” <i>Journal of Mathematical Physics</i>, vol. 62, no. 8. AIP Publishing, 2021. Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href="https://doi.org/10.1063/5.0053494">https://doi.org/10.1063/5.0053494</a> 98912021-08-12T07:08:36Z2024-10-09T21:00:48Z