# Free energy of a dilute Bose gas: Lower bound

Seiringer R. 2008. Free energy of a dilute Bose gas: Lower bound. Communications in Mathematical Physics. 279(3), 595–636.

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Abstract

A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density Q and temperature T. In the dilute regime, i.e., when a3 1, where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2 2}-[ - c]2+). Here, c(T) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and [ · ]+ = max{ ·, 0} denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., T ~ 2/3 or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [17] for estimating correlations to temperatures below the critical one.

Publishing Year

Date Published

2008-05-01

Journal Title

Communications in Mathematical Physics

Volume

279

Issue

3

Page

595 - 636

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### Cite this

Seiringer R. Free energy of a dilute Bose gas: Lower bound.

*Communications in Mathematical Physics*. 2008;279(3):595-636. doi:10.1007/s00220-008-0428-2Seiringer, R. (2008). Free energy of a dilute Bose gas: Lower bound.

*Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-008-0428-2Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.”

*Communications in Mathematical Physics*. Springer, 2008. https://doi.org/10.1007/s00220-008-0428-2.R. Seiringer, “Free energy of a dilute Bose gas: Lower bound,”

*Communications in Mathematical Physics*, vol. 279, no. 3. Springer, pp. 595–636, 2008.Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.”

*Communications in Mathematical Physics*, vol. 279, no. 3, Springer, 2008, pp. 595–636, doi:10.1007/s00220-008-0428-2.**All files available under the following license(s):**

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