---
_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
arxiv: 1
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.
corr_author: '1'
date_created: 2023-01-15T23:00:52Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2025-04-14T07:26:59Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00023-022-01252-3
ec_funded: 1
external_id:
arxiv:
- '2205.15284'
isi:
- '000910751800002'
fulldoi: https://doi.org/10.1007/s00023-022-01252-3
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
arxiv: 1
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'
fulldoi: https://doi.org/10.1142/S0129055X2350006X
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: '12869'
abstract:
- lang: eng
text: 'We introduce a stochastic cellular automaton as a model for culture and border
formation. The model can be conceptualized as a game where the expansion rate
of cultures is quantified in terms of their area and perimeter in such a way that
approximately round cultures get a competitive advantage. We first analyse the
model with periodic boundary conditions, where we study how the model can end
up in a fixed state, i.e. freezes. Then we implement the model on the European
geography with mountains and rivers. We see how the model reproduces some qualitative
features of European culture formation, namely that rivers and mountains are more
frequently borders between cultures, mountainous regions tend to have higher cultural
diversity and the central European plain has less clear cultural borders. '
acknowledgement: 'FRK acknowledges support from the Villum Foundation for support
through the QMATH center of Excellence (Grant No. 10059) and the Villum Young Investigator
(Grant No. 25452) programs. '
article_processing_charge: No
author:
- first_name: Frederik Ravn
full_name: Klausen, Frederik Ravn
last_name: Klausen
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
citation:
ama: 'Klausen FR, Lauritsen AB. Research data for: A stochastic cellular automaton
model of culture formation. 2023. doi:10.15479/AT:ISTA:12869'
apa: 'Klausen, F. R., & Lauritsen, A. B. (2023). Research data for: A stochastic
cellular automaton model of culture formation. Institute of Science and Technology
Austria. https://doi.org/10.15479/AT:ISTA:12869'
chicago: 'Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Research Data
for: A Stochastic Cellular Automaton Model of Culture Formation.” Institute of
Science and Technology Austria, 2023. https://doi.org/10.15479/AT:ISTA:12869.'
ieee: 'F. R. Klausen and A. B. Lauritsen, “Research data for: A stochastic cellular
automaton model of culture formation.” Institute of Science and Technology Austria,
2023.'
ista: 'Klausen FR, Lauritsen AB. 2023. Research data for: A stochastic cellular
automaton model of culture formation, Institute of Science and Technology Austria,
10.15479/AT:ISTA:12869.'
mla: 'Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. Research Data for:
A Stochastic Cellular Automaton Model of Culture Formation. Institute of Science
and Technology Austria, 2023, doi:10.15479/AT:ISTA:12869.'
short: F.R. Klausen, A.B. Lauritsen, (2023).
corr_author: '1'
date_created: 2023-04-26T12:34:49Z
date_published: 2023-04-26T00:00:00Z
date_updated: 2025-09-09T12:26:01Z
day: '26'
ddc:
- '000'
department:
- _id: GradSch
- _id: RoSe
doi: 10.15479/AT:ISTA:12869
file:
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date_updated: 2023-04-26T12:30:06Z
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creator: alaurits
date_created: 2023-04-26T12:27:34Z
date_updated: 2023-04-26T12:27:34Z
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file_name: simulations_era=10_flux_varied_europe.zip
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date_updated: 2023-04-26T12:29:53Z
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fulldoi: https://doi.org/10.15479/AT:ISTA:12869
has_accepted_license: '1'
license: https://creativecommons.org/publicdomain/zero/1.0/
month: '04'
oa: 1
oa_version: Published Version
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '14505'
relation: used_in_publication
status: deleted
- id: '12890'
relation: used_in_publication
status: public
status: public
title: 'Research data for: A stochastic cellular automaton model of culture formation'
tmp:
image: /images/cc_0.png
legal_code_url: https://creativecommons.org/publicdomain/zero/1.0/legalcode
name: Creative Commons Public Domain Dedication (CC0 1.0)
short: CC0 (1.0)
type: research_data
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '12890'
abstract:
- lang: eng
text: We introduce a stochastic cellular automaton as a model for culture and border
formation. The model can be conceptualized as a game where the expansion rate
of cultures is quantified in terms of their area and perimeter in such a way that
approximately geometrically round cultures get a competitive advantage. We first
analyze the model with periodic boundary conditions, where we study how the model
can end up in a fixed state, i.e., freezes. Then we implement the model on the
European geography with mountains and rivers. We see how the model reproduces
some qualitative features of European culture formation, namely, that rivers and
mountains are more frequently borders between cultures, mountainous regions tend
to have higher cultural diversity, and the central European plain has less clear
cultural borders.
acknowledgement: Thanks to Kim Sneppen, Svend Krøjer, Peter Wildemann, Peter Rasmussen
and Kent Bækgaard Lauritsen for discussions and suggestions. FRK acknowledges support
from the Villum Foundation for support through the QMATH center of Excellence (Grant
No. 10059) and the Villum Young Investigator (Grant No. 25452) programs.
article_number: '054307'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Frederik Ravn
full_name: Klausen, Frederik Ravn
last_name: Klausen
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
citation:
ama: Klausen FR, Lauritsen AB. Stochastic cellular automaton model of culture formation.
Physical Review E. 2023;108(5). doi:10.1103/PhysRevE.108.054307
apa: Klausen, F. R., & Lauritsen, A. B. (2023). Stochastic cellular automaton
model of culture formation. Physical Review E. American Physical Society.
https://doi.org/10.1103/PhysRevE.108.054307
chicago: Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Stochastic Cellular
Automaton Model of Culture Formation.” Physical Review E. American Physical
Society, 2023. https://doi.org/10.1103/PhysRevE.108.054307.
ieee: F. R. Klausen and A. B. Lauritsen, “Stochastic cellular automaton model of
culture formation,” Physical Review E, vol. 108, no. 5. American Physical
Society, 2023.
ista: Klausen FR, Lauritsen AB. 2023. Stochastic cellular automaton model of culture
formation. Physical Review E. 108(5), 054307.
mla: Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Stochastic Cellular
Automaton Model of Culture Formation.” Physical Review E, vol. 108, no.
5, 054307, American Physical Society, 2023, doi:10.1103/PhysRevE.108.054307.
short: F.R. Klausen, A.B. Lauritsen, Physical Review E 108 (2023).
corr_author: '1'
date_created: 2023-05-04T08:35:01Z
date_published: 2023-11-08T00:00:00Z
date_updated: 2025-09-09T12:26:01Z
day: '08'
department:
- _id: GradSch
- _id: RoSe
doi: 10.1103/PhysRevE.108.054307
external_id:
arxiv:
- '2305.02153'
isi:
- '001106396300005'
pmid:
- '38115445'
fulldoi: https://doi.org/10.1103/PhysRevE.108.054307
intvolume: ' 108'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2305.02153
month: '11'
oa: 1
oa_version: Preprint
pmid: 1
publication: Physical Review E
publication_identifier:
eissn:
- 2470-0053
issn:
- 2470-0045
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/FrederikRavnKlausen/model-for-culture-formation
record:
- id: '12869'
relation: research_data
status: public
scopus_import: '1'
status: public
title: Stochastic cellular automaton model of culture formation
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 108
year: '2023'
...
---
_id: '12911'
abstract:
- lang: eng
text: 'This paper establishes new connections between many-body quantum systems,
One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport
(OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional
composite quantum system at positive temperature as a non-commutative entropy
regularized Optimal Transport problem. We develop a new approach to fully characterize
the dual-primal solutions in such non-commutative setting. The mathematical formalism
is particularly relevant in quantum chemistry: numerical realizations of the many-electron
ground-state energy can be computed via a non-commutative version of Sinkhorn
algorithm. Our approach allows to prove convergence and robustness of this algorithm,
which, to our best knowledge, were unknown even in the two marginal case. Our
methods are based on a priori estimates in the dual problem, which we believe
to be of independent interest. Finally, the above results are extended in 1RDMFT
setting, where bosonic or fermionic symmetry conditions are enforced on the problem.'
acknowledgement: "This work started when A.G. was visiting the Erwin Schrödinger Institute
and then continued when D.F. and L.P visited the Theoretical Chemistry Department
of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places
and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature
suggestions in the early state of the project. The authors also thank J. Maas and
R. Seiringer for their feedback and useful comments to a first draft of the article.
Finally, we acknowledge the high quality review done by the anonymous referee of
our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F
acknowledges support by the European Research Council (ERC) under the European Union's
Horizon 2020 research and innovation programme (grant agreements No 716117 and No
694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council
under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of
his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences
and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges
support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the
Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813."
article_number: '109963'
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: Augusto
full_name: Gerolin, Augusto
last_name: Gerolin
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal
transport approach to quantum composite systems at positive temperature. Journal
of Functional Analysis. 2023;285(4). doi:10.1016/j.jfa.2023.109963
apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (2023). A non-commutative
entropic optimal transport approach to quantum composite systems at positive temperature.
Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.109963
chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative
Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.”
Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963.
ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic
optimal transport approach to quantum composite systems at positive temperature,”
Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023.
ista: Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal
transport approach to quantum composite systems at positive temperature. Journal
of Functional Analysis. 285(4), 109963.
mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach
to Quantum Composite Systems at Positive Temperature.” Journal of Functional
Analysis, vol. 285, no. 4, 109963, Elsevier, 2023, doi:10.1016/j.jfa.2023.109963.
short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis
285 (2023).
date_created: 2023-05-07T22:01:02Z
date_published: 2023-08-15T00:00:00Z
date_updated: 2025-04-15T08:31:52Z
day: '15'
department:
- _id: RoSe
- _id: JaMa
doi: 10.1016/j.jfa.2023.109963
ec_funded: 1
external_id:
arxiv:
- '2106.11217'
isi:
- '000990804300001'
fulldoi: https://doi.org/10.1016/j.jfa.2023.109963
intvolume: ' 285'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2106.11217
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '9792'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: A non-commutative entropic optimal transport approach to quantum composite
systems at positive temperature
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 285
year: '2023'
...
---
_id: '13178'
abstract:
- lang: eng
text: We consider the large polaron described by the Fröhlich Hamiltonian and study
its energy-momentum relation defined as the lowest possible energy as a function
of the total momentum. Using a suitable family of trial states, we derive an optimal
parabolic upper bound for the energy-momentum relation in the limit of strong
coupling. The upper bound consists of a momentum independent term that agrees
with the predicted two-term expansion for the ground state energy of the strongly
coupled polaron at rest and a term that is quadratic in the momentum with coefficient
given by the inverse of twice the classical effective mass introduced by Landau
and Pekar.
acknowledgement: This research was supported by the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme grant
agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie grant agreement No. 665386
(K.M.).
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Krzysztof
full_name: Mysliwy, Krzysztof
id: 316457FC-F248-11E8-B48F-1D18A9856A87
last_name: Mysliwy
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Mitrouskas DJ, Mysliwy K, Seiringer R. Optimal parabolic upper bound for the
energy-momentum relation of a strongly coupled polaron. Forum of Mathematics.
2023;11:1-52. doi:10.1017/fms.2023.45
apa: Mitrouskas, D. J., Mysliwy, K., & Seiringer, R. (2023). Optimal parabolic
upper bound for the energy-momentum relation of a strongly coupled polaron. Forum
of Mathematics. Cambridge University Press. https://doi.org/10.1017/fms.2023.45
chicago: Mitrouskas, David Johannes, Krzysztof Mysliwy, and Robert Seiringer. “Optimal
Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.”
Forum of Mathematics. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.45.
ieee: D. J. Mitrouskas, K. Mysliwy, and R. Seiringer, “Optimal parabolic upper bound
for the energy-momentum relation of a strongly coupled polaron,” Forum of Mathematics,
vol. 11. Cambridge University Press, pp. 1–52, 2023.
ista: Mitrouskas DJ, Mysliwy K, Seiringer R. 2023. Optimal parabolic upper bound
for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics.
11, 1–52.
mla: Mitrouskas, David Johannes, et al. “Optimal Parabolic Upper Bound for the Energy-Momentum
Relation of a Strongly Coupled Polaron.” Forum of Mathematics, vol. 11,
Cambridge University Press, 2023, pp. 1–52, doi:10.1017/fms.2023.45.
short: D.J. Mitrouskas, K. Mysliwy, R. Seiringer, Forum of Mathematics 11 (2023)
1–52.
corr_author: '1'
date_created: 2023-07-02T22:00:43Z
date_published: 2023-06-13T00:00:00Z
date_updated: 2025-04-14T07:26:58Z
day: '13'
ddc:
- '500'
department:
- _id: RoSe
doi: 10.1017/fms.2023.45
ec_funded: 1
external_id:
arxiv:
- '2203.02454'
isi:
- '001005008800001'
file:
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checksum: f672eb7dd015c472c9a04f1b9bf9df7d
content_type: application/pdf
creator: alisjak
date_created: 2023-07-03T10:36:25Z
date_updated: 2023-07-03T10:36:25Z
file_id: '13186'
file_name: 2023_ForumofMathematics.Sigma_Mitrouskas.pdf
file_size: 943192
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has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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oa: 1
oa_version: Published Version
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call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Forum of Mathematics
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal parabolic upper bound for the energy-momentum relation of a strongly
coupled polaron
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 11
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
arxiv: 1
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.
corr_author: '1'
date_created: 2023-07-10T16:35:45Z
date_published: 2023-05-18T00:00:00Z
date_updated: 2026-04-07T13:27:39Z
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ddc:
- '530'
department:
- _id: GradSch
- _id: RoSe
doi: 10.4171/JST/439
ec_funded: 1
external_id:
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- '2201.08090'
isi:
- '000997933500008'
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intvolume: ' 12'
isi: 1
issue: '4'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1507–1540
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- _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
scopus_import: '1'
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'
...
---
_id: '13225'
abstract:
- lang: eng
text: Recently the leading order of the correlation energy of a Fermi gas in a coupled
mean-field and semiclassical scaling regime has been derived, under the assumption
of an interaction potential with a small norm and with compact support in Fourier
space. We generalize this result to large interaction potentials, requiring only
|⋅|V^∈ℓ1(Z3). Our proof is based on approximate, collective bosonization in three
dimensions. Significant improvements compared to recent work include stronger
bounds on non-bosonizable terms and more efficient control on the bosonization
of the kinetic energy.
acknowledgement: "RS was supported by the European Research Council under the European
Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227).
MP acknowledges financial support from the European Research Council under the European
Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, Grant Agreement
No. 802901). BS acknowledges financial support from the NCCR SwissMAP, from the
Swiss National Science Foundation through the Grant “Dynamical and energetic properties
of Bose-Einstein condensates” and from the European Research Council through the
ERC AdG CLaQS (Grant Agreement No. 834782). NB and MP were supported by Gruppo Nazionale
per la Fisica Matematica (GNFM) of Italy. NB was supported by the European Research
Council’s Starting Grant FERMIMATH (Grant Agreement No. 101040991).\r\nOpen access
funding provided by Università degli Studi di Milano within the CRUI-CARE Agreement."
article_number: '65'
article_processing_charge: Yes (via OA deal)
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: 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, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly
interacting Fermi gas with large interaction potential. Archive for Rational
Mechanics and Analysis. 2023;247(4). doi:10.1007/s00205-023-01893-6
apa: Benedikter, N. P., Porta, M., Schlein, B., & Seiringer, R. (2023). Correlation
energy of a weakly interacting Fermi gas with large interaction potential. Archive
for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-023-01893-6
chicago: Benedikter, Niels P, Marcello Porta, Benjamin Schlein, and Robert Seiringer.
“Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.”
Archive for Rational Mechanics and Analysis. Springer Nature, 2023. https://doi.org/10.1007/s00205-023-01893-6.
ieee: N. P. Benedikter, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy
of a weakly interacting Fermi gas with large interaction potential,” Archive
for Rational Mechanics and Analysis, vol. 247, no. 4. Springer Nature, 2023.
ista: Benedikter NP, Porta M, Schlein B, Seiringer R. 2023. Correlation energy of
a weakly interacting Fermi gas with large interaction potential. Archive for Rational
Mechanics and Analysis. 247(4), 65.
mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi
Gas with Large Interaction Potential.” Archive for Rational Mechanics and Analysis,
vol. 247, no. 4, 65, Springer Nature, 2023, doi:10.1007/s00205-023-01893-6.
short: N.P. Benedikter, M. Porta, B. Schlein, R. Seiringer, Archive for Rational
Mechanics and Analysis 247 (2023).
date_created: 2023-07-16T22:01:08Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2025-04-14T07:26:58Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-023-01893-6
ec_funded: 1
external_id:
arxiv:
- '2106.13185'
isi:
- '001024369000001'
file:
- access_level: open_access
checksum: 2b45828d854a253b14bf7aa196ec55e9
content_type: application/pdf
creator: dernst
date_created: 2023-11-14T13:12:12Z
date_updated: 2023-11-14T13:12:12Z
file_id: '14535'
file_name: 2023_ArchiveRationalMechAnalysis_Benedikter.pdf
file_size: 851626
relation: main_file
success: 1
file_date_updated: 2023-11-14T13:12:12Z
fulldoi: https://doi.org/10.1007/s00205-023-01893-6
has_accepted_license: '1'
intvolume: ' 247'
isi: 1
issue: '4'
language:
- iso: eng
month: '08'
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: 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: Correlation energy of a weakly interacting Fermi gas with large interaction
potential
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
volume: 247
year: '2023'
...
---
OA_place: publisher
OA_type: hybrid
_id: '13226'
abstract:
- lang: eng
text: We consider the ground state and the low-energy excited states of a system
of N identical bosons with interactions in the mean-field scaling regime. For
the ground state, we derive a weak Edgeworth expansion for the fluctuations of
bounded one-body operators, which yields corrections to a central limit theorem
to any order in 1/N−−√. For suitable excited states, we show that the limiting
distribution is a polynomial times a normal distribution, and that higher-order
corrections are given by an Edgeworth-type expansion.
acknowledgement: "It is a pleasure to thank Martin Kolb, Simone Rademacher, Robert
Seiringer and Stefan Teufel for helpful discussions. Moreover, we thank the referee
for many constructive comments. L.B. gratefully acknowledges funding from the German
Research Foundation within the Munich Center of Quantum Science and Technology (EXC
2111) and from the European Union’s Horizon 2020 research and innovation programme
under the Marie Skłodowska-Curie Grant Agreement No. 754411. We thank the Mathematical
Research Institute Oberwolfach, where part of this work was done, for their hospitality.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_number: '77'
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
- 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: Bossmann L, Petrat SP. Weak Edgeworth expansion for the mean-field Bose gas.
Letters in Mathematical Physics. 2023;113(4). doi:10.1007/s11005-023-01698-4
apa: Bossmann, L., & Petrat, S. P. (2023). Weak Edgeworth expansion for the
mean-field Bose gas. Letters in Mathematical Physics. Springer Nature.
https://doi.org/10.1007/s11005-023-01698-4
chicago: Bossmann, Lea, and Sören P Petrat. “Weak Edgeworth Expansion for the Mean-Field
Bose Gas.” Letters in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s11005-023-01698-4.
ieee: L. Bossmann and S. P. Petrat, “Weak Edgeworth expansion for the mean-field
Bose gas,” Letters in Mathematical Physics, vol. 113, no. 4. Springer Nature,
2023.
ista: Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose
gas. Letters in Mathematical Physics. 113(4), 77.
mla: Bossmann, Lea, and Sören P. Petrat. “Weak Edgeworth Expansion for the Mean-Field
Bose Gas.” Letters in Mathematical Physics, vol. 113, no. 4, 77, Springer
Nature, 2023, doi:10.1007/s11005-023-01698-4.
short: L. Bossmann, S.P. Petrat, Letters in Mathematical Physics 113 (2023).
corr_author: '1'
date_created: 2023-07-16T22:01:08Z
date_published: 2023-07-03T00:00:00Z
date_updated: 2025-06-25T06:20:15Z
day: '03'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-023-01698-4
ec_funded: 1
external_id:
arxiv:
- '2208.00199'
isi:
- '001022878900002'
file:
- access_level: open_access
checksum: 995c902a989a6769fd3db456cfd41111
content_type: application/pdf
creator: dernst
date_created: 2025-06-25T06:20:02Z
date_updated: 2025-06-25T06:20:02Z
file_id: '19898'
file_name: 2023_LettersMathPhysics_Bossmann.pdf
file_size: 586698
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success: 1
file_date_updated: 2025-06-25T06:20:02Z
fulldoi: https://doi.org/10.1007/s11005-023-01698-4
has_accepted_license: '1'
intvolume: ' 113'
isi: 1
issue: '4'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Weak Edgeworth expansion for the mean-field 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: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 113
year: '2023'
...
---
_id: '14192'
abstract:
- lang: eng
text: For the Fröhlich model of the large polaron, we prove that the ground state
energy as a function of the total momentum has a unique global minimum at momentum
zero. This implies the non-existence of a ground state of the translation invariant
Fröhlich Hamiltonian and thus excludes the possibility of a localization transition
at finite coupling.
acknowledgement: D.M. and K.M. thank Robert Seiringer for helpful discussions. Open
access funding provided by Institute of Science and Technology (IST Austria). Financial
support from the Agence Nationale de la Recherche (ANR) through the projects ANR-17-CE40-0016,
ANR-17-CE40-0007-01, ANR-17-EURE-0002 (J.L.) and from the European Union’s Horizon
2020 research and innovation programme under the Maria Skłodowska-Curie grant agreement
No. 665386 (K.M.) is gratefully acknowledged.
article_number: '17'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jonas
full_name: Lampart, Jonas
last_name: Lampart
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Krzysztof
full_name: Mysliwy, Krzysztof
id: 316457FC-F248-11E8-B48F-1D18A9856A87
last_name: Mysliwy
citation:
ama: Lampart J, Mitrouskas DJ, Mysliwy K. On the global minimum of the energy–momentum
relation for the polaron. Mathematical Physics, Analysis and Geometry.
2023;26(3). doi:10.1007/s11040-023-09460-x
apa: Lampart, J., Mitrouskas, D. J., & Mysliwy, K. (2023). On the global minimum
of the energy–momentum relation for the polaron. Mathematical Physics, Analysis
and Geometry. Springer Nature. https://doi.org/10.1007/s11040-023-09460-x
chicago: Lampart, Jonas, David Johannes Mitrouskas, and Krzysztof Mysliwy. “On the
Global Minimum of the Energy–Momentum Relation for the Polaron.” Mathematical
Physics, Analysis and Geometry. Springer Nature, 2023. https://doi.org/10.1007/s11040-023-09460-x.
ieee: J. Lampart, D. J. Mitrouskas, and K. Mysliwy, “On the global minimum of the
energy–momentum relation for the polaron,” Mathematical Physics, Analysis and
Geometry, vol. 26, no. 3. Springer Nature, 2023.
ista: Lampart J, Mitrouskas DJ, Mysliwy K. 2023. On the global minimum of the energy–momentum
relation for the polaron. Mathematical Physics, Analysis and Geometry. 26(3),
17.
mla: Lampart, Jonas, et al. “On the Global Minimum of the Energy–Momentum Relation
for the Polaron.” Mathematical Physics, Analysis and Geometry, vol. 26,
no. 3, 17, Springer Nature, 2023, doi:10.1007/s11040-023-09460-x.
short: J. Lampart, D.J. Mitrouskas, K. Mysliwy, Mathematical Physics, Analysis and
Geometry 26 (2023).
corr_author: '1'
date_created: 2023-08-22T14:09:47Z
date_published: 2023-07-26T00:00:00Z
date_updated: 2024-10-09T21:06:41Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11040-023-09460-x
external_id:
arxiv:
- '2206.14708'
isi:
- '001032992600001'
file:
- access_level: open_access
checksum: f0941cc66cb3ed06a12ca4b7e356cfd6
content_type: application/pdf
creator: dernst
date_created: 2023-08-23T10:59:15Z
date_updated: 2023-08-23T10:59:15Z
file_id: '14225'
file_name: 2023_MathPhysics_Lampart.pdf
file_size: 317026
relation: main_file
success: 1
file_date_updated: 2023-08-23T10:59:15Z
fulldoi: https://doi.org/10.1007/s11040-023-09460-x
has_accepted_license: '1'
intvolume: ' 26'
isi: 1
issue: '3'
keyword:
- Geometry and Topology
- Mathematical Physics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
eissn:
- 1572-9656
issn:
- 1385-0172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the global minimum of the energy–momentum relation for the polaron
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
volume: 26
year: '2023'
...
---
_id: '14254'
abstract:
- lang: eng
text: In [10] Nam proved a Lieb–Thirring Inequality for the kinetic energy of a
fermionic quantum system, with almost optimal (semi-classical) constant and a
gradient correction term. We present a stronger version of this inequality, with
a much simplified proof. As a corollary we obtain a simple proof of the original
Lieb–Thirring inequality.
acknowledgement: J.P.S. thanks the Institute of Science and Technology Austria for
the hospitality and support during a visit where this work was done. J.P.S. was
also partially supported by the VILLUM Centre of Excellence for the Mathematics
of Quantum Theory (QMATH) (grant No. 10059).
article_number: '110129'
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: Jan Philip
full_name: Solovej, Jan Philip
last_name: Solovej
citation:
ama: Seiringer R, Solovej JP. A simple approach to Lieb-Thirring type inequalities.
Journal of Functional Analysis. 2023;285(10). doi:10.1016/j.jfa.2023.110129
apa: Seiringer, R., & Solovej, J. P. (2023). A simple approach to Lieb-Thirring
type inequalities. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.110129
chicago: Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring
Type Inequalities.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.110129.
ieee: R. Seiringer and J. P. Solovej, “A simple approach to Lieb-Thirring type inequalities,”
Journal of Functional Analysis, vol. 285, no. 10. Elsevier, 2023.
ista: Seiringer R, Solovej JP. 2023. A simple approach to Lieb-Thirring type inequalities.
Journal of Functional Analysis. 285(10), 110129.
mla: Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring
Type Inequalities.” Journal of Functional Analysis, vol. 285, no. 10, 110129,
Elsevier, 2023, doi:10.1016/j.jfa.2023.110129.
short: R. Seiringer, J.P. Solovej, Journal of Functional Analysis 285 (2023).
corr_author: '1'
date_created: 2023-09-03T22:01:14Z
date_published: 2023-11-15T00:00:00Z
date_updated: 2024-10-09T21:06:47Z
day: '15'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1016/j.jfa.2023.110129
external_id:
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- '2303.04504'
isi:
- '001071552300001'
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month: '11'
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publication: Journal of Functional Analysis
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eissn:
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publisher: Elsevier
quality_controlled: '1'
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title: A simple approach to Lieb-Thirring type inequalities
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---
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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.
corr_author: '1'
date_created: 2023-09-28T14:23:04Z
date_published: 2023-09-30T00:00:00Z
date_updated: 2026-04-07T13:27:39Z
day: '30'
ddc:
- '515'
- '539'
degree_awarded: PhD
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- _id: RoSe
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language:
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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:
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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
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short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2023'
...
---
_id: '14441'
abstract:
- lang: eng
text: We study the Fröhlich polaron model in R3, and establish the subleading term
in the strong coupling asymptotics of its ground state energy, corresponding to
the quantum corrections to the classical energy determined by the Pekar approximation.
acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation
programme under the ERC grant agreement No 694227 is acknowledged. Open access funding
provided by Institute of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Morris
full_name: Brooks, Morris
id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
last_name: Brooks
orcid: 0000-0002-6249-0928
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Brooks M, Seiringer R. The Fröhlich Polaron at strong coupling: Part I - The
quantum correction to the classical energy. Communications in Mathematical
Physics. 2023;404:287-337. doi:10.1007/s00220-023-04841-3'
apa: 'Brooks, M., & Seiringer, R. (2023). The Fröhlich Polaron at strong coupling:
Part I - The quantum correction to the classical energy. Communications in
Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04841-3'
chicago: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong
Coupling: Part I - The Quantum Correction to the Classical Energy.” Communications
in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04841-3.'
ieee: 'M. Brooks and R. Seiringer, “The Fröhlich Polaron at strong coupling: Part
I - The quantum correction to the classical energy,” Communications in Mathematical
Physics, vol. 404. Springer Nature, pp. 287–337, 2023.'
ista: 'Brooks M, Seiringer R. 2023. The Fröhlich Polaron at strong coupling: Part
I - The quantum correction to the classical energy. Communications in Mathematical
Physics. 404, 287–337.'
mla: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling:
Part I - The Quantum Correction to the Classical Energy.” Communications in
Mathematical Physics, vol. 404, Springer Nature, 2023, pp. 287–337, doi:10.1007/s00220-023-04841-3.'
short: M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023)
287–337.
corr_author: '1'
date_created: 2023-10-22T22:01:13Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2025-09-09T13:12:02Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00220-023-04841-3
ec_funded: 1
external_id:
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isi:
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isi: 1
language:
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month: '11'
oa: 1
oa_version: Published Version
page: 287-337
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 Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The Fröhlich Polaron at strong coupling: Part I - The quantum correction to
the classical energy'
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 404
year: '2023'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: diamond
_id: '14662'
abstract:
- lang: eng
text: We consider a class of polaron models, including the Fröhlich model, at zero
total momentum, and show that at sufficiently weak coupling there are no excited
eigenvalues below the essential spectrum.
article_processing_charge: Yes
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
citation:
ama: Seiringer R. Absence of excited eigenvalues for Fröhlich type polaron models
at weak coupling. Journal of Spectral Theory. 2023;13(3):1045-1055. doi:10.4171/JST/469
apa: Seiringer, R. (2023). Absence of excited eigenvalues for Fröhlich type polaron
models at weak coupling. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/JST/469
chicago: Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron
Models at Weak Coupling.” Journal of Spectral Theory. EMS Press, 2023.
https://doi.org/10.4171/JST/469.
ieee: R. Seiringer, “Absence of excited eigenvalues for Fröhlich type polaron models
at weak coupling,” Journal of Spectral Theory, vol. 13, no. 3. EMS Press,
pp. 1045–1055, 2023.
ista: Seiringer R. 2023. Absence of excited eigenvalues for Fröhlich type polaron
models at weak coupling. Journal of Spectral Theory. 13(3), 1045–1055.
mla: Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron
Models at Weak Coupling.” Journal of Spectral Theory, vol. 13, no. 3, EMS
Press, 2023, pp. 1045–55, doi:10.4171/JST/469.
short: R. Seiringer, Journal of Spectral Theory 13 (2023) 1045–1055.
corr_author: '1'
date_created: 2023-12-10T23:00:59Z
date_published: 2023-11-25T00:00:00Z
date_updated: 2025-09-09T13:40:33Z
day: '25'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.4171/JST/469
external_id:
arxiv:
- '2210.17123'
isi:
- '001127467700008'
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checksum: 9ce96ca87d56ea9a70d2eb9a32839f8d
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file_size: 201513
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file_date_updated: 2023-12-11T12:03:12Z
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isi: 1
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language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 1045-1055
publication: Journal of Spectral Theory
publication_identifier:
eissn:
- 1664-0403
issn:
- 1664-039X
publication_status: published
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 13
year: '2023'
...
---
_id: '14715'
abstract:
- lang: eng
text: We consider N trapped bosons in the mean-field limit with coupling constant
λN = 1/(N − 1). The ground state of such systems exhibits Bose–Einstein condensation.
We prove that the probability of finding ℓ particles outside the condensate wave
function decays exponentially in ℓ.
acknowledgement: We thank Lea Boßmann, Phan Thành Nam and Simone Rademacher for helpful
remarks. P.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) - Grant No. SFB/TRR 352 “Mathematics of Many-Body Quantum
Systems and Their Collective Phenomena.”
article_number: '121901'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Peter
full_name: Pickl, Peter
last_name: Pickl
citation:
ama: Mitrouskas DJ, Pickl P. Exponential decay of the number of excitations in the
weakly interacting Bose gas. Journal of Mathematical Physics. 2023;64(12).
doi:10.1063/5.0172199
apa: Mitrouskas, D. J., & Pickl, P. (2023). Exponential decay of the number
of excitations in the weakly interacting Bose gas. Journal of Mathematical
Physics. AIP Publishing. https://doi.org/10.1063/5.0172199
chicago: Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the
Number of Excitations in the Weakly Interacting Bose Gas.” Journal of Mathematical
Physics. AIP Publishing, 2023. https://doi.org/10.1063/5.0172199.
ieee: D. J. Mitrouskas and P. Pickl, “Exponential decay of the number of excitations
in the weakly interacting Bose gas,” Journal of Mathematical Physics, vol.
64, no. 12. AIP Publishing, 2023.
ista: Mitrouskas DJ, Pickl P. 2023. Exponential decay of the number of excitations
in the weakly interacting Bose gas. Journal of Mathematical Physics. 64(12), 121901.
mla: Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the Number
of Excitations in the Weakly Interacting Bose Gas.” Journal of Mathematical
Physics, vol. 64, no. 12, 121901, AIP Publishing, 2023, doi:10.1063/5.0172199.
short: D.J. Mitrouskas, P. Pickl, Journal of Mathematical Physics 64 (2023).
corr_author: '1'
date_created: 2023-12-31T23:01:02Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2025-09-09T14:05:28Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1063/5.0172199
external_id:
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- '2307.11062'
isi:
- '001127432200002'
file:
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checksum: 66572f718a36465576cf0d6b3f7e01fc
content_type: application/pdf
creator: dernst
date_created: 2024-01-02T08:45:07Z
date_updated: 2024-01-02T08:45:07Z
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success: 1
file_date_updated: 2024-01-02T08:45:07Z
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has_accepted_license: '1'
intvolume: ' 64'
isi: 1
issue: '12'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Exponential decay of the number of excitations in the weakly interacting 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: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 64
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '14854'
abstract:
- lang: eng
text: We study the spectrum of the Fröhlich Hamiltonian for the polaron at fixed
total momentum. We prove the existence of excited eigenvalues between the ground
state energy and the essential spectrum at strong coupling. In fact, our main
result shows that the number of excited energy bands diverges in the strong coupling
limit. To prove this we derive upper bounds for the min-max values of the corresponding
fiber Hamiltonians and compare them with the bottom of the essential spectrum,
a lower bound on which was recently obtained by Brooks and Seiringer (Comm. Math.
Phys. 404:1 (2023), 287–337). The upper bounds are given in terms of the ground
state energy band shifted by momentum-independent excitation energies determined
by an effective Hamiltonian of Bogoliubov type.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Mitrouskas DJ, Seiringer R. Ubiquity of bound states for the strongly coupled
polaron. Pure and Applied Analysis. 2023;5(4):973-1008. doi:10.2140/paa.2023.5.973
apa: Mitrouskas, D. J., & Seiringer, R. (2023). Ubiquity of bound states for
the strongly coupled polaron. Pure and Applied Analysis. Mathematical Sciences
Publishers. https://doi.org/10.2140/paa.2023.5.973
chicago: Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States
for the Strongly Coupled Polaron.” Pure and Applied Analysis. Mathematical
Sciences Publishers, 2023. https://doi.org/10.2140/paa.2023.5.973.
ieee: D. J. Mitrouskas and R. Seiringer, “Ubiquity of bound states for the strongly
coupled polaron,” Pure and Applied Analysis, vol. 5, no. 4. Mathematical
Sciences Publishers, pp. 973–1008, 2023.
ista: Mitrouskas DJ, Seiringer R. 2023. Ubiquity of bound states for the strongly
coupled polaron. Pure and Applied Analysis. 5(4), 973–1008.
mla: Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States
for the Strongly Coupled Polaron.” Pure and Applied Analysis, vol. 5, no.
4, Mathematical Sciences Publishers, 2023, pp. 973–1008, doi:10.2140/paa.2023.5.973.
short: D.J. Mitrouskas, R. Seiringer, Pure and Applied Analysis 5 (2023) 973–1008.
corr_author: '1'
date_created: 2024-01-22T08:24:23Z
date_published: 2023-12-15T00:00:00Z
date_updated: 2025-04-23T14:21:39Z
day: '15'
department:
- _id: RoSe
doi: 10.2140/paa.2023.5.973
external_id:
arxiv:
- '2211.03606'
fulldoi: https://doi.org/10.2140/paa.2023.5.973
intvolume: ' 5'
issue: '4'
keyword:
- General Medicine
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2211.03606
month: '12'
oa: 1
oa_version: Preprint
page: 973-1008
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: Ubiquity of bound states for the strongly coupled polaron
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2023'
...
---
_id: '14992'
abstract:
- lang: eng
text: In this chapter we first review the Levy–Lieb functional, which gives the
lowest kinetic and interaction energy that can be reached with all possible quantum
states having a given density. We discuss two possible convex generalizations
of this functional, corresponding to using mixed canonical and grand-canonical
states, respectively. We present some recent works about the local density approximation,
in which the functionals get replaced by purely local functionals constructed
using the uniform electron gas energy per unit volume. We then review the known
upper and lower bounds on the Levy–Lieb functionals. We start with the kinetic
energy alone, then turn to the classical interaction alone, before we are able
to put everything together. A later section is devoted to the Hohenberg–Kohn theorem
and the role of many-body unique continuation in its proof.
alternative_title:
- Mathematics and Molecular Modeling
article_processing_charge: No
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. Universal Functionals in Density Functional
Theory. In: Cances E, Friesecke G, eds. Density Functional Theory. 1st
ed. MAMOMO. Springer; 2023:115-182. doi:10.1007/978-3-031-22340-2_3'
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2023). Universal Functionals in
Density Functional Theory. In E. Cances & G. Friesecke (Eds.), Density
Functional Theory (1st ed., pp. 115–182). Springer. https://doi.org/10.1007/978-3-031-22340-2_3
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Universal Functionals
in Density Functional Theory.” In Density Functional Theory, edited by
Eric Cances and Gero Friesecke, 1st ed., 115–82. MAMOMO. Springer, 2023. https://doi.org/10.1007/978-3-031-22340-2_3.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Universal Functionals in Density
Functional Theory,” in Density Functional Theory, 1st ed., E. Cances and
G. Friesecke, Eds. Springer, 2023, pp. 115–182.
ista: 'Lewin M, Lieb EH, Seiringer R. 2023.Universal Functionals in Density Functional
Theory. In: Density Functional Theory. Mathematics and Molecular Modeling, , 115–182.'
mla: Lewin, Mathieu, et al. “Universal Functionals in Density Functional Theory.”
Density Functional Theory, edited by Eric Cances and Gero Friesecke, 1st
ed., Springer, 2023, pp. 115–82, doi:10.1007/978-3-031-22340-2_3.
short: M. Lewin, E.H. Lieb, R. Seiringer, in:, E. Cances, G. Friesecke (Eds.), Density
Functional Theory, 1st ed., Springer, 2023, pp. 115–182.
date_created: 2024-02-14T14:44:33Z
date_published: 2023-07-19T00:00:00Z
date_updated: 2024-02-20T08:33:06Z
day: '19'
department:
- _id: RoSe
doi: 10.1007/978-3-031-22340-2_3
edition: '1'
editor:
- first_name: Eric
full_name: Cances, Eric
last_name: Cances
- first_name: Gero
full_name: Friesecke, Gero
last_name: Friesecke
external_id:
arxiv:
- '1912.10424'
fulldoi: https://doi.org/10.1007/978-3-031-22340-2_3
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1912.10424
month: '07'
oa: 1
oa_version: Preprint
page: 115-182
publication: Density Functional Theory
publication_identifier:
eisbn:
- '9783031223402'
isbn:
- '9783031223396'
issn:
- 3005-0286
publication_status: published
publisher: Springer
quality_controlled: '1'
series_title: MAMOMO
status: public
title: Universal Functionals in Density Functional Theory
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '17074'
abstract:
- lang: eng
text: We verify Bogoliubov's approximation for translation invariant Bose gases
in the mean field regime, i.e. we prove that the ground state energy EN is given
by EN=NeH+infσ(H)+oN→∞(1), where N is the number of particles, eH is the minimal
Hartree energy and H is the Bogoliubov Hamiltonian. As an intermediate result
we show the existence of approximate ground states ΨN, i.e. states satisfying
⟨HN⟩ΨN=EN+oN→∞(1), exhibiting complete Bose--Einstein condensation with respect
to one of the Hartree minimizers.
acknowledgement: "We are grateful to Rupert Frank for helpful discussions at an early
stage of this project.\r\nFunding from the European Union’s Horizon 2020 research
and innovation programme\r\nunder the ERC grant agreement No 694227 is acknowledged."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Morris
full_name: Brooks, Morris
id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
last_name: Brooks
orcid: 0000-0002-6249-0928
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Brooks M, Seiringer R. Validity of Bogoliubov’s approximation fortranslation-invariant
Bose gases. Probability and Mathematical Physics. 2023;3(4):939-1000. doi:10.2140/pmp.2022.3.939
apa: Brooks, M., & Seiringer, R. (2023). Validity of Bogoliubov’s approximation
fortranslation-invariant Bose gases. Probability and Mathematical Physics.
Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2022.3.939
chicago: Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation
Fortranslation-Invariant Bose Gases.” Probability and Mathematical Physics.
Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/pmp.2022.3.939.
ieee: M. Brooks and R. Seiringer, “Validity of Bogoliubov’s approximation fortranslation-invariant
Bose gases,” Probability and Mathematical Physics, vol. 3, no. 4. Mathematical
Sciences Publishers, pp. 939–1000, 2023.
ista: Brooks M, Seiringer R. 2023. Validity of Bogoliubov’s approximation fortranslation-invariant
Bose gases. Probability and Mathematical Physics. 3(4), 939–1000.
mla: Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation
Fortranslation-Invariant Bose Gases.” Probability and Mathematical Physics,
vol. 3, no. 4, Mathematical Sciences Publishers, 2023, pp. 939–1000, doi:10.2140/pmp.2022.3.939.
short: M. Brooks, R. Seiringer, Probability and Mathematical Physics 3 (2023) 939–1000.
corr_author: '1'
date_created: 2024-05-29T06:12:54Z
date_published: 2023-02-21T00:00:00Z
date_updated: 2025-04-14T07:26:59Z
day: '21'
department:
- _id: RoSe
doi: 10.2140/pmp.2022.3.939
ec_funded: 1
external_id:
arxiv:
- '2111.13864'
fulldoi: https://doi.org/10.2140/pmp.2022.3.939
intvolume: ' 3'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2111.13864
month: '02'
oa: 1
oa_version: Preprint
page: 939-1000
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Probability and Mathematical Physics
publication_identifier:
eissn:
- 2690-1005
issn:
- 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2023'
...
---
_id: '10850'
abstract:
- lang: eng
text: "We study two interacting quantum particles forming a bound state in d-dimensional
free\r\nspace, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with
Neumann boundary\r\nconditions. First, we prove that the ground state energy strictly
decreases upon going from k\r\nto k+1. This shows that the particles stick to
the corner where all boundary planes intersect.\r\nSecond, we show that for all
k the resulting Hamiltonian, after removing the free part of the\r\nkinetic energy,
has only finitely many eigenvalues below the essential spectrum. This paper\r\ngeneralizes
the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444,\r\n2020)
to dimensions d > 1."
acknowledgement: We thank Rupert Frank for contributing Appendix B. Funding from the
European Union's Horizon 2020 research and innovation programme under the ERC grant
agreement No. 694227 is gratefully acknowledged.
article_number: '109455'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- 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: Roos B, Seiringer R. Two-particle bound states at interfaces and corners. Journal
of Functional Analysis. 2022;282(12). doi:10.1016/j.jfa.2022.109455
apa: Roos, B., & Seiringer, R. (2022). Two-particle bound states at interfaces
and corners. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109455
chicago: Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces
and Corners.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109455.
ieee: B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,”
Journal of Functional Analysis, vol. 282, no. 12. Elsevier, 2022.
ista: Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners.
Journal of Functional Analysis. 282(12), 109455.
mla: Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces
and Corners.” Journal of Functional Analysis, vol. 282, no. 12, 109455,
Elsevier, 2022, doi:10.1016/j.jfa.2022.109455.
short: B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022).
corr_author: '1'
date_created: 2022-03-16T08:41:53Z
date_published: 2022-06-15T00:00:00Z
date_updated: 2026-04-07T13:27:39Z
day: '15'
ddc:
- '510'
department:
- _id: GradSch
- _id: RoSe
doi: 10.1016/j.jfa.2022.109455
ec_funded: 1
external_id:
arxiv:
- '2105.04874'
isi:
- '000795160200009'
file:
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fulldoi: https://doi.org/10.1016/j.jfa.2022.109455
has_accepted_license: '1'
intvolume: ' 282'
isi: 1
issue: '12'
keyword:
- Analysis
language:
- iso: eng
month: '06'
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: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Two-particle bound states at interfaces and corners
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: 282
year: '2022'
...
---
OA_place: publisher
_id: '11473'
abstract:
- lang: eng
text: "The polaron model is a basic model of quantum field theory describing a single
particle\r\ninteracting with a bosonic field. It arises in many physical contexts.
We are mostly concerned\r\nwith models applicable in the context of an impurity
atom in a Bose-Einstein condensate as\r\nwell as the problem of electrons moving
in polar crystals.\r\nThe model has a simple structure in which the interaction
of the particle with the field is given\r\nby a term linear in the field’s creation
and annihilation operators. In this work, we investigate\r\nthe properties of
this model by providing rigorous estimates on various energies relevant to the\r\nproblem.
The estimates are obtained, for the most part, by suitable operator techniques
which\r\nconstitute the principal mathematical substance of the thesis.\r\nThe
first application of these techniques is to derive the polaron model rigorously
from first\r\nprinciples, i.e., from a full microscopic quantum-mechanical many-body
problem involving an\r\nimpurity in an otherwise homogeneous system. We accomplish
this for the N + 1 Bose gas\r\nin the mean-field regime by showing that a suitable
polaron-type Hamiltonian arises at weak\r\ninteractions as a low-energy effective
theory for this problem.\r\nIn the second part, we investigate rigorously the
ground state of the model at fixed momentum\r\nand for large values of the coupling
constant. Qualitatively, the system is expected to display\r\na transition from
the quasi-particle behavior at small momenta, where the dispersion relation\r\nis
parabolic and the particle moves through the medium dragging along a cloud of
phonons, to\r\nthe radiative behavior at larger momenta where the polaron decelerates
and emits free phonons.\r\nAt the same time, in the strong coupling regime, the
bosonic field is expected to behave purely\r\nclassically. Accordingly, the effective
mass of the polaron at strong coupling is conjectured to\r\nbe asymptotically
equal to the one obtained from the semiclassical counterpart of the problem,\r\nfirst
studied by Landau and Pekar in the 1940s. For polaron models with regularized
form\r\nfactors and phonon dispersion relations of superfluid type, i.e., bounded
below by a linear\r\nfunction of the wavenumbers for all phonon momenta as in
the interacting Bose gas, we prove\r\nthat for a large window of momenta below
the radiation threshold, the energy-momentum\r\nrelation at strong coupling is
indeed essentially a parabola with semi-latus rectum equal to the\r\nLandau–Pekar
effective mass, as expected.\r\nFor the Fröhlich polaron describing electrons
in polar crystals where the dispersion relation is\r\nof the optical type and
the form factor is formally UV–singular due to the nature of the point\r\ncharge-dipole
interaction, we are able to give the corresponding upper bound. In contrast to\r\nthe
regular case, this requires the inclusion of the quantum fluctuations of the phonon
field,\r\nwhich makes the problem considerably more difficult.\r\nThe results
are supplemented by studies on the absolute ground-state energy at strong coupling,\r\na
proof of the divergence of the effective mass with the coupling constant for a
wide class of\r\npolaron models, as well as the discussion of the apparent UV
singularity of the Fröhlich model\r\nand the application of the techniques used
for its removal for the energy estimates.\r\n"
acknowledged_ssus:
- _id: SSU
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Krzysztof
full_name: Mysliwy, Krzysztof
id: 316457FC-F248-11E8-B48F-1D18A9856A87
last_name: Mysliwy
citation:
ama: 'Mysliwy K. Polarons in Bose gases and polar crystals: Some rigorous energy
estimates. 2022. doi:10.15479/at:ista:11473'
apa: 'Mysliwy, K. (2022). Polarons in Bose gases and polar crystals: Some rigorous
energy estimates. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:11473'
chicago: 'Mysliwy, Krzysztof. “Polarons in Bose Gases and Polar Crystals: Some Rigorous
Energy Estimates.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:11473.'
ieee: 'K. Mysliwy, “Polarons in Bose gases and polar crystals: Some rigorous energy
estimates,” Institute of Science and Technology Austria, 2022.'
ista: 'Mysliwy K. 2022. Polarons in Bose gases and polar crystals: Some rigorous
energy estimates. Institute of Science and Technology Austria.'
mla: 'Mysliwy, Krzysztof. Polarons in Bose Gases and Polar Crystals: Some Rigorous
Energy Estimates. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:11473.'
short: 'K. Mysliwy, Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy
Estimates, Institute of Science and Technology Austria, 2022.'
corr_author: '1'
date_created: 2022-06-30T12:15:03Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2026-04-07T14:14:52Z
day: '01'
ddc:
- '515'
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: RoSe
doi: 10.15479/at:ista:11473
ec_funded: 1
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has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '138'
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
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relation: part_of_dissertation
status: public
- id: '8705'
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: 'Polarons in Bose gases and polar crystals: Some rigorous energy estimates'
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2022'
...