---
_id: '2369'
abstract:
- lang: eng
text: One of the most remarkable recent developments in the study of ultracold Bose
gases is the observation of a reversible transition from a Bose Einstein condensate
to a state composed of localized atoms as the strength of a periodic, optical
trapping potential is varied. In [1] a model of this phenomenon has been analyzed
rigorously. The gas is a hard core lattice gas and the optical lattice is modeled
by a periodic potential of strength λ. For small λ and temperature Bose- Einstein
condensation (BEC) is proved to occur, while at large λ BEC disappears, even in
the ground state, which is a Mott-insulator state with a characteristic gap. The
inter-particle interaction is essential for this effect. This contribution gives
a pedagogical survey of these results.
alternative_title:
- LNP
author:
- first_name: Michael
full_name: Aizenman, Michael
last_name: Aizenman
- 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
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: 'Aizenman M, Lieb É, Seiringer R, Solovej J, Yngvason J. Bose-Einstein condensation
as a quantum phase transition in an optical lattice. In: Asch J, Joye A, eds.
*Mathematical Physics of Quantum Mechanics*. Vol 690. Springer; 2006:199-215.
doi:10.1007/b11573432'
apa: Aizenman, M., Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2006).
Bose-Einstein condensation as a quantum phase transition in an optical lattice.
In J. Asch & A. Joye (Eds.), *Mathematical Physics of Quantum Mechanics*
(Vol. 690, pp. 199–215). Springer. https://doi.org/10.1007/b11573432
chicago: Aizenman, Michael, Élliott Lieb, Robert Seiringer, Jan Solovej, and Jakob
Yngvason. “Bose-Einstein Condensation as a Quantum Phase Transition in an Optical
Lattice.” In *Mathematical Physics of Quantum Mechanics*, edited by Joachim
Asch and Alain Joye, 690:199–215. Springer, 2006. https://doi.org/10.1007/b11573432.
ieee: M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, “Bose-Einstein
condensation as a quantum phase transition in an optical lattice,” in *Mathematical
Physics of Quantum Mechanics*, vol. 690, J. Asch and A. Joye, Eds. Springer,
2006, pp. 199–215.
ista: Aizenman M, Lieb É, Seiringer R, Solovej J, Yngvason J. 2006. Bose-Einstein
condensation as a quantum phase transition in an optical lattice. Mathematical
Physics of Quantum Mechanics. , LNP, vol. 690. 199–215.
mla: Aizenman, Michael, et al. “Bose-Einstein Condensation as a Quantum Phase Transition
in an Optical Lattice.” *Mathematical Physics of Quantum Mechanics*, edited
by Joachim Asch and Alain Joye, vol. 690, Springer, 2006, pp. 199–215, doi:10.1007/b11573432.
short: M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, in:, J. Asch,
A. Joye (Eds.), Mathematical Physics of Quantum Mechanics, Springer, 2006, pp.
199–215.
date_created: 2018-12-11T11:57:16Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2020-07-14T12:45:40Z
day: '01'
doi: 10.1007/b11573432
editor:
- first_name: Joachim
full_name: Asch, Joachim
last_name: Asch
- first_name: Alain
full_name: Joye, Alain
last_name: Joye
extern: 1
intvolume: ' 690'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/cond-mat/0412034
month: '01'
oa: 1
page: 199 - 215
publication: Mathematical Physics of Quantum Mechanics
publication_status: published
publisher: Springer
publist_id: '4559'
quality_controlled: 0
status: public
title: Bose-Einstein condensation as a quantum phase transition in an optical lattice
type: book_chapter
volume: 690
year: '2006'
...