---
_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: '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.
date_created: 2023-10-22T22:01:13Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2023-10-31T12:22:51Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00220-023-04841-3
ec_funded: 1
external_id:
arxiv:
- '2207.03156'
file:
- access_level: open_access
checksum: 1ae49b39247cb6b40ff75997381581b8
content_type: application/pdf
creator: dernst
date_created: 2023-10-31T12:21:39Z
date_updated: 2023-10-31T12:21:39Z
file_id: '14477'
file_name: 2023_CommMathPhysics_Brooks.pdf
file_size: 832375
relation: main_file
success: 1
file_date_updated: 2023-10-31T12:21:39Z
has_accepted_license: '1'
intvolume: ' 404'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 404
year: '2023'
...
---
_id: '14662'
abstract:
- lang: eng
text: "We consider a class of polaron models, including the Fröhlich model, at zero
total\r\nmomentum, and show that at sufficiently weak coupling there are no excited
eigenvalues below\r\nthe 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.
date_created: 2023-12-10T23:00:59Z
date_published: 2023-11-25T00:00:00Z
date_updated: 2023-12-11T12:12:14Z
day: '25'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.4171/JST/469
external_id:
arxiv:
- '2210.17123'
file:
- access_level: open_access
checksum: 9ce96ca87d56ea9a70d2eb9a32839f8d
content_type: application/pdf
creator: dernst
date_created: 2023-12-11T12:03:12Z
date_updated: 2023-12-11T12:03:12Z
file_id: '14677'
file_name: 2023_JST_Seiringer.pdf
file_size: 201513
relation: main_file
success: 1
file_date_updated: 2023-12-11T12:03:12Z
has_accepted_license: '1'
intvolume: ' 13'
issue: '3'
language:
- iso: eng
month: '11'
oa: 1
oa_version: None
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 13
year: '2023'
...
---
_id: '14854'
abstract:
- lang: eng
text: "\r\nAbstract\r\nWe 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
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.
date_created: 2024-01-22T08:24:23Z
date_published: 2023-12-15T00:00:00Z
date_updated: 2024-01-23T12:55:12Z
day: '15'
department:
- _id: RoSe
doi: 10.2140/paa.2023.5.973
intvolume: ' 5'
issue: '4'
keyword:
- General Medicine
language:
- iso: eng
month: '12'
oa_version: None
page: 973-1008
publication: Pure and Applied Analysis
publication_identifier:
issn:
- 2578-5885
- 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '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'
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: '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.
date_created: 2023-07-02T22:00:43Z
date_published: 2023-06-13T00:00:00Z
date_updated: 2023-11-02T12:30:50Z
day: '13'
ddc:
- '500'
department:
- _id: RoSe
doi: 10.1017/fms.2023.45
ec_funded: 1
external_id:
arxiv:
- '2203.02454'
isi:
- '001005008800001'
file:
- access_level: open_access
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
relation: main_file
success: 1
file_date_updated: 2023-07-03T10:36:25Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 1-52
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
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.
date_created: 2023-07-10T16:35:45Z
date_published: 2023-05-18T00:00:00Z
date_updated: 2023-10-27T10:37:29Z
day: '18'
ddc:
- '530'
department:
- _id: GradSch
- _id: RoSe
doi: 10.4171/JST/439
ec_funded: 1
external_id:
arxiv:
- '2201.08090'
isi:
- '000997933500008'
file:
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checksum: 5501da33be010b5c81440438287584d5
content_type: application/pdf
creator: alisjak
date_created: 2023-07-11T08:19:15Z
date_updated: 2023-07-11T08:19:15Z
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relation: main_file
success: 1
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intvolume: ' 12'
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month: '05'
oa: 1
oa_version: Published Version
page: 1507–1540
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Journal of Spectral Theory
publication_identifier:
eissn:
- 1664-0403
issn:
- 1664-039X
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
record:
- id: '14374'
relation: dissertation_contains
status: public
status: public
title: Boundary superconductivity in the BCS model
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 12
year: '2023'
...
---
_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: 2023-12-13T11:31:14Z
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
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'
...
---
_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).
date_created: 2023-09-03T22:01:14Z
date_published: 2023-11-15T00:00:00Z
date_updated: 2024-01-30T14:17:23Z
day: '15'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1016/j.jfa.2023.110129
external_id:
arxiv:
- '2303.04504'
isi:
- '001071552300001'
file:
- access_level: open_access
checksum: 28e424ad91be6219e9d321054ce3a412
content_type: application/pdf
creator: dernst
date_created: 2024-01-30T14:15:16Z
date_updated: 2024-01-30T14:15:16Z
file_id: '14915'
file_name: 2023_JourFunctionalAnalysis_Seiringer.pdf
file_size: 232934
relation: main_file
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file_date_updated: 2024-01-30T14:15:16Z
has_accepted_license: '1'
intvolume: ' 285'
isi: 1
issue: '10'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: A simple approach to Lieb-Thirring type inequalities
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: 285
year: '2023'
...
---
_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.
date_created: 2023-01-15T23:00:52Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2023-08-16T11:34:03Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00023-022-01252-3
ec_funded: 1
external_id:
arxiv:
- '2205.15284'
isi:
- '000910751800002'
intvolume: ' 24'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2205.15284
month: '05'
oa: 1
oa_version: Preprint
page: 1505-1560
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Bose Gas in a box with Neumann boundary conditions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...
---
_id: '10755'
abstract:
- lang: eng
text: We provide a definition of the effective mass for the classical polaron described
by the Landau–Pekar (LP) equations. It is based on a novel variational principle,
minimizing the energy functional over states with given (initial) velocity. The
resulting formula for the polaron's effective mass agrees with the prediction
by LP (1948 J. Exp. Theor. Phys. 18 419–423).
acknowledgement: "We thank Herbert Spohn for helpful comments. Funding from the European
Union’s Horizon\r\n2020 research and innovation programme under the ERC Grant Agreement
No. 694227\r\n(DF and RS) and under the Marie Skłodowska-Curie Grant Agreement No.
754411 (SR) is\r\ngratefully acknowledged."
article_number: '015201'
article_processing_charge: Yes (via OA deal)
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: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for
the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical.
2022;55(1). doi:10.1088/1751-8121/ac3947'
apa: 'Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2022). The effective
mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical
and Theoretical. IOP Publishing. https://doi.org/10.1088/1751-8121/ac3947'
chicago: 'Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
“The Effective Mass Problem for the Landau-Pekar Equations.” Journal of Physics
A: Mathematical and Theoretical. IOP Publishing, 2022. https://doi.org/10.1088/1751-8121/ac3947.'
ieee: 'D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass
problem for the Landau-Pekar equations,” Journal of Physics A: Mathematical
and Theoretical, vol. 55, no. 1. IOP Publishing, 2022.'
ista: 'Feliciangeli D, Rademacher SAE, Seiringer R. 2022. The effective mass problem
for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical.
55(1), 015201.'
mla: 'Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar
Equations.” Journal of Physics A: Mathematical and Theoretical, vol. 55,
no. 1, 015201, IOP Publishing, 2022, doi:10.1088/1751-8121/ac3947.'
short: 'D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Journal of Physics A:
Mathematical and Theoretical 55 (2022).'
date_created: 2022-02-13T23:01:35Z
date_published: 2022-01-19T00:00:00Z
date_updated: 2024-03-06T12:30:44Z
day: '19'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1088/1751-8121/ac3947
ec_funded: 1
external_id:
arxiv:
- '2107.03720'
file:
- access_level: open_access
checksum: 0875e562705563053d6dd98fba4d8578
content_type: application/pdf
creator: dernst
date_created: 2022-02-14T08:20:19Z
date_updated: 2022-02-14T08:20:19Z
file_id: '10757'
file_name: 2022_JournalPhysicsA_Feliciangeli.pdf
file_size: 1132380
relation: main_file
success: 1
file_date_updated: 2022-02-14T08:20:19Z
has_accepted_license: '1'
intvolume: ' 55'
issue: '1'
language:
- iso: eng
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: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
eissn:
- 1751-8121
issn:
- 1751-8113
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
related_material:
record:
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relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The effective mass problem for the Landau-Pekar equations
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: 55
year: '2022'
...
---
_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).
date_created: 2022-03-16T08:41:53Z
date_published: 2022-06-15T00:00:00Z
date_updated: 2023-10-27T10:37:29Z
day: '15'
ddc:
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- _id: RoSe
doi: 10.1016/j.jfa.2022.109455
ec_funded: 1
external_id:
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- '2105.04874'
isi:
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keyword:
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month: '06'
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oa_version: Published Version
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call_identifier: H2020
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name: Analysis of quantum many-body systems
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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'
...
---
_id: '10564'
abstract:
- lang: eng
text: We study a class of polaron-type Hamiltonians with sufficiently regular form
factor in the interaction term. We investigate the strong-coupling limit of the
model, and prove suitable bounds on the ground state energy as a function of the
total momentum of the system. These bounds agree with the semiclassical approximation
to leading order. The latter corresponds here to the situation when the particle
undergoes harmonic motion in a potential well whose frequency is determined by
the corresponding Pekar functional. We show that for all such models the effective
mass diverges in the strong coupling limit, in all spatial dimensions. Moreover,
for the case when the phonon dispersion relation grows at least linearly with
momentum, the bounds result in an asymptotic formula for the effective mass quotient,
a quantity generalizing the usual notion of the effective mass. This asymptotic
form agrees with the semiclassical Landau–Pekar formula and can be regarded as
the first rigorous confirmation, in a slightly weaker sense than usually considered,
of the validity of the semiclassical formula for the effective mass.
acknowledgement: Financial support through 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.)
is gratefully acknowledged. Open access funding provided by Institute of Science
and Technology (IST Austria).
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- 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: Mysliwy K, Seiringer R. Polaron models with regular interactions at strong
coupling. Journal of Statistical Physics. 2022;186(1). doi:10.1007/s10955-021-02851-w
apa: Mysliwy, K., & Seiringer, R. (2022). Polaron models with regular interactions
at strong coupling. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-021-02851-w
chicago: Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular
Interactions at Strong Coupling.” Journal of Statistical Physics. Springer
Nature, 2022. https://doi.org/10.1007/s10955-021-02851-w.
ieee: K. Mysliwy and R. Seiringer, “Polaron models with regular interactions at
strong coupling,” Journal of Statistical Physics, vol. 186, no. 1. Springer
Nature, 2022.
ista: Mysliwy K, Seiringer R. 2022. Polaron models with regular interactions at
strong coupling. Journal of Statistical Physics. 186(1), 5.
mla: Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions
at Strong Coupling.” Journal of Statistical Physics, vol. 186, no. 1, 5,
Springer Nature, 2022, doi:10.1007/s10955-021-02851-w.
short: K. Mysliwy, R. Seiringer, Journal of Statistical Physics 186 (2022).
date_created: 2021-12-19T23:01:32Z
date_published: 2022-01-01T00:00:00Z
date_updated: 2023-09-07T13:43:51Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s10955-021-02851-w
ec_funded: 1
external_id:
arxiv:
- '2106.09328'
isi:
- '000726275600001'
file:
- access_level: open_access
checksum: da03f6d293c4b9802091bce9471b1d29
content_type: application/pdf
creator: cchlebak
date_created: 2022-02-02T14:24:41Z
date_updated: 2022-02-02T14:24:41Z
file_id: '10716'
file_name: 2022_JournalStatPhys_Myśliwy.pdf
file_size: 434957
relation: main_file
success: 1
file_date_updated: 2022-02-02T14:24:41Z
has_accepted_license: '1'
intvolume: ' 186'
isi: 1
issue: '1'
language:
- iso: eng
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: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '11473'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Polaron models with regular interactions at strong 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 186
year: '2022'
...
---
_id: '11917'
abstract:
- lang: eng
text: We study the many-body dynamics of an initially factorized bosonic wave function
in the mean-field regime. We prove large deviation estimates for the fluctuations
around the condensate. We derive an upper bound extending a recent result to more
general interactions. Furthermore, we derive a new lower bound which agrees with
the upper bound in leading order.
acknowledgement: "The authors thank Gérard Ben Arous for pointing out the question
of a lower bound. Funding from the European Union’s Horizon 2020 research and innovation
programme under the ERC Grant Agreement No. 694227 (R.S.) and under the Marie Skłodowska-Curie
Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.\r\nOpen access funding
provided by IST Austria."
article_number: '9'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Rademacher SAE, Seiringer R. Large deviation estimates for weakly interacting
bosons. Journal of Statistical Physics. 2022;188. doi:10.1007/s10955-022-02940-4
apa: Rademacher, S. A. E., & Seiringer, R. (2022). Large deviation estimates
for weakly interacting bosons. Journal of Statistical Physics. Springer
Nature. https://doi.org/10.1007/s10955-022-02940-4
chicago: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation
Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics.
Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02940-4.
ieee: S. A. E. Rademacher and R. Seiringer, “Large deviation estimates for weakly
interacting bosons,” Journal of Statistical Physics, vol. 188. Springer
Nature, 2022.
ista: Rademacher SAE, Seiringer R. 2022. Large deviation estimates for weakly interacting
bosons. Journal of Statistical Physics. 188, 9.
mla: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates
for Weakly Interacting Bosons.” Journal of Statistical Physics, vol. 188,
9, Springer Nature, 2022, doi:10.1007/s10955-022-02940-4.
short: S.A.E. Rademacher, R. Seiringer, Journal of Statistical Physics 188 (2022).
date_created: 2022-08-18T07:23:26Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-08-03T12:55:58Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s10955-022-02940-4
ec_funded: 1
external_id:
isi:
- '000805175000001'
file:
- access_level: open_access
checksum: 44418cb44f07fa21ed3907f85abf7f39
content_type: application/pdf
creator: dernst
date_created: 2022-08-18T08:09:00Z
date_updated: 2022-08-18T08:09:00Z
file_id: '11922'
file_name: 2022_JournalStatisticalPhysics_Rademacher.pdf
file_size: 483481
relation: main_file
success: 1
file_date_updated: 2022-08-18T08:09:00Z
has_accepted_license: '1'
intvolume: ' 188'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '07'
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: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Large deviation estimates for weakly interacting bosons
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 188
year: '2022'
...
---
_id: '12246'
abstract:
- lang: eng
text: The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of
a classical system of N identical charges only in terms of their one-particle
density. We prove here a new estimate on the best constant in this inequality.
Numerical evaluation provides the value 1.58, which is a significant improvement
to the previously known value 1.64. The best constant has recently been shown
to be larger than 1.44. In a second part, we prove that the constant can be reduced
to 1.25 when the inequality is restricted to Hartree–Fock states. This is the
first proof that the exchange term is always much lower than the full indirect
Coulomb energy.
acknowledgement: We would like to thank David Gontier for useful advice on the numerical
simulations. This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation program (Grant
Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful
for the hospitality of the Institut Henri Poincaré in Paris, where part of this
work was done.
article_number: '92'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Elliott H.
full_name: Lieb, Elliott H.
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Lewin M, Lieb EH, Seiringer R. Improved Lieb–Oxford bound on the indirect and
exchange energies. Letters in Mathematical Physics. 2022;112(5). doi:10.1007/s11005-022-01584-5
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2022). Improved Lieb–Oxford bound
on the indirect and exchange energies. Letters in Mathematical Physics.
Springer Nature. https://doi.org/10.1007/s11005-022-01584-5
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford
Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics.
Springer Nature, 2022. https://doi.org/10.1007/s11005-022-01584-5.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the
indirect and exchange energies,” Letters in Mathematical Physics, vol.
112, no. 5. Springer Nature, 2022.
ista: Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect
and exchange energies. Letters in Mathematical Physics. 112(5), 92.
mla: Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange
Energies.” Letters in Mathematical Physics, vol. 112, no. 5, 92, Springer
Nature, 2022, doi:10.1007/s11005-022-01584-5.
short: M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022).
date_created: 2023-01-16T09:53:54Z
date_published: 2022-09-15T00:00:00Z
date_updated: 2023-09-05T15:17:34Z
day: '15'
department:
- _id: RoSe
doi: 10.1007/s11005-022-01584-5
ec_funded: 1
external_id:
arxiv:
- '2203.12473'
isi:
- '000854762600001'
intvolume: ' 112'
isi: 1
issue: '5'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2203.12473
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: 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: Improved Lieb–Oxford bound on the indirect and exchange energies
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 112
year: '2022'
...
---
_id: '10738'
abstract:
- lang: eng
text: We prove an adiabatic theorem for the Landau–Pekar equations. This allows
us to derive new results on the accuracy of their use as effective equations for
the time evolution generated by the Fröhlich Hamiltonian with large coupling constant
α. In particular, we show that the time evolution of Pekar product states with
coherent phonon field and the electron being trapped by the phonons is well approximated
by the Landau–Pekar equations until times short compared to α2.
acknowledgement: "N. L. and R. S. gratefully acknowledge financial support by the
European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research
and innovation programme (grant\r\nagreement No 694227). B. S. acknowledges support
from the Swiss National Science Foundation (grant 200020_172623) and from the NCCR
SwissMAP. N. L. would like to thank\r\nAndreas Deuchert and David Mitrouskas for
interesting discussions. B. S. and R. S. would\r\nlike to thank Rupert Frank for
stimulating discussions about the time-evolution of a polaron.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nikolai K
full_name: Leopold, Nikolai K
id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
last_name: Leopold
orcid: 0000-0002-0495-6822
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
- 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: 'Leopold NK, Rademacher SAE, Schlein B, Seiringer R. The Landau–Pekar equations:
Adiabatic theorem and accuracy. Analysis and PDE. 2021;14(7):2079-2100.
doi:10.2140/APDE.2021.14.2079'
apa: 'Leopold, N. K., Rademacher, S. A. E., Schlein, B., & Seiringer, R. (2021). The
Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE.
Mathematical Sciences Publishers. https://doi.org/10.2140/APDE.2021.14.2079'
chicago: 'Leopold, Nikolai K, Simone Anna Elvira Rademacher, Benjamin Schlein, and
Robert Seiringer. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.”
Analysis and PDE. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/APDE.2021.14.2079.'
ieee: 'N. K. Leopold, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “ The Landau–Pekar
equations: Adiabatic theorem and accuracy,” Analysis and PDE, vol. 14,
no. 7. Mathematical Sciences Publishers, pp. 2079–2100, 2021.'
ista: 'Leopold NK, Rademacher SAE, Schlein B, Seiringer R. 2021. The Landau–Pekar
equations: Adiabatic theorem and accuracy. Analysis and PDE. 14(7), 2079–2100.'
mla: 'Leopold, Nikolai K., et al. “ The Landau–Pekar Equations: Adiabatic Theorem
and Accuracy.” Analysis and PDE, vol. 14, no. 7, Mathematical Sciences
Publishers, 2021, pp. 2079–100, doi:10.2140/APDE.2021.14.2079.'
short: N.K. Leopold, S.A.E. Rademacher, B. Schlein, R. Seiringer, Analysis and PDE
14 (2021) 2079–2100.
date_created: 2022-02-06T23:01:33Z
date_published: 2021-11-10T00:00:00Z
date_updated: 2023-10-17T11:26:45Z
day: '10'
department:
- _id: RoSe
doi: 10.2140/APDE.2021.14.2079
ec_funded: 1
external_id:
arxiv:
- '1904.12532'
isi:
- '000733976600004'
intvolume: ' 14'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1904.12532
month: '11'
oa: 1
oa_version: Preprint
page: 2079-2100
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Analysis and PDE
publication_identifier:
eissn:
- 1948-206X
issn:
- 2157-5045
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' The Landau–Pekar equations: Adiabatic theorem and accuracy'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2021'
...
---
_id: '10852'
abstract:
- lang: eng
text: ' We review old and new results on the Fröhlich polaron model. The discussion
includes the validity of the (classical) Pekar approximation in the strong coupling
limit, quantum corrections to this limit, as well as the divergence of the effective
polaron mass.'
acknowledgement: This work was supported by the European Research Council (ERC) under
the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo.
694227).
article_number: '2060012'
article_processing_charge: No
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. The polaron at strong coupling. Reviews in Mathematical Physics.
2021;33(01). doi:10.1142/s0129055x20600120
apa: Seiringer, R. (2021). The polaron at strong coupling. Reviews in Mathematical
Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600120
chicago: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical
Physics. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600120.
ieee: R. Seiringer, “The polaron at strong coupling,” Reviews in Mathematical
Physics, vol. 33, no. 01. World Scientific Publishing, 2021.
ista: Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical
Physics. 33(01), 2060012.
mla: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical
Physics, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600120.
short: R. Seiringer, Reviews in Mathematical Physics 33 (2021).
date_created: 2022-03-18T08:11:34Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-09-05T16:08:02Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600120
ec_funded: 1
external_id:
arxiv:
- '1912.12509'
isi:
- '000613313200013'
intvolume: ' 33'
isi: 1
issue: '01'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1912.12509
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Reviews in Mathematical Physics
publication_identifier:
eissn:
- 1793-6659
issn:
- 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The polaron at strong coupling
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...
---
_id: '7901'
abstract:
- lang: eng
text: We derive rigorously the leading order of the correlation energy of a Fermi
gas in a scaling regime of high density and weak interaction. The result verifies
the prediction of the random-phase approximation. Our proof refines the method
of collective bosonization in three dimensions. We approximately diagonalize an
effective Hamiltonian describing approximately bosonic collective excitations
around the Hartree–Fock state, while showing that gapless and non-collective excitations
have only a negligible effect on the ground state energy.
acknowledgement: We thank Christian Hainzl for helpful discussions and a referee for
very careful reading of the paper and many helpful suggestions. NB and RS were supported
by the European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation programme (grant agreement No. 694227). Part of the research of NB
was conducted on the RZD18 Nice–Milan–Vienna–Moscow. NB thanks Elliott H. Lieb and
Peter Otte for explanations about the Luttinger model. PTN has received funding
from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under
Germany’s Excellence Strategy (EXC-2111-390814868). MP acknowledges financial support
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (ERC StG MaMBoQ, grant agreement No. 802901).
BS gratefully 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). All authors acknowledge support for
workshop participation from Mathematisches Forschungsinstitut Oberwolfach (Leibniz
Association). NB, PTN, BS, and RS acknowledge support for workshop participation
from Fondation des Treilles.
article_processing_charge: Yes (via OA deal)
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author:
- first_name: Niels P
full_name: Benedikter, Niels P
id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
last_name: Benedikter
orcid: 0000-0002-1071-6091
- first_name: Phan Thành
full_name: Nam, Phan Thành
last_name: Nam
- first_name: Marcello
full_name: Porta, Marcello
last_name: Porta
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Correlation energy
of a weakly interacting Fermi gas. Inventiones Mathematicae. 2021;225:885-979.
doi:10.1007/s00222-021-01041-5
apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R.
(2021). Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae.
Springer. https://doi.org/10.1007/s00222-021-01041-5
chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas.”
Inventiones Mathematicae. Springer, 2021. https://doi.org/10.1007/s00222-021-01041-5.
ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Correlation
energy of a weakly interacting Fermi gas,” Inventiones Mathematicae, vol.
225. Springer, pp. 885–979, 2021.
ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Correlation
energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 225, 885–979.
mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi
Gas.” Inventiones Mathematicae, vol. 225, Springer, 2021, pp. 885–979,
doi:10.1007/s00222-021-01041-5.
short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Inventiones
Mathematicae 225 (2021) 885–979.
date_created: 2020-05-28T16:48:20Z
date_published: 2021-05-03T00:00:00Z
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ddc:
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department:
- _id: RoSe
doi: 10.1007/s00222-021-01041-5
ec_funded: 1
external_id:
arxiv:
- '2005.08933'
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- '000646573600001'
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name: IST Austria Open Access Fund
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call_identifier: H2020
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name: Analysis of quantum many-body systems
publication: Inventiones Mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
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publisher: Springer
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title: Correlation energy of a weakly interacting Fermi gas
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
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volume: 225
year: '2021'
...
---
_id: '8603'
abstract:
- lang: eng
text: We consider the Fröhlich polaron model in the strong coupling limit. It is
well‐known that to leading order the ground state energy is given by the (classical)
Pekar energy. In this work, we establish the subleading correction, describing
quantum fluctuation about the classical limit. Our proof applies to a model of
a confined polaron, where both the electron and the polarization field are restricted
to a set of finite volume, with linear size determined by the natural length scale
of the Pekar problem.
acknowledgement: Partial support through National Science Foundation GrantDMS-1363432
(R.L.F.) and the European Research Council (ERC) under the Euro-pean Union’s Horizon
2020 research and innovation programme (grant agreementNo 694227; R.S.), is acknowledged.
Open access funding enabled and organizedby Projekt DEAL.
article_processing_charge: No
article_type: original
author:
- first_name: Rupert
full_name: Frank, Rupert
last_name: Frank
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Frank R, Seiringer R. Quantum corrections to the Pekar asymptotics of a strongly
coupled polaron. Communications on Pure and Applied Mathematics. 2021;74(3):544-588.
doi:10.1002/cpa.21944
apa: Frank, R., & Seiringer, R. (2021). Quantum corrections to the Pekar asymptotics
of a strongly coupled polaron. Communications on Pure and Applied Mathematics.
Wiley. https://doi.org/10.1002/cpa.21944
chicago: Frank, Rupert, and Robert Seiringer. “Quantum Corrections to the Pekar
Asymptotics of a Strongly Coupled Polaron.” Communications on Pure and Applied
Mathematics. Wiley, 2021. https://doi.org/10.1002/cpa.21944.
ieee: R. Frank and R. Seiringer, “Quantum corrections to the Pekar asymptotics of
a strongly coupled polaron,” Communications on Pure and Applied Mathematics,
vol. 74, no. 3. Wiley, pp. 544–588, 2021.
ista: Frank R, Seiringer R. 2021. Quantum corrections to the Pekar asymptotics of
a strongly coupled polaron. Communications on Pure and Applied Mathematics. 74(3),
544–588.
mla: Frank, Rupert, and Robert Seiringer. “Quantum Corrections to the Pekar Asymptotics
of a Strongly Coupled Polaron.” Communications on Pure and Applied Mathematics,
vol. 74, no. 3, Wiley, 2021, pp. 544–88, doi:10.1002/cpa.21944.
short: R. Frank, R. Seiringer, Communications on Pure and Applied Mathematics 74
(2021) 544–588.
date_created: 2020-10-04T22:01:37Z
date_published: 2021-03-01T00:00:00Z
date_updated: 2023-08-04T11:02:16Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1002/cpa.21944
ec_funded: 1
external_id:
isi:
- '000572991500001'
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file_name: 2021_CommPureApplMath_Frank.pdf
file_size: 334987
relation: main_file
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file_date_updated: 2021-03-11T10:03:30Z
has_accepted_license: '1'
intvolume: ' 74'
isi: 1
issue: '3'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 544-588
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications on Pure and Applied Mathematics
publication_identifier:
eissn:
- '10970312'
issn:
- '00103640'
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantum corrections to the Pekar asymptotics 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 74
year: '2021'
...
---
_id: '14889'
abstract:
- lang: eng
text: We consider the Fröhlich Hamiltonian with large coupling constant α. For initial
data of Pekar product form with coherent phonon field and with the electron minimizing
the corresponding energy, we provide a norm approximation of the evolution, valid
up to times of order α2. The approximation is given in terms of a Pekar product
state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics
taking quantum fluctuations into account. This allows us to show that the Landau-Pekar
equations approximately describe the evolution of the electron- and one-phonon
reduced density matrices under the Fröhlich dynamics up to times of order α2.
acknowledgement: "Financial support by the European Union’s Horizon 2020 research
and innovation programme\r\nunder the Marie Skłodowska-Curie grant agreement No.
754411 (S.R.) and the European\r\nResearch Council under grant agreement No. 694227
(N.L. and R.S.), as well as by the SNSF\r\nEccellenza project PCEFP2 181153 (N.L.),
the NCCR SwissMAP (N.L. and B.S.) and by the\r\nDeutsche Forschungsgemeinschaft
(DFG) through the Research Training Group 1838: Spectral\r\nTheory and Dynamics
of Quantum Systems (D.M.) is gratefully acknowledged. B.S. gratefully\r\nacknowledges
financial support from the Swiss National Science Foundation through the Grant\r\n“Dynamical
and energetic properties of Bose-Einstein condensates” and from the European\r\nResearch
Council through the ERC-AdG CLaQS (grant agreement No 834782). D.M. thanks\r\nMarcel
Griesemer for helpful discussions."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nikolai K
full_name: Leopold, Nikolai K
id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
last_name: Leopold
orcid: 0000-0002-0495-6822
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
- 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: Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. Landau–Pekar
equations and quantum fluctuations for the dynamics of a strongly coupled polaron.
Pure and Applied Analysis. 2021;3(4):653-676. doi:10.2140/paa.2021.3.653
apa: Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., &
Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the
dynamics of a strongly coupled polaron. Pure and Applied Analysis. Mathematical
Sciences Publishers. https://doi.org/10.2140/paa.2021.3.653
chicago: Leopold, Nikolai K, David Johannes Mitrouskas, Simone Anna Elvira Rademacher,
Benjamin Schlein, and Robert Seiringer. “Landau–Pekar Equations and Quantum Fluctuations
for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis.
Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/paa.2021.3.653.
ieee: N. K. Leopold, D. J. Mitrouskas, S. A. E. Rademacher, B. Schlein, and R. Seiringer,
“Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly
coupled polaron,” Pure and Applied Analysis, vol. 3, no. 4. Mathematical
Sciences Publishers, pp. 653–676, 2021.
ista: Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. 2021. Landau–Pekar
equations and quantum fluctuations for the dynamics of a strongly coupled polaron.
Pure and Applied Analysis. 3(4), 653–676.
mla: Leopold, Nikolai K., et al. “Landau–Pekar Equations and Quantum Fluctuations
for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis,
vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:10.2140/paa.2021.3.653.
short: N.K. Leopold, D.J. Mitrouskas, S.A.E. Rademacher, B. Schlein, R. Seiringer,
Pure and Applied Analysis 3 (2021) 653–676.
date_created: 2024-01-28T23:01:43Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2024-02-05T10:02:45Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2021.3.653
ec_funded: 1
external_id:
arxiv:
- '2005.02098'
intvolume: ' 3'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2005.02098
month: '10'
oa: 1
oa_version: Preprint
page: 653-676
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
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: Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly
coupled polaron
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2021'
...