---
_id: '9462'
abstract:
- lang: eng
text: We consider a system of N trapped bosons with repulsive interactions in a
combined semiclassical mean-field limit at positive temperature. We show that
the free energy is well approximated by the minimum of the Hartree free energy
functional – a natural extension of the Hartree energy functional to positive
temperatures. The Hartree free energy functional converges in the same limit to
a semiclassical free energy functional, and we show that the system displays Bose–Einstein
condensation if and only if it occurs in the semiclassical free energy functional.
This allows us to show that for weak coupling the critical temperature decreases
due to the repulsive interactions.
acknowledgement: 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 Sklodowska-Curie
grant agreement No 836146 (A.D.) is gratefully acknowledged. A.D. acknowledges support
of the Swiss National Science Foundation through the Ambizione grant PZ00P2 185851.
article_number: '109096'
article_processing_charge: No
article_type: original
author:
- first_name: Andreas
full_name: Deuchert, Andreas
last_name: Deuchert
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Deuchert A, Seiringer R. Semiclassical approximation and critical temperature
shift for weakly interacting trapped bosons. Journal of Functional Analysis.
2021;281(6). doi:10.1016/j.jfa.2021.109096
apa: Deuchert, A., & Seiringer, R. (2021). Semiclassical approximation and critical
temperature shift for weakly interacting trapped bosons. Journal of Functional
Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2021.109096
chicago: Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and
Critical Temperature Shift for Weakly Interacting Trapped Bosons.” Journal
of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109096.
ieee: A. Deuchert and R. Seiringer, “Semiclassical approximation and critical temperature
shift for weakly interacting trapped bosons,” Journal of Functional Analysis,
vol. 281, no. 6. Elsevier, 2021.
ista: Deuchert A, Seiringer R. 2021. Semiclassical approximation and critical temperature
shift for weakly interacting trapped bosons. Journal of Functional Analysis. 281(6),
109096.
mla: Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical
Temperature Shift for Weakly Interacting Trapped Bosons.” Journal of Functional
Analysis, vol. 281, no. 6, 109096, Elsevier, 2021, doi:10.1016/j.jfa.2021.109096.
short: A. Deuchert, R. Seiringer, Journal of Functional Analysis 281 (2021).
date_created: 2021-06-06T22:01:28Z
date_published: 2021-09-15T00:00:00Z
date_updated: 2023-08-08T13:56:27Z
day: '15'
department:
- _id: RoSe
doi: 10.1016/j.jfa.2021.109096
ec_funded: 1
external_id:
arxiv:
- '2009.00992'
isi:
- '000656508600008'
intvolume: ' 281'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2009.00992
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: 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: Semiclassical approximation and critical temperature shift for weakly interacting
trapped bosons
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 281
year: '2021'
...
---
_id: '9891'
abstract:
- lang: eng
text: 'Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127
(2019)], we present a modified “floating crystal” trial state for jellium (also
known as the classical homogeneous electron gas) with density equal to a characteristic
function. This allows us to show that three definitions of the jellium energy
coincide in dimensions d ≥ 2, thus extending the result of Cotar and Petrache
[“Equality of the Jellium and uniform electron gas next-order asymptotic terms
for Coulomb and Riesz potentials,” arXiv: 1707.07664 (2019)] and Lewin, Lieb,
and Seiringer [Phys. Rev. B 100, 035127 (2019)] that the three definitions coincide
in dimension d ≥ 3. We show that the jellium energy is also equivalent to a “renormalized
energy” studied in a series of papers by Serfaty and others, and thus, by the
work of Bétermin and Sandier [Constr. Approximation 47, 39–74 (2018)], we relate
the jellium energy to the order n term in the logarithmic energy of n points on
the unit 2-sphere. We improve upon known lower bounds for this renormalized energy.
Additionally, we derive formulas for the jellium energy of periodic configurations.'
acknowledgement: The author would like to thank Robert Seiringer for guidance and
many helpful comments on this project. The author would also like to thank Mathieu
Lewin for his comments on the manuscript and Lorenzo Portinale for providing his
lecture notes for the course “Mathematics of quantum many-body systems” in spring
2020, taught by Robert Seiringer. The Proof of Theorem III.1 is inspired by these
lecture notes.
article_number: '083305'
article_processing_charge: No
article_type: original
author:
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
citation:
ama: Lauritsen AB. Floating Wigner crystal and periodic jellium configurations.
Journal of Mathematical Physics. 2021;62(8). doi:10.1063/5.0053494
apa: Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations.
Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0053494
chicago: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium
Configurations.” Journal of Mathematical Physics. AIP Publishing, 2021.
https://doi.org/10.1063/5.0053494.
ieee: A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,”
Journal of Mathematical Physics, vol. 62, no. 8. AIP Publishing, 2021.
ista: Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations.
Journal of Mathematical Physics. 62(8), 083305.
mla: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium
Configurations.” Journal of Mathematical Physics, vol. 62, no. 8, 083305,
AIP Publishing, 2021, doi:10.1063/5.0053494.
short: A.B. Lauritsen, Journal of Mathematical Physics 62 (2021).
date_created: 2021-08-12T07:08:36Z
date_published: 2021-08-01T00:00:00Z
date_updated: 2023-08-11T10:29:48Z
day: '01'
ddc:
- '530'
department:
- _id: GradSch
- _id: RoSe
doi: 10.1063/5.0053494
external_id:
arxiv:
- '2103.07975'
isi:
- '000683960800003'
file:
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content_type: application/pdf
creator: cziletti
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- Statistical and Nonlinear Physics
language:
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month: '08'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
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publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Floating Wigner crystal and periodic jellium configurations
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: 62
year: '2021'
...
---
_id: '10224'
abstract:
- lang: eng
text: We investigate the Fröhlich polaron model on a three-dimensional torus, and
give a proof of the second-order quantum corrections to its ground-state energy
in the strong-coupling limit. Compared to previous work in the confined case,
the translational symmetry (and its breaking in the Pekar approximation) makes
the analysis substantially more challenging.
acknowledgement: "Funding from the European Union’s Horizon 2020 research and innovation
programme under the ERC grant agreement No 694227 is gratefully acknowledged. We
would also like to thank Rupert Frank for many helpful discussions, especially related
to the Gross coordinate transformation defined in Def. 4.7.\r\nOpen access funding
provided by Institute of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum
corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis.
2021;242(3):1835–1906. doi:10.1007/s00205-021-01715-7'
apa: 'Feliciangeli, D., & Seiringer, R. (2021). The strongly coupled polaron
on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational
Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01715-7'
chicago: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron
on the Torus: Quantum Corrections to the Pekar Asymptotics.” Archive for Rational
Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01715-7.'
ieee: 'D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus:
Quantum corrections to the Pekar asymptotics,” Archive for Rational Mechanics
and Analysis, vol. 242, no. 3. Springer Nature, pp. 1835–1906, 2021.'
ista: 'Feliciangeli D, Seiringer R. 2021. The strongly coupled polaron on the torus:
Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and
Analysis. 242(3), 1835–1906.'
mla: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on
the Torus: Quantum Corrections to the Pekar Asymptotics.” Archive for Rational
Mechanics and Analysis, vol. 242, no. 3, Springer Nature, 2021, pp. 1835–1906,
doi:10.1007/s00205-021-01715-7.'
short: D. Feliciangeli, R. Seiringer, Archive for Rational Mechanics and Analysis
242 (2021) 1835–1906.
date_created: 2021-11-07T23:01:26Z
date_published: 2021-10-25T00:00:00Z
date_updated: 2023-08-14T10:32:19Z
day: '25'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00205-021-01715-7
ec_funded: 1
external_id:
arxiv:
- '2101.12566'
isi:
- '000710850600001'
file:
- access_level: open_access
checksum: 672e9c21b20f1a50854b7c821edbb92f
content_type: application/pdf
creator: alisjak
date_created: 2021-12-14T08:35:42Z
date_updated: 2021-12-14T08:35:42Z
file_id: '10544'
file_name: 2021_Springer_Feliciangeli.pdf
file_size: 990529
relation: main_file
success: 1
file_date_updated: 2021-12-14T08:35:42Z
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intvolume: ' 242'
isi: 1
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language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1835–1906
project:
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call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
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issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '9787'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: 'The strongly coupled polaron on the torus: Quantum corrections to the Pekar
asymptotics'
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: 242
year: '2021'
...
---
_id: '10537'
abstract:
- lang: eng
text: We consider the quantum many-body evolution of a homogeneous Fermi gas in
three dimensions in the coupled semiclassical and mean-field scaling regime. We
study a class of initial data describing collective particle–hole pair excitations
on the Fermi ball. Using a rigorous version of approximate bosonization, we prove
that the many-body evolution can be approximated in Fock space norm by a quasi-free
bosonic evolution of the collective particle–hole excitations.
acknowledgement: NB was supported by Gruppo Nazionale per la Fisica Matematica (GNFM).
RS was supported by the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation program (Grant Agreement No. 694227). PTN was
supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)
under Germany’s Excellence Strategy (EXC-2111-390814868). MP was supported by the
European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation program (ERC StG MaMBoQ, Grant Agreement No. 802901). BS was supported
by the NCCR SwissMAP, the Swiss National Science Foundation through the Grant “Dynamical
and energetic properties of Bose-Einstein condensates,” and the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation program
through the ERC-AdG CLaQS (Grant Agreement No. 834782).
article_processing_charge: No
article_type: original
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. Bosonization of fermionic
many-body dynamics. Annales Henri Poincaré. 2021. doi:10.1007/s00023-021-01136-y
apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R.
(2021). Bosonization of fermionic many-body dynamics. Annales Henri Poincaré.
Springer Nature. https://doi.org/10.1007/s00023-021-01136-y
chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
and Robert Seiringer. “Bosonization of Fermionic Many-Body Dynamics.” Annales
Henri Poincaré. Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01136-y.
ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Bosonization
of fermionic many-body dynamics,” Annales Henri Poincaré. Springer Nature,
2021.
ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Bosonization
of fermionic many-body dynamics. Annales Henri Poincaré.
mla: Benedikter, Niels P., et al. “Bosonization of Fermionic Many-Body Dynamics.”
Annales Henri Poincaré, Springer Nature, 2021, doi:10.1007/s00023-021-01136-y.
short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Annales Henri
Poincaré (2021).
date_created: 2021-12-12T23:01:28Z
date_published: 2021-12-02T00:00:00Z
date_updated: 2023-08-17T06:19:14Z
day: '02'
department:
- _id: RoSe
doi: 10.1007/s00023-021-01136-y
ec_funded: 1
external_id:
arxiv:
- '2103.08224'
isi:
- '000725405700001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.08224
month: '12'
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: Annales Henri Poincaré
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bosonization of fermionic many-body dynamics
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
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)
article_type: original
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
date_updated: 2023-08-21T06:30:30Z
day: '03'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00222-021-01041-5
ec_funded: 1
external_id:
arxiv:
- '2005.08933'
isi:
- '000646573600001'
file:
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checksum: f38c79dfd828cdc7f49a34b37b83d376
content_type: application/pdf
creator: dernst
date_created: 2022-05-16T12:23:40Z
date_updated: 2022-05-16T12:23:40Z
file_id: '11386'
file_name: 2021_InventMath_Benedikter.pdf
file_size: 1089319
relation: main_file
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file_date_updated: 2022-05-16T12:23:40Z
has_accepted_license: '1'
intvolume: ' 225'
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language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 885-979
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Inventiones Mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Correlation energy of a weakly interacting Fermi gas
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 225
year: '2021'
...
---
_id: '7900'
abstract:
- lang: eng
text: Hartree–Fock theory has been justified as a mean-field approximation for fermionic
systems. However, it suffers from some defects in predicting physical properties,
making necessary a theory of quantum correlations. Recently, bosonization of many-body
correlations has been rigorously justified as an upper bound on the correlation
energy at high density with weak interactions. We review the bosonic approximation,
deriving an effective Hamiltonian. We then show that for systems with Coulomb
interaction this effective theory predicts collective excitations (plasmons) in
accordance with the random phase approximation of Bohm and Pines, and with experimental
observation.
article_number: '2060009'
article_processing_charge: No
article_type: original
author:
- first_name: Niels P
full_name: Benedikter, Niels P
id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
last_name: Benedikter
orcid: 0000-0002-1071-6091
citation:
ama: Benedikter NP. Bosonic collective excitations in Fermi gases. Reviews in
Mathematical Physics. 2021;33(1). doi:10.1142/s0129055x20600090
apa: Benedikter, N. P. (2021). Bosonic collective excitations in Fermi gases. Reviews
in Mathematical Physics. World Scientific. https://doi.org/10.1142/s0129055x20600090
chicago: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews
in Mathematical Physics. World Scientific, 2021. https://doi.org/10.1142/s0129055x20600090.
ieee: N. P. Benedikter, “Bosonic collective excitations in Fermi gases,” Reviews
in Mathematical Physics, vol. 33, no. 1. World Scientific, 2021.
ista: Benedikter NP. 2021. Bosonic collective excitations in Fermi gases. Reviews
in Mathematical Physics. 33(1), 2060009.
mla: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews
in Mathematical Physics, vol. 33, no. 1, 2060009, World Scientific, 2021,
doi:10.1142/s0129055x20600090.
short: N.P. Benedikter, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-05-28T16:47:55Z
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date_updated: 2023-09-05T16:07:40Z
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doi: 10.1142/s0129055x20600090
ec_funded: 1
external_id:
arxiv:
- '1910.08190'
isi:
- '000613313200010'
intvolume: ' 33'
isi: 1
issue: '1'
language:
- iso: eng
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url: https://arxiv.org/abs/1910.08190
month: '01'
oa: 1
oa_version: Preprint
project:
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call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Reviews in Mathematical Physics
publication_identifier:
eissn:
- 1793-6659
issn:
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publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bosonic collective excitations in Fermi gases
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
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
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
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month: '02'
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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: '9225'
abstract:
- lang: eng
text: "The Landau–Pekar equations describe the dynamics of a strongly coupled polaron.\r\nHere,
we provide a class of initial data for which the associated effective Hamiltonian\r\nhas
a uniform spectral gap for all times. For such initial data, this allows us to
extend the\r\nresults on the adiabatic theorem for the Landau–Pekar equations
and their derivation\r\nfrom the Fröhlich model obtained in previous works to
larger times."
acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation
programme under the ERC Grant Agreement No 694227 (D.F. and R.S.) and under the
Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.
Open Access funding provided by Institute of Science and Technology (IST Austria)
article_number: '19'
article_processing_charge: Yes (via OA deal)
article_type: original
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. Persistence of the spectral gap
for the Landau–Pekar equations. Letters in Mathematical Physics. 2021;111.
doi:10.1007/s11005-020-01350-5
apa: Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2021). Persistence
of the spectral gap for the Landau–Pekar equations. Letters in Mathematical
Physics. Springer Nature. https://doi.org/10.1007/s11005-020-01350-5
chicago: Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
“Persistence of the Spectral Gap for the Landau–Pekar Equations.” Letters in
Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s11005-020-01350-5.
ieee: D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “Persistence of the
spectral gap for the Landau–Pekar equations,” Letters in Mathematical Physics,
vol. 111. Springer Nature, 2021.
ista: Feliciangeli D, Rademacher SAE, Seiringer R. 2021. Persistence of the spectral
gap for the Landau–Pekar equations. Letters in Mathematical Physics. 111, 19.
mla: Feliciangeli, Dario, et al. “Persistence of the Spectral Gap for the Landau–Pekar
Equations.” Letters in Mathematical Physics, vol. 111, 19, Springer Nature,
2021, doi:10.1007/s11005-020-01350-5.
short: D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Letters in Mathematical
Physics 111 (2021).
date_created: 2021-03-07T23:01:25Z
date_published: 2021-02-11T00:00:00Z
date_updated: 2023-09-07T13:30:11Z
day: '11'
ddc:
- '510'
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doi: 10.1007/s11005-020-01350-5
ec_funded: 1
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oa_version: Published Version
project:
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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
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name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_identifier:
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publisher: Springer Nature
quality_controlled: '1'
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- id: '9733'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Persistence of the spectral gap 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 111
year: '2021'
...
---
_id: '9787'
abstract:
- lang: eng
text: We investigate the Fröhlich polaron model on a three-dimensional torus, and
give a proof of the second-order quantum corrections to its ground-state energy
in the strong-coupling limit. Compared to previous work in the confined case,
the translational symmetry (and its breaking in the Pekar approximation) makes
the analysis substantially more challenging.
acknowledgement: "Funding from the European Union’s Horizon 2020 research and innovation
programme under the ERC grant agreement No 694227 is gratefully acknowledged. We
would also like to thank Rupert Frank for many helpful discussions, especially related
to the Gross coordinate transformation defined in Def. 4.1.\r\n"
article_number: '2101.12566'
article_processing_charge: No
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum
corrections to the Pekar asymptotics. arXiv.'
apa: 'Feliciangeli, D., & Seiringer, R. (n.d.). The strongly coupled polaron
on the torus: Quantum corrections to the Pekar asymptotics. arXiv.'
chicago: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron
on the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, n.d.'
ieee: 'D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus:
Quantum corrections to the Pekar asymptotics,” arXiv. .'
ista: 'Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum
corrections to the Pekar asymptotics. arXiv, 2101.12566.'
mla: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on
the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, 2101.12566.'
short: D. Feliciangeli, R. Seiringer, ArXiv (n.d.).
date_created: 2021-08-06T08:25:57Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-09-07T13:30:10Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
ec_funded: 1
external_id:
arxiv:
- '2101.12566'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2101.12566
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: arXiv
publication_status: submitted
related_material:
record:
- id: '10224'
relation: later_version
status: public
- id: '9733'
relation: dissertation_contains
status: public
status: public
title: 'The strongly coupled polaron on the torus: Quantum corrections to the Pekar
asymptotics'
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: preprint
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
year: '2021'
...
---
_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
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'
...