---
_id: '14931'
abstract:
- lang: eng
text: We prove an upper bound on the ground state energy of the dilute spin-polarized
Fermi gas capturing the leading correction to the kinetic energy resulting from
repulsive interactions. One of the main ingredients in the proof is a rigorous
implementation of the fermionic cluster expansion of Gaudin et al. (1971) [15].
acknowledgement: A.B.L. would like to thank Johannes Agerskov and Jan Philip Solovej
for valuable discussions. We thank Alessandro Giuliani for helpful discussions and
for pointing out the reference [18]. Funding from the European Union's Horizon 2020
research and innovation programme under the ERC grant agreement No 694227 is acknowledged.
Financial support by the Austrian Science Fund (FWF) through project number I 6427-N
(as part of the SFB/TRR 352) is gratefully acknowledged.
article_number: '110320'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Lauritsen AB, Seiringer R. Ground state energy of the dilute spin-polarized
Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis.
2024;286(7). doi:10.1016/j.jfa.2024.110320'
apa: 'Lauritsen, A. B., & Seiringer, R. (2024). Ground state energy of the dilute
spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional
Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110320'
chicago: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy
of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” Journal
of Functional Analysis. Elsevier, 2024. https://doi.org/10.1016/j.jfa.2024.110320.'
ieee: 'A. B. Lauritsen and R. Seiringer, “Ground state energy of the dilute spin-polarized
Fermi gas: Upper bound via cluster expansion,” Journal of Functional Analysis,
vol. 286, no. 7. Elsevier, 2024.'
ista: 'Lauritsen AB, Seiringer R. 2024. Ground state energy of the dilute spin-polarized
Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis.
286(7), 110320.'
mla: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of
the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” Journal
of Functional Analysis, vol. 286, no. 7, 110320, Elsevier, 2024, doi:10.1016/j.jfa.2024.110320.'
short: A.B. Lauritsen, R. Seiringer, Journal of Functional Analysis 286 (2024).
date_created: 2024-02-04T23:00:53Z
date_published: 2024-01-24T00:00:00Z
date_updated: 2024-03-28T10:54:02Z
day: '24'
department:
- _id: RoSe
doi: 10.1016/j.jfa.2024.110320
ec_funded: 1
external_id:
arxiv:
- '2301.04894'
intvolume: ' 286'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1016/j.jfa.2024.110320
month: '01'
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
- _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b
grant_number: I06427
name: Mathematical Challenges in BCS Theory of Superconductivity
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096--0783
issn:
- 0022-1236
publication_status: epub_ahead
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via
cluster expansion'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 286
year: '2024'
...
---
_id: '12183'
abstract:
- lang: eng
text: We consider a gas of n bosonic particles confined in a box [−ℓ/2,ℓ/2]3 with
Neumann boundary conditions. We prove Bose–Einstein condensation in the Gross–Pitaevskii
regime, with an optimal bound on the condensate depletion. Moreover, our lower
bound for the ground state energy in a small box [−ℓ/2,ℓ/2]3 implies (via Neumann
bracketing) a lower bound for the ground state energy of N bosons in a large box
[−L/2,L/2]3 with density ρ=N/L3 in the thermodynamic limit.
acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation
programme under the ERC grant agreement No 694227 is gratefully acknowledged.
article_processing_charge: No
article_type: original
author:
- first_name: Chiara
full_name: Boccato, Chiara
id: 342E7E22-F248-11E8-B48F-1D18A9856A87
last_name: Boccato
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Boccato C, Seiringer R. The Bose Gas in a box with Neumann boundary conditions.
Annales Henri Poincare. 2023;24:1505-1560. doi:10.1007/s00023-022-01252-3
apa: Boccato, C., & Seiringer, R. (2023). The Bose Gas in a box with Neumann
boundary conditions. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01252-3
chicago: Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann
Boundary Conditions.” Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-022-01252-3.
ieee: C. Boccato and R. Seiringer, “The Bose Gas in a box with Neumann boundary
conditions,” Annales Henri Poincare, vol. 24. Springer Nature, pp. 1505–1560,
2023.
ista: Boccato C, Seiringer R. 2023. The Bose Gas in a box with Neumann boundary
conditions. Annales Henri Poincare. 24, 1505–1560.
mla: Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann
Boundary Conditions.” Annales Henri Poincare, vol. 24, Springer Nature,
2023, pp. 1505–60, doi:10.1007/s00023-022-01252-3.
short: C. Boccato, R. Seiringer, Annales Henri Poincare 24 (2023) 1505–1560.
date_created: 2023-01-15T23:00:52Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2023-08-16T11:34:03Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00023-022-01252-3
ec_funded: 1
external_id:
arxiv:
- '2205.15284'
isi:
- '000910751800002'
intvolume: ' 24'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2205.15284
month: '05'
oa: 1
oa_version: Preprint
page: 1505-1560
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Bose Gas in a box with Neumann boundary conditions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...
---
_id: '12430'
abstract:
- lang: eng
text: We study the time evolution of the Nelson model in a mean-field limit in which
N nonrelativistic bosons weakly couple (with respect to the particle number) to
a positive or zero mass quantized scalar field. Our main result is the derivation
of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove
the convergence of the approximate wave function to the many-body wave function
in norm, with a convergence rate proportional to the number of corrections taken
into account in the approximation. We prove an analogous result for the unitary
propagator. As an application, we derive a simple system of partial differential
equations describing the time evolution of the first- and second-order approximations
to the one-particle reduced density matrices of the particles and the quantum
field, respectively.
article_number: '2350006'
article_processing_charge: No
article_type: original
author:
- first_name: Marco
full_name: Falconi, Marco
last_name: Falconi
- 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: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- 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: Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. Bogoliubov dynamics and higher-order
corrections for the regularized Nelson model. Reviews in Mathematical Physics.
2023;35(4). doi:10.1142/S0129055X2350006X
apa: Falconi, M., Leopold, N. K., Mitrouskas, D. J., & Petrat, S. P. (2023).
Bogoliubov dynamics and higher-order corrections for the regularized Nelson model.
Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X2350006X
chicago: Falconi, Marco, Nikolai K Leopold, David Johannes Mitrouskas, and Sören
P Petrat. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized
Nelson Model.” Reviews in Mathematical Physics. World Scientific Publishing,
2023. https://doi.org/10.1142/S0129055X2350006X.
ieee: M. Falconi, N. K. Leopold, D. J. Mitrouskas, and S. P. Petrat, “Bogoliubov
dynamics and higher-order corrections for the regularized Nelson model,” Reviews
in Mathematical Physics, vol. 35, no. 4. World Scientific Publishing, 2023.
ista: Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. 2023. Bogoliubov dynamics
and higher-order corrections for the regularized Nelson model. Reviews in Mathematical
Physics. 35(4), 2350006.
mla: Falconi, Marco, et al. “Bogoliubov Dynamics and Higher-Order Corrections for
the Regularized Nelson Model.” Reviews in Mathematical Physics, vol. 35,
no. 4, 2350006, World Scientific Publishing, 2023, doi:10.1142/S0129055X2350006X.
short: M. Falconi, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Reviews in Mathematical
Physics 35 (2023).
date_created: 2023-01-29T23:00:59Z
date_published: 2023-01-09T00:00:00Z
date_updated: 2023-08-16T11:47:27Z
day: '09'
department:
- _id: RoSe
doi: 10.1142/S0129055X2350006X
external_id:
arxiv:
- '2110.00458'
isi:
- '000909760300001'
intvolume: ' 35'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2110.00458'
month: '01'
oa: 1
oa_version: Preprint
publication: Reviews in Mathematical Physics
publication_identifier:
issn:
- 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bogoliubov dynamics and higher-order corrections for the regularized Nelson
model
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2023'
...
---
_id: '14374'
abstract:
- lang: eng
text: "Superconductivity has many important applications ranging from levitating
trains over qubits to MRI scanners. The phenomenon is successfully modeled by
Bardeen-Cooper-Schrieffer (BCS) theory. From a mathematical perspective, BCS theory
has been studied extensively for systems without boundary. However, little is
known in the presence of boundaries. With the help of numerical methods physicists
observed that the critical temperature may increase in the presence of a boundary.
The goal of this thesis is to understand the influence of boundaries on the critical
temperature in BCS theory and to give a first rigorous justification of these
observations. On the way, we also study two-body Schrödinger operators on domains
with boundaries and prove additional results for superconductors without boundary.\r\n\r\nBCS
theory is based on a non-linear functional, where the minimizer indicates whether
the system is superconducting or in the normal, non-superconducting state. By
considering the Hessian of the BCS functional at the normal state, one can analyze
whether the normal state is possibly a minimum of the BCS functional and estimate
the critical temperature. The Hessian turns out to be a linear operator resembling
a Schrödinger operator for two interacting particles, but with more complicated
kinetic energy. As a first step, we study the two-body Schrödinger operator in
the presence of boundaries.\r\nFor Neumann boundary conditions, we prove that
the addition of a boundary can create new eigenvalues, which correspond to the
two particles forming a bound state close to the boundary.\r\n\r\nSecond, we need
to understand superconductivity in the translation invariant setting. While in
three dimensions this has been extensively studied, there is no mathematical literature
for the one and two dimensional cases. In dimensions one and two, we compute the
weak coupling asymptotics of the critical temperature and the energy gap in the
translation invariant setting. We also prove that their ratio is independent of
the microscopic details of the model in the weak coupling limit; this property
is referred to as universality.\r\n\r\nIn the third part, we study the critical
temperature of superconductors in the presence of boundaries. We start by considering
the one-dimensional case of a half-line with contact interaction. Then, we generalize
the results to generic interactions and half-spaces in one, two and three dimensions.
Finally, we compare the critical temperature of a quarter space in two dimensions
to the critical temperatures of a half-space and of the full space."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Barbara
full_name: Roos, Barbara
id: 5DA90512-D80F-11E9-8994-2E2EE6697425
last_name: Roos
orcid: 0000-0002-9071-5880
citation:
ama: Roos B. Boundary superconductivity in BCS theory. 2023. doi:10.15479/at:ista:14374
apa: Roos, B. (2023). Boundary superconductivity in BCS theory. Institute
of Science and Technology Austria. https://doi.org/10.15479/at:ista:14374
chicago: Roos, Barbara. “Boundary Superconductivity in BCS Theory.” Institute of
Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14374.
ieee: B. Roos, “Boundary superconductivity in BCS theory,” Institute of Science
and Technology Austria, 2023.
ista: Roos B. 2023. Boundary superconductivity in BCS theory. Institute of Science
and Technology Austria.
mla: Roos, Barbara. Boundary Superconductivity in BCS Theory. Institute of
Science and Technology Austria, 2023, doi:10.15479/at:ista:14374.
short: B. Roos, Boundary Superconductivity in BCS Theory, Institute of Science and
Technology Austria, 2023.
date_created: 2023-09-28T14:23:04Z
date_published: 2023-09-30T00:00:00Z
date_updated: 2023-10-27T10:37:30Z
day: '30'
ddc:
- '515'
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: RoSe
doi: 10.15479/at:ista:14374
ec_funded: 1
file:
- access_level: open_access
checksum: ef039ffc3de2cb8dee5b14110938e9b6
content_type: application/pdf
creator: broos
date_created: 2023-10-06T11:35:56Z
date_updated: 2023-10-06T11:35:56Z
file_id: '14398'
file_name: phd-thesis-draft_pdfa_acrobat.pdf
file_size: 2365702
relation: main_file
- access_level: closed
checksum: 81dcac33daeefaf0111db52f41bb1fd0
content_type: application/x-zip-compressed
creator: broos
date_created: 2023-10-06T11:38:01Z
date_updated: 2023-10-06T11:38:01Z
file_id: '14399'
file_name: Version5.zip
file_size: 4691734
relation: source_file
file_date_updated: 2023-10-06T11:38:01Z
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '09'
oa: 1
oa_version: Published Version
page: '206'
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b
grant_number: I06427
name: Mathematical Challenges in BCS Theory of Superconductivity
publication_identifier:
issn:
- 2663 - 337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '13207'
relation: part_of_dissertation
status: public
- id: '10850'
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: Boundary superconductivity in BCS theory
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2023'
...
---
_id: '13207'
abstract:
- lang: eng
text: We consider the linear BCS equation, determining the BCS critical temperature,
in the presence of a boundary, where Dirichlet boundary conditions are imposed.
In the one-dimensional case with point interactions, we prove that the critical
temperature is strictly larger than the bulk value, at least at weak coupling.
In particular, the Cooper-pair wave function localizes near the boundary, an effect
that cannot be modeled by effective Neumann boundary conditions on the order parameter
as often imposed in Ginzburg–Landau theory. We also show that the relative shift
in critical temperature vanishes if the coupling constant either goes to zero
or to infinity.
acknowledgement: We thank Egor Babaev for encouraging us to study this problem, and
Rupert Frank for many fruitful discussions. scussions. Funding. Funding from the
European Union’s Horizon 2020 research and innovation programme under the ERC grant
agreement No. 694227 (Barbara Roos and Robert Seiringer) is gratefully acknowledged.
article_processing_charge: No
article_type: original
author:
- first_name: Christian
full_name: Hainzl, Christian
last_name: Hainzl
- first_name: Barbara
full_name: Roos, Barbara
id: 5DA90512-D80F-11E9-8994-2E2EE6697425
last_name: Roos
orcid: 0000-0002-9071-5880
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Hainzl C, Roos B, Seiringer R. Boundary superconductivity in the BCS model.
Journal of Spectral Theory. 2023;12(4):1507–1540. doi:10.4171/JST/439
apa: Hainzl, C., Roos, B., & Seiringer, R. (2023). Boundary superconductivity
in the BCS model. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/JST/439
chicago: Hainzl, Christian, Barbara Roos, and Robert Seiringer. “Boundary Superconductivity
in the BCS Model.” Journal of Spectral Theory. EMS Press, 2023. https://doi.org/10.4171/JST/439.
ieee: C. Hainzl, B. Roos, and R. Seiringer, “Boundary superconductivity in the BCS
model,” Journal of Spectral Theory, vol. 12, no. 4. EMS Press, pp. 1507–1540,
2023.
ista: Hainzl C, Roos B, Seiringer R. 2023. Boundary superconductivity in the BCS
model. Journal of Spectral Theory. 12(4), 1507–1540.
mla: Hainzl, Christian, et al. “Boundary Superconductivity in the BCS Model.” Journal
of Spectral Theory, vol. 12, no. 4, EMS Press, 2023, pp. 1507–1540, doi:10.4171/JST/439.
short: C. Hainzl, B. Roos, R. Seiringer, Journal of Spectral Theory 12 (2023) 1507–1540.
date_created: 2023-07-10T16:35:45Z
date_published: 2023-05-18T00:00:00Z
date_updated: 2023-10-27T10:37:29Z
day: '18'
ddc:
- '530'
department:
- _id: GradSch
- _id: RoSe
doi: 10.4171/JST/439
ec_funded: 1
external_id:
arxiv:
- '2201.08090'
isi:
- '000997933500008'
file:
- access_level: open_access
checksum: 5501da33be010b5c81440438287584d5
content_type: application/pdf
creator: alisjak
date_created: 2023-07-11T08:19:15Z
date_updated: 2023-07-11T08:19:15Z
file_id: '13208'
file_name: 2023_EMS_Hainzl.pdf
file_size: 304619
relation: main_file
success: 1
file_date_updated: 2023-07-11T08:19:15Z
has_accepted_license: '1'
intvolume: ' 12'
isi: 1
issue: '4'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '05'
oa: 1
oa_version: Published Version
page: 1507–1540
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Journal of Spectral Theory
publication_identifier:
eissn:
- 1664-0403
issn:
- 1664-039X
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
record:
- id: '14374'
relation: dissertation_contains
status: public
status: public
title: Boundary superconductivity in the BCS model
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: 12
year: '2023'
...