---
_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 (in subscription journal)
article_type: original
arxiv: 1
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: 2024-02-05T12:53:21Z
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 286
year: '2024'
...
---
_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
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: '14542'
abstract:
- lang: eng
text: "It is a remarkable property of BCS theory that the ratio of the energy gap
at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given
by a universal constant, independent of the microscopic details of the fermionic
interaction. This universality has rigorously been proven quite recently in three
spatial dimensions and three different limiting regimes: weak coupling, low density
and high density. The goal of this short note is to extend the universal behavior
to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit."
acknowledgement: We thank Robert Seiringer for comments on the paper. J. H. gratefully
acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond”No.
101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber
I6427.
article_number: '2360005 '
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- 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: Barbara
full_name: Roos, Barbara
id: 5DA90512-D80F-11E9-8994-2E2EE6697425
last_name: Roos
orcid: 0000-0002-9071-5880
citation:
ama: Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory.
Reviews in Mathematical Physics. 2023. doi:10.1142/s0129055x2360005x
apa: Henheik, S. J., Lauritsen, A. B., & Roos, B. (2023). Universality in low-dimensional
BCS theory. Reviews in Mathematical Physics. World Scientific Publishing.
https://doi.org/10.1142/s0129055x2360005x
chicago: Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality
in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics. World
Scientific Publishing, 2023. https://doi.org/10.1142/s0129055x2360005x.
ieee: S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional
BCS theory,” Reviews in Mathematical Physics. World Scientific Publishing,
2023.
ista: Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS
theory. Reviews in Mathematical Physics., 2360005.
mla: Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.”
Reviews in Mathematical Physics, 2360005, World Scientific Publishing,
2023, doi:10.1142/s0129055x2360005x.
short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023).
date_created: 2023-11-15T23:48:14Z
date_published: 2023-10-31T00:00:00Z
date_updated: 2023-11-20T10:04:38Z
day: '31'
department:
- _id: GradSch
- _id: LaEr
- _id: RoSe
doi: 10.1142/s0129055x2360005x
ec_funded: 1
external_id:
arxiv:
- '2301.05621'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1142/S0129055X2360005X
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
- _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b
grant_number: I06427
name: Mathematical Challenges in BCS Theory of Superconductivity
publication: Reviews in Mathematical Physics
publication_identifier:
eissn:
- 1793-6659
issn:
- 0129-055X
publication_status: epub_ahead
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Universality in low-dimensional BCS theory
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...