Bose–Einstein condensation in a dilute, trapped gas at positive temperature

article Bose–Einstein condensation in a dilute, trapped gas at positive temperature published yes Andreas Deuchert author 4DA65CD0-F248-11E8-B48F-1D18A9856A870000-0003-3146-6746 Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 Jakob Yngvason author RoSe department Analysis of quantum many-body systems project Structure of the Excitation Spectrum for Many-Body Quantum Systems project We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose–Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer. https://research-explorer.ista.ac.at/download/80/5688/2018_CommunMathPhys_Deuchert.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Springer2019 eng Communications in Mathematical Physics 00046779680000710.1007/s00220-018-3239-0 3682723-776 Deuchert, A., Seiringer, R., & Yngvason, J. (2019). Bose–Einstein condensation in a dilute, trapped gas at positive temperature. Communications in Mathematical Physics. Springer. <a href="https://doi.org/10.1007/s00220-018-3239-0">https://doi.org/10.1007/s00220-018-3239-0</a> Deuchert, Andreas, et al. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.” Communications in Mathematical Physics, vol. 368, no. 2, Springer, 2019, pp. 723–76, doi:<a href="https://doi.org/10.1007/s00220-018-3239-0">10.1007/s00220-018-3239-0</a>. A. Deuchert, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 368 (2019) 723–776. Deuchert A, Seiringer R, Yngvason J. 2019. Bose–Einstein condensation in a dilute, trapped gas at positive temperature. Communications in Mathematical Physics. 368(2), 723–776. A. Deuchert, R. Seiringer, and J. Yngvason, “Bose–Einstein condensation in a dilute, trapped gas at positive temperature,” Communications in Mathematical Physics, vol. 368, no. 2. Springer, pp. 723–776, 2019. Deuchert, Andreas, Robert Seiringer, and Jakob Yngvason. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.” Communications in Mathematical Physics. Springer, 2019. <a href="https://doi.org/10.1007/s00220-018-3239-0">https://doi.org/10.1007/s00220-018-3239-0</a>. Deuchert A, Seiringer R, Yngvason J. Bose–Einstein condensation in a dilute, trapped gas at positive temperature. Communications in Mathematical Physics. 2019;368(2):723-776. doi:<a href="https://doi.org/10.1007/s00220-018-3239-0">10.1007/s00220-018-3239-0</a> 802018-12-11T11:44:31Z2025-04-14T07:27:00Z