---
_id: '2363'
abstract:
- lang: eng
text: ' We prove that the Gross-Pitaevskii equation correctly describes the
ground state energy and corresponding one-particle density matrix of rotating,
dilute, trapped Bose gases with repulsive two-body interactions. We also show
that there is 100% Bose-Einstein condensation. While a proof that the GP equation
correctly describes non-rotating or slowly rotating gases was known for some time,
the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground
state is not the lowest eigenstate of the Hamiltonian in this case. We have been
able to overcome this difficulty with the aid of coherent states. Our proof also
conceptually simplifies the previous proof for the slowly rotating case. In the
case of axially symmetric traps, our results show that the appearance of quantized
vortices causes spontaneous symmetry breaking in the ground state. '
author:
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Lieb É, Seiringer R. Derivation of the Gross-Pitaevskii equation for rotating
Bose gases. *Communications in Mathematical Physics*. 2006;264(2):505-537.
doi:10.1007/s00220-006-1524-9
apa: Lieb, É., & Seiringer, R. (2006). Derivation of the Gross-Pitaevskii equation
for rotating Bose gases. *Communications in Mathematical Physics*. Springer.
https://doi.org/10.1007/s00220-006-1524-9
chicago: Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii
Equation for Rotating Bose Gases.” *Communications in Mathematical Physics*.
Springer, 2006. https://doi.org/10.1007/s00220-006-1524-9.
ieee: É. Lieb and R. Seiringer, “Derivation of the Gross-Pitaevskii equation for
rotating Bose gases,” *Communications in Mathematical Physics*, vol. 264,
no. 2. Springer, pp. 505–537, 2006.
ista: Lieb É, Seiringer R. 2006. Derivation of the Gross-Pitaevskii equation for
rotating Bose gases. Communications in Mathematical Physics. 264(2), 505–537.
mla: Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii Equation
for Rotating Bose Gases.” *Communications in Mathematical Physics*, vol.
264, no. 2, Springer, 2006, pp. 505–37, doi:10.1007/s00220-006-1524-9.
short: É. Lieb, R. Seiringer, Communications in Mathematical Physics 264 (2006)
505–537.
date_created: 2018-12-11T11:57:13Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2020-07-14T12:45:40Z
day: '01'
doi: 10.1007/s00220-006-1524-9
extern: 1
intvolume: ' 264'
issue: '2'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0504042
month: '01'
oa: 1
page: 505 - 537
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4561'
quality_controlled: 0
status: public
title: Derivation of the Gross-Pitaevskii equation for rotating Bose gases
type: review
volume: 264
year: '2006'
...