Floating Wigner crystal and periodic jellium configurations
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 nextorder 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, 3974 (2018)], we relate the jellium energy to the order n term in the logarithmic energy of n points on the unit 2sphere. We improve upon known lower bounds for this renormalized energy. Additionally, we derive formulas for the jellium energy of periodic configurations.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 August 2021
 DOI:
 10.1063/5.0053494
 Bibcode:
 2021JMP....62h3305L