article published yes Mathieu Lewin author Elliott H. Lieb author Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 RoSe department Analysis of quantum many-body systems project We modify the "floating crystal" trial state for the classical homogeneous electron gas (also known as jellium), in order to suppress the boundary charge fluctuations that are known to lead to a macroscopic increase of the energy. The argument is to melt a thin layer of the crystal close to the boundary and consequently replace it by an incompressible fluid. With the aid of this trial state we show that three different definitions of the ground-state energy of jellium coincide. In the first point of view the electrons are placed in a neutralizing uniform background. In the second definition there is no background but the electrons are submitted to the constraint that their density is constant, as is appropriate in density functional theory. Finally, in the third system each electron interacts with a periodic image of itself; that is, periodic boundary conditions are imposed on the interaction potential. American Physical Society2019 eng 2469-9950 2469-9969 1905.09138 00047788820000110.1103/physrevb.100.035127 1003 Lewin, Mathieu, et al. “Floating Wigner Crystal with No Boundary Charge Fluctuations.” <i>Physical Review B</i>, vol. 100, no. 3, 035127, American Physical Society, 2019, doi:<a href="https://doi.org/10.1103/physrevb.100.035127">10.1103/physrevb.100.035127</a>. Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2019). Floating Wigner crystal with no boundary charge fluctuations. <i>Physical Review B</i>. American Physical Society. <a href="https://doi.org/10.1103/physrevb.100.035127">https://doi.org/10.1103/physrevb.100.035127</a> Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Floating Wigner Crystal with No Boundary Charge Fluctuations.” <i>Physical Review B</i>. American Physical Society, 2019. <a href="https://doi.org/10.1103/physrevb.100.035127">https://doi.org/10.1103/physrevb.100.035127</a>. M. Lewin, E.H. Lieb, R. Seiringer, Physical Review B 100 (2019). Lewin M, Lieb EH, Seiringer R. Floating Wigner crystal with no boundary charge fluctuations. <i>Physical Review B</i>. 2019;100(3). doi:<a href="https://doi.org/10.1103/physrevb.100.035127">10.1103/physrevb.100.035127</a> M. Lewin, E. H. Lieb, and R. Seiringer, “Floating Wigner crystal with no boundary charge fluctuations,” <i>Physical Review B</i>, vol. 100, no. 3. American Physical Society, 2019. Lewin M, Lieb EH, Seiringer R. 2019. Floating Wigner crystal with no boundary charge fluctuations. Physical Review B. 100(3), 035127. 70152019-11-13T08:41:48Z2025-04-14T07:27:00Z