---
_id: '7514'
abstract:
- lang: eng
text: "We study the interacting homogeneous Bose gas in two spatial dimensions in
the thermodynamic limit at fixed density. We shall be concerned with some mathematical
aspects of this complicated problem in many-body quantum mechanics. More specifically,
we consider the dilute limit where the scattering length of the interaction potential,
which is a measure for the effective range of the potential, is small compared
to the average distance between the particles. We are interested in a setting
with positive (i.e., non-zero) temperature. After giving a survey of the relevant
literature in the field, we provide some facts and examples to set expectations
for the two-dimensional system. The crucial difference to the three-dimensional
system is that there is no Bose–Einstein condensate at positive temperature due
to the Hohenberg–Mermin–Wagner theorem. However, it turns out that an asymptotic
formula for the free energy holds similarly to the three-dimensional case.\r\nWe
motivate this formula by considering a toy model with δ interaction potential.
By restricting this model Hamiltonian to certain trial states with a quasi-condensate
we obtain an upper bound for the free energy that still has the quasi-condensate
fraction as a free parameter. When minimizing over the quasi-condensate fraction,
we obtain the Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity,
which plays an important role in our rigorous contribution. The mathematically
rigorous result that we prove concerns the specific free energy in the dilute
limit. We give upper and lower bounds on the free energy in terms of the free
energy of the non-interacting system and a correction term coming from the interaction.
Both bounds match and thus we obtain the leading term of an asymptotic approximation
in the dilute limit, provided the thermal wavelength of the particles is of the
same order (or larger) than the average distance between the particles. The remarkable
feature of this result is its generality: the correction term depends on the interaction
potential only through its scattering length and it holds for all nonnegative
interaction potentials with finite scattering length that are measurable. In particular,
this allows to model an interaction of hard disks."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Simon
full_name: Mayer, Simon
id: 30C4630A-F248-11E8-B48F-1D18A9856A87
last_name: Mayer
citation:
ama: Mayer S. The free energy of a dilute two-dimensional Bose gas. 2020. doi:10.15479/AT:ISTA:7514
apa: Mayer, S. (2020). The free energy of a dilute two-dimensional Bose gas.
Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7514
chicago: Mayer, Simon. “The Free Energy of a Dilute Two-Dimensional Bose Gas.” Institute
of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7514.
ieee: S. Mayer, “The free energy of a dilute two-dimensional Bose gas,” Institute
of Science and Technology Austria, 2020.
ista: Mayer S. 2020. The free energy of a dilute two-dimensional Bose gas. Institute
of Science and Technology Austria.
mla: Mayer, Simon. The Free Energy of a Dilute Two-Dimensional Bose Gas.
Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7514.
short: S. Mayer, The Free Energy of a Dilute Two-Dimensional Bose Gas, Institute
of Science and Technology Austria, 2020.
date_created: 2020-02-24T09:17:27Z
date_published: 2020-02-24T00:00:00Z
date_updated: 2023-09-07T13:12:42Z
day: '24'
ddc:
- '510'
degree_awarded: PhD
department:
- _id: RoSe
- _id: GradSch
doi: 10.15479/AT:ISTA:7514
ec_funded: 1
file:
- access_level: open_access
checksum: b4de7579ddc1dbdd44ff3f17c48395f6
content_type: application/pdf
creator: dernst
date_created: 2020-02-24T09:15:06Z
date_updated: 2020-07-14T12:47:59Z
file_id: '7515'
file_name: thesis.pdf
file_size: 1563429
relation: main_file
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content_type: application/x-zip-compressed
creator: dernst
date_created: 2020-02-24T09:15:16Z
date_updated: 2020-07-14T12:47:59Z
file_id: '7516'
file_name: thesis_source.zip
file_size: 2028038
relation: source_file
file_date_updated: 2020-07-14T12:47:59Z
has_accepted_license: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: '148'
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '7524'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
title: The free energy of a dilute two-dimensional Bose gas
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2020'
...
---
_id: '7611'
abstract:
- lang: eng
text: We consider a system of N bosons in the limit N→∞, interacting through singular
potentials. For initial data exhibiting Bose–Einstein condensation, the many-body
time evolution is well approximated through a quadratic fluctuation dynamics around
a cubic nonlinear Schrödinger equation of the condensate wave function. We show
that these fluctuations satisfy a (multi-variate) central limit theorem.
acknowledgement: "Simone Rademacher acknowledges partial support from the NCCR SwissMAP.
This project has received\r\nfunding from the European Union’s Horizon 2020 research
and innovation program under the Marie\r\nSkłodowska-Curie Grant Agreement No. 754411.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria).\r\nS.R.
would like to thank Benjamin Schlein for many fruitful discussions."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
citation:
ama: Rademacher SAE. Central limit theorem for Bose gases interacting through singular
potentials. Letters in Mathematical Physics. 2020;110:2143-2174. doi:10.1007/s11005-020-01286-w
apa: Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting
through singular potentials. Letters in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s11005-020-01286-w
chicago: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
through Singular Potentials.” Letters in Mathematical Physics. Springer
Nature, 2020. https://doi.org/10.1007/s11005-020-01286-w.
ieee: S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through
singular potentials,” Letters in Mathematical Physics, vol. 110. Springer
Nature, pp. 2143–2174, 2020.
ista: Rademacher SAE. 2020. Central limit theorem for Bose gases interacting through
singular potentials. Letters in Mathematical Physics. 110, 2143–2174.
mla: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
through Singular Potentials.” Letters in Mathematical Physics, vol. 110,
Springer Nature, 2020, pp. 2143–74, doi:10.1007/s11005-020-01286-w.
short: S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174.
date_created: 2020-03-23T11:11:47Z
date_published: 2020-03-12T00:00:00Z
date_updated: 2023-09-05T15:14:50Z
day: '12'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-020-01286-w
ec_funded: 1
external_id:
isi:
- '000551556000006'
file:
- access_level: open_access
checksum: 3bdd41f10ad947b67a45b98f507a7d4a
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T12:04:26Z
date_updated: 2020-11-20T12:04:26Z
file_id: '8784'
file_name: 2020_LettersMathPhysics_Rademacher.pdf
file_size: 478683
relation: main_file
success: 1
file_date_updated: 2020-11-20T12:04:26Z
has_accepted_license: '1'
intvolume: ' 110'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 2143-2174
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_identifier:
eissn:
- 1573-0530
issn:
- 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Central limit theorem for Bose gases interacting through singular potentials
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 110
year: '2020'
...
---
_id: '7650'
abstract:
- lang: eng
text: We consider a dilute, homogeneous Bose gas at positive temperature. The system
is investigated in the Gross–Pitaevskii limit, where the scattering length a is
so small that the interaction energy is of the same order of magnitude as the
spectral gap of the Laplacian, and for temperatures that are comparable to the
critical temperature of the ideal gas. We show that the difference between the
specific free energy of the interacting system and the one of the ideal gas is
to leading order given by 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system
and ϱ0 is the expected condensate density of the ideal gas. Additionally, we show
that the one-particle density matrix of any approximate minimizer of the Gibbs
free energy functional is to leading order given by the one of the ideal gas.
This in particular proves Bose–Einstein condensation with critical temperature
given by the one of the ideal gas to leading order. One key ingredient of our
proof is a novel use of the Gibbs variational principle that goes hand in hand
with the c-number substitution.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). It is a pleasure to thank Jakob Yngvason for helpful discussions.
Financial support by the European Research Council (ERC) under the European Union’sHorizon
2020 research and innovation programme (Grant Agreement No. 694227) is gratefully
acknowledged. A. D. acknowledges funding from the European Union’s Horizon 2020
research and innovation programme under the Marie Sklodowska-Curie Grant Agreement
No. 836146.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Deuchert A, Seiringer R. Gross-Pitaevskii limit of a homogeneous Bose gas at
positive temperature. Archive for Rational Mechanics and Analysis. 2020;236(6):1217-1271.
doi:10.1007/s00205-020-01489-4
apa: Deuchert, A., & Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous
Bose gas at positive temperature. Archive for Rational Mechanics and Analysis.
Springer Nature. https://doi.org/10.1007/s00205-020-01489-4
chicago: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous
Bose Gas at Positive Temperature.” Archive for Rational Mechanics and Analysis.
Springer Nature, 2020. https://doi.org/10.1007/s00205-020-01489-4.
ieee: A. Deuchert and R. Seiringer, “Gross-Pitaevskii limit of a homogeneous Bose
gas at positive temperature,” Archive for Rational Mechanics and Analysis,
vol. 236, no. 6. Springer Nature, pp. 1217–1271, 2020.
ista: Deuchert A, Seiringer R. 2020. Gross-Pitaevskii limit of a homogeneous Bose
gas at positive temperature. Archive for Rational Mechanics and Analysis. 236(6),
1217–1271.
mla: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous
Bose Gas at Positive Temperature.” Archive for Rational Mechanics and Analysis,
vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:10.1007/s00205-020-01489-4.
short: A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236
(2020) 1217–1271.
date_created: 2020-04-08T15:18:03Z
date_published: 2020-03-09T00:00:00Z
date_updated: 2023-09-05T14:18:49Z
day: '09'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-020-01489-4
ec_funded: 1
external_id:
arxiv:
- '1901.11363'
isi:
- '000519415000001'
file:
- access_level: open_access
checksum: b645fb64bfe95bbc05b3eea374109a9c
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T13:17:42Z
date_updated: 2020-11-20T13:17:42Z
file_id: '8785'
file_name: 2020_ArchRatMechanicsAnalysis_Deuchert.pdf
file_size: 704633
relation: main_file
success: 1
file_date_updated: 2020-11-20T13:17:42Z
has_accepted_license: '1'
intvolume: ' 236'
isi: 1
issue: '6'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 1217-1271
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 236
year: '2020'
...
---
_id: '7790'
abstract:
- lang: eng
text: "We prove a lower bound for the free energy (per unit volume) of the two-dimensional
Bose gas in the thermodynamic limit. We show that the free energy at density \U0001D70C
and inverse temperature \U0001D6FD differs from the one of the noninteracting
system by the correction term \U0001D70B\U0001D70C\U0001D70C\U0001D6FD\U0001D6FD
. Here, is the scattering length of the interaction potential, and \U0001D6FD
is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity.
The result is valid in the dilute limit \U0001D70C and if \U0001D6FD\U0001D70C
."
article_number: e20
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- first_name: Simon
full_name: Mayer, Simon
id: 30C4630A-F248-11E8-B48F-1D18A9856A87
last_name: Mayer
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute
Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 2020;8. doi:10.1017/fms.2020.17
apa: Deuchert, A., Mayer, S., & Seiringer, R. (2020). The free energy of the
two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma.
Cambridge University Press. https://doi.org/10.1017/fms.2020.17
chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy
of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” Forum of Mathematics,
Sigma. Cambridge University Press, 2020. https://doi.org/10.1017/fms.2020.17.
ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional
dilute Bose gas. I. Lower bound,” Forum of Mathematics, Sigma, vol. 8.
Cambridge University Press, 2020.
ista: Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional
dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20.
mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose
Gas. I. Lower Bound.” Forum of Mathematics, Sigma, vol. 8, e20, Cambridge
University Press, 2020, doi:10.1017/fms.2020.17.
short: A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020).
date_created: 2020-05-03T22:00:48Z
date_published: 2020-03-14T00:00:00Z
date_updated: 2023-08-21T06:18:49Z
day: '14'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1017/fms.2020.17
ec_funded: 1
external_id:
arxiv:
- '1910.03372'
isi:
- '000527342000001'
file:
- access_level: open_access
checksum: 8a64da99d107686997876d7cad8cfe1e
content_type: application/pdf
creator: dernst
date_created: 2020-05-04T12:02:41Z
date_updated: 2020-07-14T12:48:03Z
file_id: '7797'
file_name: 2020_ForumMath_Deuchert.pdf
file_size: 692530
relation: main_file
file_date_updated: 2020-07-14T12:48:03Z
has_accepted_license: '1'
intvolume: ' 8'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- '20505094'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
record:
- id: '7524'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 8
year: '2020'
...
---
_id: '8042'
abstract:
- lang: eng
text: We consider systems of N bosons in a box of volume one, interacting through
a repulsive two-body potential of the form κN3β−1V(Nβx). For all 0<β<1, and for
sufficiently small coupling constant κ>0, we establish the validity of Bogolyubov
theory, identifying the ground state energy and the low-lying excitation spectrum
up to errors that vanish in the limit of large N.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
full_name: Boccato, Chiara
id: 342E7E22-F248-11E8-B48F-1D18A9856A87
last_name: Boccato
- first_name: Christian
full_name: Brennecke, Christian
last_name: Brennecke
- first_name: Serena
full_name: Cenatiempo, Serena
last_name: Cenatiempo
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
citation:
ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. The excitation spectrum of
Bose gases interacting through singular potentials. Journal of the European
Mathematical Society. 2020;22(7):2331-2403. doi:10.4171/JEMS/966
apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2020). The excitation
spectrum of Bose gases interacting through singular potentials. Journal of
the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/966
chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
“The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.”
Journal of the European Mathematical Society. European Mathematical Society,
2020. https://doi.org/10.4171/JEMS/966.
ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “The excitation spectrum
of Bose gases interacting through singular potentials,” Journal of the European
Mathematical Society, vol. 22, no. 7. European Mathematical Society, pp. 2331–2403,
2020.
ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. The excitation spectrum
of Bose gases interacting through singular potentials. Journal of the European
Mathematical Society. 22(7), 2331–2403.
mla: Boccato, Chiara, et al. “The Excitation Spectrum of Bose Gases Interacting
through Singular Potentials.” Journal of the European Mathematical Society,
vol. 22, no. 7, European Mathematical Society, 2020, pp. 2331–403, doi:10.4171/JEMS/966.
short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Journal of the European
Mathematical Society 22 (2020) 2331–2403.
date_created: 2020-06-29T07:59:35Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2023-08-22T07:47:04Z
day: '01'
department:
- _id: RoSe
doi: 10.4171/JEMS/966
external_id:
arxiv:
- '1704.04819'
isi:
- '000548174700006'
intvolume: ' 22'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1704.04819
month: '07'
oa: 1
oa_version: Preprint
page: 2331-2403
publication: Journal of the European Mathematical Society
publication_identifier:
issn:
- '14359855'
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: The excitation spectrum of Bose gases interacting through singular potentials
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
year: '2020'
...
---
_id: '8091'
abstract:
- lang: eng
text: In the setting of the fractional quantum Hall effect we study the effects
of strong, repulsive two-body interaction potentials of short range. We prove
that Haldane’s pseudo-potential operators, including their pre-factors, emerge
as mathematically rigorous limits of such interactions when the range of the potential
tends to zero while its strength tends to infinity. In a common approach the interaction
potential is expanded in angular momentum eigenstates in the lowest Landau level,
which amounts to taking the pre-factors to be the moments of the potential. Such
a procedure is not appropriate for very strong interactions, however, in particular
not in the case of hard spheres. We derive the formulas valid in the short-range
case, which involve the scattering lengths of the interaction potential in different
angular momentum channels rather than its moments. Our results hold for bosons
and fermions alike and generalize previous results in [6], which apply to bosons
in the lowest angular momentum channel. Our main theorem asserts the convergence
in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after
appropriate energy scalings, to Hamiltonians with contact interactions in the
lowest Landau level.
acknowledgement: "Open access funding provided by Institute of Science and Technology
(IST Austria).\r\nThe work of R.S. was supported by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No 694227). J.Y. gratefully acknowledges hospitality at the LPMMC
Grenoble and valuable discussions with Alessandro Olgiati and Nicolas Rougerie. "
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems
with short-range interactions. Journal of Statistical Physics. 2020;181:448-464.
doi:10.1007/s10955-020-02586-0
apa: Seiringer, R., & Yngvason, J. (2020). Emergence of Haldane pseudo-potentials
in systems with short-range interactions. Journal of Statistical Physics.
Springer. https://doi.org/10.1007/s10955-020-02586-0
chicago: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials
in Systems with Short-Range Interactions.” Journal of Statistical Physics.
Springer, 2020. https://doi.org/10.1007/s10955-020-02586-0.
ieee: R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems
with short-range interactions,” Journal of Statistical Physics, vol. 181.
Springer, pp. 448–464, 2020.
ista: Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems
with short-range interactions. Journal of Statistical Physics. 181, 448–464.
mla: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials
in Systems with Short-Range Interactions.” Journal of Statistical Physics,
vol. 181, Springer, 2020, pp. 448–64, doi:10.1007/s10955-020-02586-0.
short: R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464.
date_created: 2020-07-05T22:00:46Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2023-08-22T07:51:47Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s10955-020-02586-0
ec_funded: 1
external_id:
arxiv:
- '2001.07144'
isi:
- '000543030000002'
file:
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checksum: 5cbeef52caf18d0d952f17fed7b5545a
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creator: dernst
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date_updated: 2020-11-25T15:05:04Z
file_id: '8812'
file_name: 2020_JourStatPhysics_Seiringer.pdf
file_size: 404778
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language:
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month: '10'
oa: 1
oa_version: Published Version
page: 448-464
project:
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name: IST Austria Open Access Fund
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- '15729613'
issn:
- '00224715'
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Emergence of Haldane pseudo-potentials in systems with short-range interactions
tmp:
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 181
year: '2020'
...
---
_id: '8130'
abstract:
- lang: eng
text: We study the dynamics of a system of N interacting bosons in a disc-shaped
trap, which is realised by an external potential that confines the bosons in one
spatial dimension to an interval of length of order ε. The interaction is non-negative
and scaled in such a way that its scattering length is of order ε/N, while its
range is proportional to (ε/N)β with scaling parameter β∈(0,1]. We consider the
simultaneous limit (N,ε)→(∞,0) and assume that the system initially exhibits Bose–Einstein
condensation. We prove that condensation is preserved by the N-body dynamics,
where the time-evolved condensate wave function is the solution of a two-dimensional
non-linear equation. The strength of the non-linearity depends on the scaling
parameter β. For β∈(0,1), we obtain a cubic defocusing non-linear Schrödinger
equation, while the choice β=1 yields a Gross–Pitaevskii equation featuring the
scattering length of the interaction. In both cases, the coupling parameter depends
on the confining potential.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). I thank Stefan Teufel for helpful remarks and for his involvement
in the closely related joint project [10]. Helpful discussions with Serena Cenatiempo
and Nikolai Leopold are gratefully acknowledged. This work was supported by the
German Research Foundation within the Research Training Group 1838 “Spectral Theory
and Dynamics of Quantum Systems” and has received funding from the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
full_name: Bossmann, Lea
id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
last_name: Bossmann
orcid: 0000-0002-6854-1343
citation:
ama: Bossmann L. Derivation of the 2d Gross–Pitaevskii equation for strongly confined
3d Bosons. Archive for Rational Mechanics and Analysis. 2020;238(11):541-606.
doi:10.1007/s00205-020-01548-w
apa: Bossmann, L. (2020). Derivation of the 2d Gross–Pitaevskii equation for strongly
confined 3d Bosons. Archive for Rational Mechanics and Analysis. Springer
Nature. https://doi.org/10.1007/s00205-020-01548-w
chicago: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly
Confined 3d Bosons.” Archive for Rational Mechanics and Analysis. Springer
Nature, 2020. https://doi.org/10.1007/s00205-020-01548-w.
ieee: L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly
confined 3d Bosons,” Archive for Rational Mechanics and Analysis, vol.
238, no. 11. Springer Nature, pp. 541–606, 2020.
ista: Bossmann L. 2020. Derivation of the 2d Gross–Pitaevskii equation for strongly
confined 3d Bosons. Archive for Rational Mechanics and Analysis. 238(11), 541–606.
mla: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly
Confined 3d Bosons.” Archive for Rational Mechanics and Analysis, vol.
238, no. 11, Springer Nature, 2020, pp. 541–606, doi:10.1007/s00205-020-01548-w.
short: L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.
date_created: 2020-07-18T15:06:35Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2023-09-05T14:19:06Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-020-01548-w
ec_funded: 1
external_id:
arxiv:
- '1907.04547'
isi:
- '000550164400001'
file:
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checksum: cc67a79a67bef441625fcb1cd031db3d
content_type: application/pdf
creator: dernst
date_created: 2020-12-02T08:50:38Z
date_updated: 2020-12-02T08:50:38Z
file_id: '8826'
file_name: 2020_ArchiveRatMech_Bossmann.pdf
file_size: 942343
relation: main_file
success: 1
file_date_updated: 2020-12-02T08:50:38Z
has_accepted_license: '1'
intvolume: ' 238'
isi: 1
issue: '11'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 541-606
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 238
year: '2020'
...
---
_id: '8134'
abstract:
- lang: eng
text: We prove an upper bound on the free energy of a two-dimensional homogeneous
Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the
free energy per unit volume differs from the one of the non-interacting system
by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]2+) to leading order, where a is the scattering
length of the two-body interaction potential, ρ is the density, β is the inverse
temperature, and βc is the inverse Berezinskii–Kosterlitz–Thouless critical temperature
for superfluidity. In combination with the corresponding matching lower bound
proved by Deuchert et al. [Forum Math. Sigma 8, e20 (2020)], this shows equality
in the asymptotic expansion.
article_number: '061901'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Simon
full_name: Mayer, Simon
id: 30C4630A-F248-11E8-B48F-1D18A9856A87
last_name: Mayer
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas.
II. Upper bound. Journal of Mathematical Physics. 2020;61(6). doi:10.1063/5.0005950
apa: Mayer, S., & Seiringer, R. (2020). The free energy of the two-dimensional
dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. AIP
Publishing. https://doi.org/10.1063/5.0005950
chicago: Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional
Dilute Bose Gas. II. Upper Bound.” Journal of Mathematical Physics. AIP
Publishing, 2020. https://doi.org/10.1063/5.0005950.
ieee: S. Mayer and R. Seiringer, “The free energy of the two-dimensional dilute
Bose gas. II. Upper bound,” Journal of Mathematical Physics, vol. 61, no.
6. AIP Publishing, 2020.
ista: Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute
Bose gas. II. Upper bound. Journal of Mathematical Physics. 61(6), 061901.
mla: Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional
Dilute Bose Gas. II. Upper Bound.” Journal of Mathematical Physics, vol.
61, no. 6, 061901, AIP Publishing, 2020, doi:10.1063/5.0005950.
short: S. Mayer, R. Seiringer, Journal of Mathematical Physics 61 (2020).
date_created: 2020-07-19T22:00:59Z
date_published: 2020-06-22T00:00:00Z
date_updated: 2023-08-22T08:12:40Z
day: '22'
department:
- _id: RoSe
doi: 10.1063/5.0005950
ec_funded: 1
external_id:
arxiv:
- '2002.08281'
isi:
- '000544595100001'
intvolume: ' 61'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2002.08281
month: '06'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Journal of Mathematical Physics
publication_identifier:
issn:
- '00222488'
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The free energy of the two-dimensional dilute Bose gas. II. Upper bound
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 61
year: '2020'
...
---
_id: '14891'
abstract:
- lang: eng
text: We give the first mathematically rigorous justification of the local density
approximation in density functional theory. We provide a quantitative estimate
on the difference between the grand-canonical Levy–Lieb energy of a given density
(the lowest possible energy of all quantum states having this density) and the
integral over the uniform electron gas energy of this density. The error involves
gradient terms and justifies the use of the local density approximation in the
situation where the density is very flat on sufficiently large regions in space.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Elliott H.
full_name: Lieb, Elliott H.
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Lewin M, Lieb EH, Seiringer R. The local density approximation in density
functional theory. Pure and Applied Analysis. 2020;2(1):35-73. doi:10.2140/paa.2020.2.35
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2020). The local density approximation
in density functional theory. Pure and Applied Analysis. Mathematical Sciences
Publishers. https://doi.org/10.2140/paa.2020.2.35
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “ The Local Density
Approximation in Density Functional Theory.” Pure and Applied Analysis.
Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/paa.2020.2.35.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “ The local density approximation
in density functional theory,” Pure and Applied Analysis, vol. 2, no. 1.
Mathematical Sciences Publishers, pp. 35–73, 2020.
ista: Lewin M, Lieb EH, Seiringer R. 2020. The local density approximation in density
functional theory. Pure and Applied Analysis. 2(1), 35–73.
mla: Lewin, Mathieu, et al. “ The Local Density Approximation in Density Functional
Theory.” Pure and Applied Analysis, vol. 2, no. 1, Mathematical Sciences
Publishers, 2020, pp. 35–73, doi:10.2140/paa.2020.2.35.
short: M. Lewin, E.H. Lieb, R. Seiringer, Pure and Applied Analysis 2 (2020) 35–73.
date_created: 2024-01-28T23:01:44Z
date_published: 2020-01-01T00:00:00Z
date_updated: 2024-01-29T09:01:12Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2020.2.35
external_id:
arxiv:
- '1903.04046'
intvolume: ' 2'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1903.04046
month: '01'
oa: 1
oa_version: Preprint
page: 35-73
publication: Pure and Applied Analysis
publication_identifier:
eissn:
- 2578-5885
issn:
- 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' The local density approximation in density functional theory'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2020'
...
---
_id: '6649'
abstract:
- lang: eng
text: "While Hartree–Fock theory is well established as a fundamental approximation
for interacting fermions, it has been unclear how to describe corrections to it
due to many-body correlations. In this paper we start from the Hartree–Fock state
given by plane waves and introduce collective particle–hole pair excitations.
These pairs can be approximately described by a bosonic quadratic Hamiltonian.
We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type
upper bound to the ground state energy. Our result justifies the random-phase
approximation in the mean-field scaling regime, for repulsive, regular interaction
potentials.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Niels P
full_name: Benedikter, Niels P
id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
last_name: Benedikter
orcid: 0000-0002-1071-6091
- first_name: Phan Thành
full_name: Nam, Phan Thành
last_name: Nam
- first_name: Marcello
full_name: Porta, Marcello
last_name: Porta
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Optimal upper bound
for the correlation energy of a Fermi gas in the mean-field regime. Communications
in Mathematical Physics. 2020;374:2097–2150. doi:10.1007/s00220-019-03505-5
apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R.
(2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field
regime. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03505-5
chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi
Gas in the Mean-Field Regime.” Communications in Mathematical Physics.
Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03505-5.
ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal
upper bound for the correlation energy of a Fermi gas in the mean-field regime,”
Communications in Mathematical Physics, vol. 374. Springer Nature, pp.
2097–2150, 2020.
ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper
bound for the correlation energy of a Fermi gas in the mean-field regime. Communications
in Mathematical Physics. 374, 2097–2150.
mla: Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy
of a Fermi Gas in the Mean-Field Regime.” Communications in Mathematical Physics,
vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:10.1007/s00220-019-03505-5.
short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications
in Mathematical Physics 374 (2020) 2097–2150.
date_created: 2019-07-18T13:30:04Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2023-08-17T13:51:50Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00220-019-03505-5
ec_funded: 1
external_id:
arxiv:
- '1809.01902'
isi:
- '000527910700019'
file:
- access_level: open_access
checksum: f9dd6dd615a698f1d3636c4a092fed23
content_type: application/pdf
creator: dernst
date_created: 2019-07-24T07:19:10Z
date_updated: 2020-07-14T12:47:35Z
file_id: '6668'
file_name: 2019_CommMathPhysics_Benedikter.pdf
file_size: 853289
relation: main_file
file_date_updated: 2020-07-14T12:47:35Z
has_accepted_license: '1'
intvolume: ' 374'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 2097–2150
project:
- _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1
call_identifier: FWF
name: FWF Open Access Fund
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal upper bound for the correlation energy of a Fermi gas in the mean-field
regime
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 374
year: '2020'
...
---
_id: '6906'
abstract:
- lang: eng
text: We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime.
We show that low-energy states exhibit complete Bose–Einstein condensation with
an optimal bound on the number of orthogonal excitations. This extends recent
results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing
the assumption of small interaction potential.
acknowledgement: "We would like to thank P. T. Nam and R. Seiringer for several useful
discussions and\r\nfor suggesting us to use the localization techniques from [9].
C. Boccato has received funding from the\r\nEuropean Research Council (ERC) under
the programme Horizon 2020 (Grant Agreement 694227). B. Schlein gratefully acknowledges
support from the NCCR SwissMAP and from the Swiss National Foundation of Science
(Grant No. 200020_1726230) through the SNF Grant “Dynamical and energetic properties
of Bose–Einstein condensates”."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
full_name: Boccato, Chiara
id: 342E7E22-F248-11E8-B48F-1D18A9856A87
last_name: Boccato
- first_name: Christian
full_name: Brennecke, Christian
last_name: Brennecke
- first_name: Serena
full_name: Cenatiempo, Serena
last_name: Cenatiempo
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
citation:
ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. Optimal rate for Bose-Einstein
condensation in the Gross-Pitaevskii regime. Communications in Mathematical
Physics. 2020;376:1311-1395. doi:10.1007/s00220-019-03555-9
apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2020). Optimal
rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. Communications
in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-019-03555-9
chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
“Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.”
Communications in Mathematical Physics. Springer, 2020. https://doi.org/10.1007/s00220-019-03555-9.
ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Optimal rate for
Bose-Einstein condensation in the Gross-Pitaevskii regime,” Communications
in Mathematical Physics, vol. 376. Springer, pp. 1311–1395, 2020.
ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. Optimal rate for Bose-Einstein
condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics.
376, 1311–1395.
mla: Boccato, Chiara, et al. “Optimal Rate for Bose-Einstein Condensation in the
Gross-Pitaevskii Regime.” Communications in Mathematical Physics, vol.
376, Springer, 2020, pp. 1311–95, doi:10.1007/s00220-019-03555-9.
short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical
Physics 376 (2020) 1311–1395.
date_created: 2019-09-24T17:30:59Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2024-02-22T13:33:02Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00220-019-03555-9
ec_funded: 1
external_id:
arxiv:
- '1812.03086'
isi:
- '000536053300012'
intvolume: ' 376'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1812.03086
month: '06'
oa: 1
oa_version: Preprint
page: 1311-1395
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 376
year: '2020'
...
---
_id: '9781'
abstract:
- lang: eng
text: We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers,
and a quadratic lower bound in terms of the distance to the minimizer. The latter
follows from nondegeneracy of the Hessian at the minimum.
acknowledgement: We are grateful for the hospitality at the Mittag-Leffler Institute,
where part of this work has been done. The work of the authors was supported by
the European Research Council (ERC)under the European Union's Horizon 2020 research
and innovation programme grant 694227.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Feliciangeli D, Seiringer R. Uniqueness and nondegeneracy of minimizers of
the Pekar functional on a ball. SIAM Journal on Mathematical Analysis.
2020;52(1):605-622. doi:10.1137/19m126284x
apa: Feliciangeli, D., & Seiringer, R. (2020). Uniqueness and nondegeneracy
of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical
Analysis. Society for Industrial & Applied Mathematics . https://doi.org/10.1137/19m126284x
chicago: Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy
of Minimizers of the Pekar Functional on a Ball.” SIAM Journal on Mathematical
Analysis. Society for Industrial & Applied Mathematics , 2020. https://doi.org/10.1137/19m126284x.
ieee: D. Feliciangeli and R. Seiringer, “Uniqueness and nondegeneracy of minimizers
of the Pekar functional on a ball,” SIAM Journal on Mathematical Analysis,
vol. 52, no. 1. Society for Industrial & Applied Mathematics , pp. 605–622,
2020.
ista: Feliciangeli D, Seiringer R. 2020. Uniqueness and nondegeneracy of minimizers
of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 52(1),
605–622.
mla: Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of
Minimizers of the Pekar Functional on a Ball.” SIAM Journal on Mathematical
Analysis, vol. 52, no. 1, Society for Industrial & Applied Mathematics
, 2020, pp. 605–22, doi:10.1137/19m126284x.
short: D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020)
605–622.
date_created: 2021-08-06T07:34:16Z
date_published: 2020-02-12T00:00:00Z
date_updated: 2023-09-07T13:30:11Z
day: '12'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1137/19m126284x
ec_funded: 1
external_id:
arxiv:
- '1904.08647 '
isi:
- '000546967700022'
has_accepted_license: '1'
intvolume: ' 52'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1904.08647
month: '02'
oa: 1
oa_version: Preprint
page: 605-622
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: 'Society for Industrial & Applied Mathematics '
quality_controlled: '1'
related_material:
record:
- id: '9733'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 52
year: '2020'
...
---
_id: '7015'
abstract:
- lang: eng
text: We modify the "floating crystal" trial state for the classical homogeneous
electron gas (also known as jellium), in order to suppress the boundary charge
fluctuations that are known to lead to a macroscopic increase of the energy. The
argument is to melt a thin layer of the crystal close to the boundary and consequently
replace it by an incompressible fluid. With the aid of this trial state we show
that three different definitions of the ground-state energy of jellium coincide.
In the first point of view the electrons are placed in a neutralizing uniform
background. In the second definition there is no background but the electrons
are submitted to the constraint that their density is constant, as is appropriate
in density functional theory. Finally, in the third system each electron interacts
with a periodic image of itself; that is, periodic boundary conditions are imposed
on the interaction potential.
article_number: '035127'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Elliott H.
full_name: Lieb, Elliott H.
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Lewin M, Lieb EH, Seiringer R. Floating Wigner crystal with no boundary charge
fluctuations. Physical Review B. 2019;100(3). doi:10.1103/physrevb.100.035127
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2019). Floating Wigner crystal
with no boundary charge fluctuations. Physical Review B. American Physical
Society. https://doi.org/10.1103/physrevb.100.035127
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Floating Wigner
Crystal with No Boundary Charge Fluctuations.” Physical Review B. American
Physical Society, 2019. https://doi.org/10.1103/physrevb.100.035127.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Floating Wigner crystal with no boundary
charge fluctuations,” Physical Review B, vol. 100, no. 3. American Physical
Society, 2019.
ista: Lewin M, Lieb EH, Seiringer R. 2019. Floating Wigner crystal with no boundary
charge fluctuations. Physical Review B. 100(3), 035127.
mla: Lewin, Mathieu, et al. “Floating Wigner Crystal with No Boundary Charge Fluctuations.”
Physical Review B, vol. 100, no. 3, 035127, American Physical Society,
2019, doi:10.1103/physrevb.100.035127.
short: M. Lewin, E.H. Lieb, R. Seiringer, Physical Review B 100 (2019).
date_created: 2019-11-13T08:41:48Z
date_published: 2019-07-25T00:00:00Z
date_updated: 2024-02-28T13:13:23Z
day: '25'
department:
- _id: RoSe
doi: 10.1103/physrevb.100.035127
ec_funded: 1
external_id:
arxiv:
- '1905.09138'
isi:
- '000477888200001'
intvolume: ' 100'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1905.09138
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Physical Review B
publication_identifier:
eissn:
- 2469-9969
issn:
- 2469-9950
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Floating Wigner crystal with no boundary charge fluctuations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 100
year: '2019'
...
---
_id: '7100'
abstract:
- lang: eng
text: We present microscopic derivations of the defocusing two-dimensional cubic
nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman
interacting N-particle system of bosons. We consider the interaction potential
to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx),
for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R).
In both cases we prove the convergence of the reduced density corresponding to
the exact time evolution to the projector onto the solution of the corresponding
nonlinear Schrödinger equation in trace norm. For the latter potential VN we show
that it is crucial to take the microscopic structure of the condensate into account
in order to obtain the correct dynamics.
acknowledgement: OA fund by IST Austria
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Maximilian
full_name: Jeblick, Maximilian
last_name: Jeblick
- first_name: Nikolai K
full_name: Leopold, Nikolai K
id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
last_name: Leopold
orcid: 0000-0002-0495-6822
- first_name: Peter
full_name: Pickl, Peter
last_name: Pickl
citation:
ama: Jeblick M, Leopold NK, Pickl P. Derivation of the time dependent Gross–Pitaevskii
equation in two dimensions. Communications in Mathematical Physics. 2019;372(1):1-69.
doi:10.1007/s00220-019-03599-x
apa: Jeblick, M., Leopold, N. K., & Pickl, P. (2019). Derivation of the time
dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical
Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03599-x
chicago: Jeblick, Maximilian, Nikolai K Leopold, and Peter Pickl. “Derivation of
the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” Communications
in Mathematical Physics. Springer Nature, 2019. https://doi.org/10.1007/s00220-019-03599-x.
ieee: M. Jeblick, N. K. Leopold, and P. Pickl, “Derivation of the time dependent
Gross–Pitaevskii equation in two dimensions,” Communications in Mathematical
Physics, vol. 372, no. 1. Springer Nature, pp. 1–69, 2019.
ista: Jeblick M, Leopold NK, Pickl P. 2019. Derivation of the time dependent Gross–Pitaevskii
equation in two dimensions. Communications in Mathematical Physics. 372(1), 1–69.
mla: Jeblick, Maximilian, et al. “Derivation of the Time Dependent Gross–Pitaevskii
Equation in Two Dimensions.” Communications in Mathematical Physics, vol.
372, no. 1, Springer Nature, 2019, pp. 1–69, doi:10.1007/s00220-019-03599-x.
short: M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics
372 (2019) 1–69.
date_created: 2019-11-25T08:08:02Z
date_published: 2019-11-08T00:00:00Z
date_updated: 2023-09-06T10:47:43Z
day: '08'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00220-019-03599-x
ec_funded: 1
external_id:
isi:
- '000495193700002'
file:
- access_level: open_access
checksum: cd283b475dd739e04655315abd46f528
content_type: application/pdf
creator: dernst
date_created: 2019-11-25T08:11:11Z
date_updated: 2020-07-14T12:47:49Z
file_id: '7101'
file_name: 2019_CommMathPhys_Jeblick.pdf
file_size: 884469
relation: main_file
file_date_updated: 2020-07-14T12:47:49Z
has_accepted_license: '1'
intvolume: ' 372'
isi: 1
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 1-69
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivation of the time dependent Gross–Pitaevskii equation in two dimensions
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 372
year: '2019'
...
---
_id: '7226'
article_number: '123504'
article_processing_charge: No
article_type: letter_note
author:
- first_name: Vojkan
full_name: Jaksic, Vojkan
last_name: Jaksic
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Jaksic V, Seiringer R. Introduction to the Special Collection: International
Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical Physics.
2019;60(12). doi:10.1063/1.5138135'
apa: 'Jaksic, V., & Seiringer, R. (2019). Introduction to the Special Collection:
International Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical
Physics. AIP Publishing. https://doi.org/10.1063/1.5138135'
chicago: 'Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection:
International Congress on Mathematical Physics (ICMP) 2018.” Journal of Mathematical
Physics. AIP Publishing, 2019. https://doi.org/10.1063/1.5138135.'
ieee: 'V. Jaksic and R. Seiringer, “Introduction to the Special Collection: International
Congress on Mathematical Physics (ICMP) 2018,” Journal of Mathematical Physics,
vol. 60, no. 12. AIP Publishing, 2019.'
ista: 'Jaksic V, Seiringer R. 2019. Introduction to the Special Collection: International
Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical Physics.
60(12), 123504.'
mla: 'Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection:
International Congress on Mathematical Physics (ICMP) 2018.” Journal of Mathematical
Physics, vol. 60, no. 12, 123504, AIP Publishing, 2019, doi:10.1063/1.5138135.'
short: V. Jaksic, R. Seiringer, Journal of Mathematical Physics 60 (2019).
date_created: 2020-01-05T23:00:46Z
date_published: 2019-12-01T00:00:00Z
date_updated: 2024-02-28T13:01:45Z
day: '01'
ddc:
- '500'
department:
- _id: RoSe
doi: 10.1063/1.5138135
external_id:
isi:
- '000505529800002'
file:
- access_level: open_access
checksum: bbd12ad1999a9ad7ba4d3c6f2e579c22
content_type: application/pdf
creator: dernst
date_created: 2020-01-07T14:59:13Z
date_updated: 2020-07-14T12:47:54Z
file_id: '7244'
file_name: 2019_JournalMathPhysics_Jaksic.pdf
file_size: 1025015
relation: main_file
file_date_updated: 2020-07-14T12:47:54Z
has_accepted_license: '1'
intvolume: ' 60'
isi: 1
issue: '12'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Physics
publication_identifier:
issn:
- '00222488'
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Introduction to the Special Collection: International Congress on Mathematical
Physics (ICMP) 2018'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 60
year: '2019'
...
---
_id: '7413'
abstract:
- lang: eng
text: We consider Bose gases consisting of N particles trapped in a box with volume
one and interacting through a repulsive potential with scattering length of order
N−1 (Gross–Pitaevskii regime). We determine the ground state energy and the low-energy
excitation spectrum, up to errors vanishing as N→∞. Our results confirm Bogoliubov’s
predictions.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
full_name: Boccato, Chiara
id: 342E7E22-F248-11E8-B48F-1D18A9856A87
last_name: Boccato
- first_name: Christian
full_name: Brennecke, Christian
last_name: Brennecke
- first_name: Serena
full_name: Cenatiempo, Serena
last_name: Cenatiempo
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
citation:
ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. Bogoliubov theory in the Gross–Pitaevskii
limit. Acta Mathematica. 2019;222(2):219-335. doi:10.4310/acta.2019.v222.n2.a1
apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2019). Bogoliubov
theory in the Gross–Pitaevskii limit. Acta Mathematica. International Press
of Boston. https://doi.org/10.4310/acta.2019.v222.n2.a1
chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
“Bogoliubov Theory in the Gross–Pitaevskii Limit.” Acta Mathematica. International
Press of Boston, 2019. https://doi.org/10.4310/acta.2019.v222.n2.a1.
ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Bogoliubov theory
in the Gross–Pitaevskii limit,” Acta Mathematica, vol. 222, no. 2. International
Press of Boston, pp. 219–335, 2019.
ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2019. Bogoliubov theory in
the Gross–Pitaevskii limit. Acta Mathematica. 222(2), 219–335.
mla: Boccato, Chiara, et al. “Bogoliubov Theory in the Gross–Pitaevskii Limit.”
Acta Mathematica, vol. 222, no. 2, International Press of Boston, 2019,
pp. 219–335, doi:10.4310/acta.2019.v222.n2.a1.
short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Acta Mathematica 222
(2019) 219–335.
date_created: 2020-01-30T09:30:41Z
date_published: 2019-06-07T00:00:00Z
date_updated: 2023-09-06T15:24:31Z
day: '07'
department:
- _id: RoSe
doi: 10.4310/acta.2019.v222.n2.a1
external_id:
arxiv:
- '1801.01389'
isi:
- '000495865300001'
intvolume: ' 222'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1801.01389
month: '06'
oa: 1
oa_version: Preprint
page: 219-335
publication: Acta Mathematica
publication_identifier:
eissn:
- 1871-2509
issn:
- 0001-5962
publication_status: published
publisher: International Press of Boston
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bogoliubov theory in the Gross–Pitaevskii limit
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 222
year: '2019'
...
---
_id: '7524'
abstract:
- lang: eng
text: "We prove a lower bound for the free energy (per unit volume) of the two-dimensional
Bose gas in the thermodynamic limit. We show that the free energy at density $\\rho$
and inverse temperature $\\beta$ differs from the one of the non-interacting system
by the correction term $4 \\pi \\rho^2 |\\ln a^2 \\rho|^{-1} (2 - [1 - \\beta_{\\mathrm{c}}/\\beta]_+^2)$.
Here $a$ is the scattering length of the interaction potential, $[\\cdot]_+ =
\\max\\{ 0, \\cdot \\}$ and $\\beta_{\\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless
critical temperature for superfluidity. The result is valid in the dilute limit\r\n$a^2\\rho
\\ll 1$ and if $\\beta \\rho \\gtrsim 1$."
article_processing_charge: No
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- first_name: Simon
full_name: Mayer, Simon
id: 30C4630A-F248-11E8-B48F-1D18A9856A87
last_name: Mayer
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute
Bose gas. I. Lower bound. arXiv:191003372.
apa: Deuchert, A., Mayer, S., & Seiringer, R. (n.d.). The free energy of the
two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372. ArXiv.
chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy
of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv:1910.03372.
ArXiv, n.d.
ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional
dilute Bose gas. I. Lower bound,” arXiv:1910.03372. ArXiv.
ista: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute
Bose gas. I. Lower bound. arXiv:1910.03372, .
mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose
Gas. I. Lower Bound.” ArXiv:1910.03372, ArXiv.
short: A. Deuchert, S. Mayer, R. Seiringer, ArXiv:1910.03372 (n.d.).
date_created: 2020-02-26T08:46:40Z
date_published: 2019-10-08T00:00:00Z
date_updated: 2023-09-07T13:12:41Z
day: '08'
department:
- _id: RoSe
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.03372
month: '10'
oa: 1
oa_version: Preprint
page: '61'
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: arXiv:1910.03372
publication_status: draft
publisher: ArXiv
related_material:
record:
- id: '7790'
relation: later_version
status: public
- id: '7514'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '80'
abstract:
- lang: eng
text: 'We consider an interacting, dilute Bose gas trapped in a harmonic potential
at a positive temperature. The system is analyzed in a combination of a thermodynamic
and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature
T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering
length is so small that the interaction energy per particle around the center
of the trap is of the same order of magnitude as the spectral gap in the trap.
We prove that the difference between the canonical free energy of the interacting
gas and the one of the noninteracting system can be obtained by minimizing the
GP energy functional. We also prove Bose–Einstein condensation in the following
sense: The one-particle density matrix of any approximate minimizer of the canonical
free energy functional is to leading order given by that of the noninteracting
gas but with the free condensate wavefunction replaced by the GP minimizer.'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: Deuchert A, Seiringer R, Yngvason J. Bose–Einstein condensation in a dilute,
trapped gas at positive temperature. Communications in Mathematical Physics.
2019;368(2):723-776. doi:10.1007/s00220-018-3239-0
apa: Deuchert, A., Seiringer, R., & Yngvason, J. (2019). Bose–Einstein condensation
in a dilute, trapped gas at positive temperature. Communications in Mathematical
Physics. Springer. https://doi.org/10.1007/s00220-018-3239-0
chicago: Deuchert, Andreas, Robert Seiringer, and Jakob Yngvason. “Bose–Einstein
Condensation in a Dilute, Trapped Gas at Positive Temperature.” Communications
in Mathematical Physics. Springer, 2019. https://doi.org/10.1007/s00220-018-3239-0.
ieee: A. Deuchert, R. Seiringer, and J. Yngvason, “Bose–Einstein condensation in
a dilute, trapped gas at positive temperature,” Communications in Mathematical
Physics, vol. 368, no. 2. Springer, pp. 723–776, 2019.
ista: Deuchert A, Seiringer R, Yngvason J. 2019. Bose–Einstein condensation in a
dilute, trapped gas at positive temperature. Communications in Mathematical Physics.
368(2), 723–776.
mla: Deuchert, Andreas, et al. “Bose–Einstein Condensation in a Dilute, Trapped
Gas at Positive Temperature.” Communications in Mathematical Physics, vol.
368, no. 2, Springer, 2019, pp. 723–76, doi:10.1007/s00220-018-3239-0.
short: A. Deuchert, R. Seiringer, J. Yngvason, Communications in Mathematical Physics
368 (2019) 723–776.
date_created: 2018-12-11T11:44:31Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-08-24T14:27:51Z
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publication: Communications in Mathematical Physics
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title: Bose–Einstein condensation in a dilute, trapped gas at positive temperature
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---
_id: '5856'
abstract:
- lang: eng
text: We give a bound on the ground-state energy of a system of N non-interacting
fermions in a three-dimensional cubic box interacting with an impurity particle
via point interactions. We show that the change in energy compared to the system
in the absence of the impurity is bounded in terms of the gas density and the
scattering length of the interaction, independently of N. Our bound holds as long
as the ratio of the mass of the impurity to the one of the gas particles is larger
than a critical value m∗ ∗≈ 0.36 , which is the same regime for which we recently
showed stability of the system.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Thomas
full_name: Moser, Thomas
id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87
last_name: Moser
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Moser T, Seiringer R. Energy contribution of a point-interacting impurity in
a Fermi gas. Annales Henri Poincare. 2019;20(4):1325–1365. doi:10.1007/s00023-018-00757-0
apa: Moser, T., & Seiringer, R. (2019). Energy contribution of a point-interacting
impurity in a Fermi gas. Annales Henri Poincare. Springer. https://doi.org/10.1007/s00023-018-00757-0
chicago: Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting
Impurity in a Fermi Gas.” Annales Henri Poincare. Springer, 2019. https://doi.org/10.1007/s00023-018-00757-0.
ieee: T. Moser and R. Seiringer, “Energy contribution of a point-interacting impurity
in a Fermi gas,” Annales Henri Poincare, vol. 20, no. 4. Springer, pp.
1325–1365, 2019.
ista: Moser T, Seiringer R. 2019. Energy contribution of a point-interacting impurity
in a Fermi gas. Annales Henri Poincare. 20(4), 1325–1365.
mla: Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting
Impurity in a Fermi Gas.” Annales Henri Poincare, vol. 20, no. 4, Springer,
2019, pp. 1325–1365, doi:10.1007/s00023-018-00757-0.
short: T. Moser, R. Seiringer, Annales Henri Poincare 20 (2019) 1325–1365.
date_created: 2019-01-20T22:59:17Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2023-09-07T12:37:42Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00023-018-00757-0
ec_funded: 1
external_id:
arxiv:
- '1807.00739'
isi:
- '000462444300008'
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file_name: 2019_Annales_Moser.pdf
file_size: 859846
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file_date_updated: 2020-07-14T12:47:12Z
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isi: 1
issue: '4'
language:
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month: '04'
oa: 1
oa_version: Published Version
page: 1325–1365
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call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
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call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
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name: IST Austria Open Access Fund
publication: Annales Henri Poincare
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issn:
- '14240637'
publication_status: published
publisher: Springer
quality_controlled: '1'
related_material:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Energy contribution of a point-interacting impurity in a Fermi gas
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
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...
---
_id: '6788'
abstract:
- lang: eng
text: We consider the Nelson model with ultraviolet cutoff, which describes the
interaction between non-relativistic particles and a positive or zero mass quantized
scalar field. We take the non-relativistic particles to obey Fermi statistics
and discuss the time evolution in a mean-field limit of many fermions. In this
case, the limit is known to be also a semiclassical limit. We prove convergence
in terms of reduced density matrices of the many-body state to a tensor product
of a Slater determinant with semiclassical structure and a coherent state, which
evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Nikolai K
full_name: Leopold, Nikolai K
id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
last_name: Leopold
orcid: 0000-0002-0495-6822
- first_name: Sören P
full_name: Petrat, Sören P
id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
last_name: Petrat
orcid: 0000-0002-9166-5889
citation:
ama: Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions.
Annales Henri Poincare. 2019;20(10):3471–3508. doi:10.1007/s00023-019-00828-w
apa: Leopold, N. K., & Petrat, S. P. (2019). Mean-field dynamics for the Nelson
model with fermions. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-019-00828-w
chicago: Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson
Model with Fermions.” Annales Henri Poincare. Springer Nature, 2019. https://doi.org/10.1007/s00023-019-00828-w.
ieee: N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model
with fermions,” Annales Henri Poincare, vol. 20, no. 10. Springer Nature,
pp. 3471–3508, 2019.
ista: Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with
fermions. Annales Henri Poincare. 20(10), 3471–3508.
mla: Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson
Model with Fermions.” Annales Henri Poincare, vol. 20, no. 10, Springer
Nature, 2019, pp. 3471–3508, doi:10.1007/s00023-019-00828-w.
short: N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 3471–3508.
date_created: 2019-08-11T21:59:21Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2023-08-29T07:09:06Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00023-019-00828-w
ec_funded: 1
external_id:
arxiv:
- '1807.06781'
isi:
- '000487036900008'
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date_updated: 2020-07-14T12:47:40Z
file_id: '6801'
file_name: 2019_AnnalesHenriPoincare_Leopold.pdf
file_size: 681139
relation: main_file
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intvolume: ' 20'
isi: 1
issue: '10'
language:
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month: '10'
oa: 1
oa_version: Published Version
page: 3471–3508
project:
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call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Annales Henri Poincare
publication_identifier:
eissn:
- 1424-0661
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
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scopus_import: '1'
status: public
title: Mean-field dynamics for the Nelson model with fermions
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type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
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...