article published yes Chiara Boccato author 342E7E22-F248-11E8-B48F-1D18A9856A87 Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 RoSe department Analysis of quantum many-body systems project We consider a gas of n bosonic particles confined in a box [−ℓ/2,ℓ/2]3 with Neumann boundary conditions. We prove Bose–Einstein condensation in the Gross–Pitaevskii regime, with an optimal bound on the condensate depletion. Moreover, our lower bound for the ground state energy in a small box [−ℓ/2,ℓ/2]3 implies (via Neumann bracketing) a lower bound for the ground state energy of N bosons in a large box [−L/2,L/2]3 with density ρ=N/L3 in the thermodynamic limit. Springer Nature2023 eng 1424-0637 2205.15284 00091075180000210.1007/s00023-022-01252-3 241505-1560 Boccato, C., &#38; Seiringer, R. (2023). The Bose Gas in a box with Neumann boundary conditions. <i>Annales Henri Poincare</i>. Springer Nature. <a href="https://doi.org/10.1007/s00023-022-01252-3">https://doi.org/10.1007/s00023-022-01252-3</a> Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature, 2023, pp. 1505–60, doi:<a href="https://doi.org/10.1007/s00023-022-01252-3">10.1007/s00023-022-01252-3</a>. Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00023-022-01252-3">https://doi.org/10.1007/s00023-022-01252-3</a>. Boccato C, Seiringer R. The Bose Gas in a box with Neumann boundary conditions. <i>Annales Henri Poincare</i>. 2023;24:1505-1560. doi:<a href="https://doi.org/10.1007/s00023-022-01252-3">10.1007/s00023-022-01252-3</a> Boccato C, Seiringer R. 2023. The Bose Gas in a box with Neumann boundary conditions. Annales Henri Poincare. 24, 1505–1560. C. Boccato and R. Seiringer, “The Bose Gas in a box with Neumann boundary conditions,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 1505–1560, 2023. C. Boccato, R. Seiringer, Annales Henri Poincare 24 (2023) 1505–1560. 121832023-01-15T23:00:52Z2025-04-14T07:26:59Z