---
_id: '2374'
abstract:
- lang: eng
text: 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.
author:
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Seiringer R. Free energy of a dilute Bose gas: Lower bound. *Communications
in Mathematical Physics*. 2008;279(3):595-636. doi:10.1007/s00220-008-0428-2'
apa: 'Seiringer, R. (2008). Free energy of a dilute Bose gas: Lower bound. *Communications
in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-008-0428-2'
chicago: 'Seiringer, 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.'
ieee: 'R. Seiringer, “Free energy of a dilute Bose gas: Lower bound,” *Communications
in Mathematical Physics*, vol. 279, no. 3. Springer, pp. 595–636, 2008.'
ista: 'Seiringer R. 2008. Free energy of a dilute Bose gas: Lower bound. Communications
in Mathematical Physics. 279(3), 595–636.'
mla: '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.'
short: R. Seiringer, Communications in Mathematical Physics 279 (2008) 595–636.
date_created: 2018-12-11T11:57:17Z
date_published: 2008-05-01T00:00:00Z
date_updated: 2021-01-12T06:57:06Z
day: '01'
doi: 10.1007/s00220-008-0428-2
extern: 1
intvolume: ' 279'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0608069
month: '05'
oa: 1
page: 595 - 636
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4551'
quality_controlled: 0
status: public
title: 'Free energy of a dilute Bose gas: Lower bound'
type: journal_article
volume: 279
year: '2008'
...