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

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.

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Abstract

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.

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Date Published

2019-06-01

Journal Title

Communications in Mathematical Physics

Volume

368

Issue

2

Page

723-776

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### Cite this

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:10.1007/s00220-018-3239-0Deuchert, A., Seiringer, R., & Yngvason, J. (2019). Bose–Einstein condensation in a dilute, trapped gas at positive temperature.

*Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-018-3239-0Deuchert, Andreas, Robert Seiringer, and Jakob Yngvason. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.”

*Communications in Mathematical Physics*. Springer, 2019. https://doi.org/10.1007/s00220-018-3239-0.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, 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:10.1007/s00220-018-3239-0.**All files available under the following license(s):**

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