---
_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'
...
---
_id: '2364'
abstract:
- lang: eng
text: We present an inequality that gives a lower bound on the expectation value
of certain two-body interaction potentials in a general state on Fock space in
terms of the corresponding expectation value for thermal equilibrium states of
non-interacting systems and the difference in the free energy. This bound can
be viewed as a rigorous version of first-order perturbation theory for many-body
systems at positive temperature. As an application, we give a proof of the first
two terms in a high density (and high temperature) expansion of the free energy
of jellium with Coulomb interactions, both in the fermionic and bosonic case.
For bosons, our method works above the transition temperature (for the non-interacting
gas) for Bose-Einstein condensation.
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. A correlation estimate for quantum many-body systems at positive
temperature. Reviews in Mathematical Physics. 2006;18(3):233-253. doi:10.1142/S0129055X06002632
apa: Seiringer, R. (2006). A correlation estimate for quantum many-body systems
at positive temperature. Reviews in Mathematical Physics. World Scientific
Publishing. https://doi.org/10.1142/S0129055X06002632
chicago: Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems
at Positive Temperature.” Reviews in Mathematical Physics. World Scientific
Publishing, 2006. https://doi.org/10.1142/S0129055X06002632.
ieee: R. Seiringer, “A correlation estimate for quantum many-body systems at positive
temperature,” Reviews in Mathematical Physics, vol. 18, no. 3. World Scientific
Publishing, pp. 233–253, 2006.
ista: Seiringer R. 2006. A correlation estimate for quantum many-body systems at
positive temperature. Reviews in Mathematical Physics. 18(3), 233–253.
mla: Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems at
Positive Temperature.” Reviews in Mathematical Physics, vol. 18, no. 3,
World Scientific Publishing, 2006, pp. 233–53, doi:10.1142/S0129055X06002632.
short: R. Seiringer, Reviews in Mathematical Physics 18 (2006) 233–253.
date_created: 2018-12-11T11:57:14Z
date_published: 2006-04-01T00:00:00Z
date_updated: 2021-01-12T06:57:02Z
day: '01'
doi: 10.1142/S0129055X06002632
extern: 1
intvolume: ' 18'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0601051
month: '04'
oa: 1
page: 233 - 253
publication: Reviews in Mathematical Physics
publication_status: published
publisher: World Scientific Publishing
publist_id: '4562'
quality_controlled: 0
status: public
title: A correlation estimate for quantum many-body systems at positive temperature
type: journal_article
volume: 18
year: '2006'
...
---
_id: '2365'
abstract:
- lang: eng
text: We consider a gas of fermions with non-zero spin at temperature T and chemical
potential μ. We show that if the range of the interparticle interaction is small
compared to the mean particle distance, the thermodynamic pressure differs to
leading order from the corresponding expression for non-interacting particles
by a term proportional to the scattering length of the interparticle interaction.
This is true for any repulsive interaction, including hard cores. The result is
uniform in the temperature as long as T is of the same order as the Fermi temperature,
or smaller.
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. The thermodynamic pressure of a dilute fermi gas. Communications
in Mathematical Physics. 2006;261(3):729-757. doi:10.1007/s00220-005-1433-3
apa: Seiringer, R. (2006). The thermodynamic pressure of a dilute fermi gas. Communications
in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-005-1433-3
chicago: Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.”
Communications in Mathematical Physics. Springer, 2006. https://doi.org/10.1007/s00220-005-1433-3.
ieee: R. Seiringer, “The thermodynamic pressure of a dilute fermi gas,” Communications
in Mathematical Physics, vol. 261, no. 3. Springer, pp. 729–757, 2006.
ista: Seiringer R. 2006. The thermodynamic pressure of a dilute fermi gas. Communications
in Mathematical Physics. 261(3), 729–757.
mla: Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.” Communications
in Mathematical Physics, vol. 261, no. 3, Springer, 2006, pp. 729–57, doi:10.1007/s00220-005-1433-3.
short: R. Seiringer, Communications in Mathematical Physics 261 (2006) 729–757.
date_created: 2018-12-11T11:57:14Z
date_published: 2006-02-01T00:00:00Z
date_updated: 2021-01-12T06:57:02Z
day: '01'
doi: 10.1007/s00220-005-1433-3
extern: 1
intvolume: ' 261'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0412086
month: '02'
oa: 1
page: 729 - 757
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4563'
quality_controlled: 0
status: public
title: The thermodynamic pressure of a dilute fermi gas
type: journal_article
volume: 261
year: '2006'
...
---
_id: '2366'
abstract:
- lang: eng
text: Inequalities are derived for power sums of the real part and the modulus of
the eigenvalues of a Schrödinger operator with a complex-valued potential.
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Ari
full_name: Laptev, Ari
last_name: Laptev
- 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: Frank R, Laptev A, Lieb É, Seiringer R. Lieb-Thirring inequalities for Schrödinger
operators with complex-valued potentials. Letters in Mathematical Physics.
2006;77(3):309-316. doi:10.1007/s11005-006-0095-1
apa: Frank, R., Laptev, A., Lieb, É., & Seiringer, R. (2006). Lieb-Thirring
inequalities for Schrödinger operators with complex-valued potentials. Letters
in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-006-0095-1
chicago: Frank, Rupert, Ari Laptev, Élliott Lieb, and Robert Seiringer. “Lieb-Thirring
Inequalities for Schrödinger Operators with Complex-Valued Potentials.” Letters
in Mathematical Physics. Springer, 2006. https://doi.org/10.1007/s11005-006-0095-1.
ieee: R. Frank, A. Laptev, É. Lieb, and R. Seiringer, “Lieb-Thirring inequalities
for Schrödinger operators with complex-valued potentials,” Letters in Mathematical
Physics, vol. 77, no. 3. Springer, pp. 309–316, 2006.
ista: Frank R, Laptev A, Lieb É, Seiringer R. 2006. Lieb-Thirring inequalities for
Schrödinger operators with complex-valued potentials. Letters in Mathematical
Physics. 77(3), 309–316.
mla: Frank, Rupert, et al. “Lieb-Thirring Inequalities for Schrödinger Operators
with Complex-Valued Potentials.” Letters in Mathematical Physics, vol.
77, no. 3, Springer, 2006, pp. 309–16, doi:10.1007/s11005-006-0095-1.
short: R. Frank, A. Laptev, É. Lieb, R. Seiringer, Letters in Mathematical Physics
77 (2006) 309–316.
date_created: 2018-12-11T11:57:15Z
date_published: 2006-09-01T00:00:00Z
date_updated: 2021-01-12T06:57:03Z
day: '01'
doi: 10.1007/s11005-006-0095-1
extern: 1
intvolume: ' 77'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0605017
month: '09'
oa: 1
page: 309 - 316
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4560'
quality_controlled: 0
status: public
title: Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
type: journal_article
volume: 77
year: '2006'
...
---
_id: '2368'
abstract:
- lang: eng
text: The recent experimental success in creating Bose-Einstein condensates of alkali
atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest
in the mathematical description of interacting Bose gases.
alternative_title:
- LNP
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. Dilute, trapped Bose gases and Bose-Einstein condensation. In:
Dereziński J, Siedentop H, eds. Large Coulomb Systems. Vol 695. Springer;
2006:249-274. doi:10.1007/3-540-32579-4_6'
apa: Seiringer, R. (2006). Dilute, trapped Bose gases and Bose-Einstein condensation.
In J. Dereziński & H. Siedentop (Eds.), Large Coulomb Systems (Vol.
695, pp. 249–274). Springer. https://doi.org/10.1007/3-540-32579-4_6
chicago: Seiringer, Robert. “Dilute, Trapped Bose Gases and Bose-Einstein Condensation.”
In Large Coulomb Systems, edited by Jan Dereziński and Heinz Siedentop,
695:249–74. Springer, 2006. https://doi.org/10.1007/3-540-32579-4_6.
ieee: R. Seiringer, “Dilute, trapped Bose gases and Bose-Einstein condensation,”
in Large Coulomb Systems, vol. 695, J. Dereziński and H. Siedentop, Eds.
Springer, 2006, pp. 249–274.
ista: 'Seiringer R. 2006.Dilute, trapped Bose gases and Bose-Einstein condensation.
In: Large Coulomb Systems. LNP, vol. 695, 249–274.'
mla: Seiringer, Robert. “Dilute, Trapped Bose Gases and Bose-Einstein Condensation.”
Large Coulomb Systems, edited by Jan Dereziński and Heinz Siedentop, vol.
695, Springer, 2006, pp. 249–74, doi:10.1007/3-540-32579-4_6.
short: R. Seiringer, in:, J. Dereziński, H. Siedentop (Eds.), Large Coulomb Systems,
Springer, 2006, pp. 249–274.
date_created: 2018-12-11T11:57:15Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:03Z
day: '01'
doi: 10.1007/3-540-32579-4_6
editor:
- first_name: Jan
full_name: Dereziński, Jan
last_name: Dereziński
- first_name: Heinz
full_name: Siedentop, Heinz
last_name: Siedentop
extern: 1
intvolume: ' 695'
month: '01'
page: 249 - 274
publication: Large Coulomb Systems
publication_status: published
publisher: Springer
publist_id: '4558'
quality_controlled: 0
status: public
title: Dilute, trapped Bose gases and Bose-Einstein condensation
type: book_chapter
volume: 695
year: '2006'
...