---
_id: '7685'
abstract:
- lang: eng
text: We consider a gas of interacting bosons trapped in a box of side length one
in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s
prediction for the ground state energy and the low-energy excitation spectrum.
This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.
article_number: '2060006'
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
citation:
ama: Boccato C. The excitation spectrum of the Bose gas in the Gross-Pitaevskii
regime. Reviews in Mathematical Physics. 2021;33(1). doi:10.1142/S0129055X20600065
apa: Boccato, C. (2021). The excitation spectrum of the Bose gas in the Gross-Pitaevskii
regime. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X20600065
chicago: Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii
Regime.” Reviews in Mathematical Physics. World Scientific Publishing,
2021. https://doi.org/10.1142/S0129055X20600065.
ieee: C. Boccato, “The excitation spectrum of the Bose gas in the Gross-Pitaevskii
regime,” Reviews in Mathematical Physics, vol. 33, no. 1. World Scientific
Publishing, 2021.
ista: Boccato C. 2021. The excitation spectrum of the Bose gas in the Gross-Pitaevskii
regime. Reviews in Mathematical Physics. 33(1), 2060006.
mla: Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii
Regime.” Reviews in Mathematical Physics, vol. 33, no. 1, 2060006, World
Scientific Publishing, 2021, doi:10.1142/S0129055X20600065.
short: C. Boccato, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-04-26T22:00:45Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2025-05-14T10:49:57Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/S0129055X20600065
ec_funded: 1
external_id:
arxiv:
- '2001.00497'
isi:
- '000613313200007'
intvolume: ' 33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2001.00497
month: '01'
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:
issn:
- 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
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
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
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 Publishing. https://doi.org/10.1142/s0129055x20600090
chicago: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews
in Mathematical Physics. World Scientific Publishing, 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 Publishing, 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 Publishing,
2021, doi:10.1142/s0129055x20600090.
short: N.P. Benedikter, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-05-28T16:47:55Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2025-05-14T10:49:46Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600090
ec_funded: 1
external_id:
arxiv:
- '1910.08190'
isi:
- '000613313200010'
intvolume: ' 33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.08190
month: '01'
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: Bosonic collective excitations in Fermi gases
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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)
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: 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: 2025-04-14T07:27:00Z
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:
- access_level: open_access
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
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file_date_updated: 2022-05-16T12:23:40Z
has_accepted_license: '1'
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isi: 1
language:
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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: '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: 2025-07-10T11:57:12Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1002/cpa.21944
ec_funded: 1
external_id:
isi:
- '000572991500001'
file:
- access_level: open_access
checksum: 5f665ffa6e6dd958aec5c3040cbcfa84
content_type: application/pdf
creator: dernst
date_created: 2021-03-11T10:03:30Z
date_updated: 2021-03-11T10:03:30Z
file_id: '9236'
file_name: 2021_CommPureApplMath_Frank.pdf
file_size: 334987
relation: main_file
success: 1
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:
- 1097-0312
issn:
- 0010-3640
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 74
year: '2021'
...
---
_id: '9246'
abstract:
- lang: eng
text: We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic
particles weakly couple to the quantized phonon field. For large particle numbers
and a suitably small coupling, we show that the dynamics of the system is approximately
described by the Landau–Pekar equations. These describe a Bose–Einstein condensate
interacting with a classical polarization field, whose dynamics is effected by
the condensate, i.e., the back-reaction of the phonons that are created by the
particles during the time evolution is of leading order.
acknowledgement: "Financial support by the European Research Council (ERC) under the\r\nEuropean
Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo 694227;
N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the\r\nDeutsche
Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral\r\nTheory
and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.\r\ngratefully
acknowledges support from the NCCRSwissMAP and would like to thank Simone\r\nRademacher
and Benjamin Schlein for interesting discussions about the time-evolution of\r\nthe
polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for\r\nextensive
discussions about the Fröhlich polaron."
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: 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, Seiringer R. Derivation of the Landau–Pekar equations
in a many-body mean-field limit. Archive for Rational Mechanics and Analysis.
2021;240:383-417. doi:10.1007/s00205-021-01616-9
apa: Leopold, N. K., Mitrouskas, D. J., & Seiringer, R. (2021). Derivation of
the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational
Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01616-9
chicago: Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation
of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” Archive for
Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01616-9.
ieee: N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar
equations in a many-body mean-field limit,” Archive for Rational Mechanics
and Analysis, vol. 240. Springer Nature, pp. 383–417, 2021.
ista: Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar
equations in a many-body mean-field limit. Archive for Rational Mechanics and
Analysis. 240, 383–417.
mla: Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a
Many-Body Mean-Field Limit.” Archive for Rational Mechanics and Analysis,
vol. 240, Springer Nature, 2021, pp. 383–417, doi:10.1007/s00205-021-01616-9.
short: N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics
and Analysis 240 (2021) 383–417.
date_created: 2021-03-14T23:01:34Z
date_published: 2021-02-26T00:00:00Z
date_updated: 2025-06-12T06:35:22Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-021-01616-9
ec_funded: 1
external_id:
arxiv:
- '2001.03993'
isi:
- '000622226200001'
pmid:
- '33785964'
file:
- access_level: open_access
checksum: 23449e44dc5132501a5c86e70638800f
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T08:31:29Z
date_updated: 2021-03-22T08:31:29Z
file_id: '9270'
file_name: 2021_ArchRationalMechAnal_Leopold.pdf
file_size: 558006
relation: main_file
success: 1
file_date_updated: 2021-03-22T08:31:29Z
has_accepted_license: '1'
intvolume: ' 240'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 383-417
pmid: 1
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: Derivation of the Landau–Pekar equations in a many-body mean-field limit
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: 240
year: '2021'
...
---
_id: '9348'
abstract:
- lang: eng
text: We consider the stochastic quantization of a quartic double-well energy functional
in the semiclassical regime and derive optimal asymptotics for the exponentially
small splitting of the ground state energy. Our result provides an infinite-dimensional
version of some sharp tunneling estimates known in finite dimensions for semiclassical
Witten Laplacians in degree zero. From a stochastic point of view it proves that
the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite
volume satisfies a Kramers-type formula in the limit of vanishing noise. We work
with finite-dimensional lattice approximations and establish semiclassical estimates
which are uniform in the dimension. Our key estimate shows that the constant separating
the two exponentially small eigenvalues from the rest of the spectrum can be taken
independently of the dimension.
acknowledgement: GDG gratefully acknowledges the financial support of HIM Bonn in
the framework of the 2019 Junior Trimester Programs “Kinetic Theory” and “Randomness,
PDEs and Nonlinear Fluctuations” and the hospitality at the University of Rome La
Sapienza during his frequent visits.
article_number: '109029'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Morris
full_name: Brooks, Morris
id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
last_name: Brooks
orcid: 0000-0002-6249-0928
- first_name: Giacomo
full_name: Di Gesù, Giacomo
last_name: Di Gesù
citation:
ama: Brooks M, Di Gesù G. Sharp tunneling estimates for a double-well model in infinite
dimension. Journal of Functional Analysis. 2021;281(3). doi:10.1016/j.jfa.2021.109029
apa: Brooks, M., & Di Gesù, G. (2021). Sharp tunneling estimates for a double-well
model in infinite dimension. Journal of Functional Analysis. Elsevier.
https://doi.org/10.1016/j.jfa.2021.109029
chicago: Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well
Model in Infinite Dimension.” Journal of Functional Analysis. Elsevier,
2021. https://doi.org/10.1016/j.jfa.2021.109029.
ieee: M. Brooks and G. Di Gesù, “Sharp tunneling estimates for a double-well model
in infinite dimension,” Journal of Functional Analysis, vol. 281, no. 3.
Elsevier, 2021.
ista: Brooks M, Di Gesù G. 2021. Sharp tunneling estimates for a double-well model
in infinite dimension. Journal of Functional Analysis. 281(3), 109029.
mla: Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well
Model in Infinite Dimension.” Journal of Functional Analysis, vol. 281,
no. 3, 109029, Elsevier, 2021, doi:10.1016/j.jfa.2021.109029.
short: M. Brooks, G. Di Gesù, Journal of Functional Analysis 281 (2021).
date_created: 2021-04-25T22:01:29Z
date_published: 2021-04-07T00:00:00Z
date_updated: 2023-08-08T13:15:11Z
day: '07'
department:
- _id: RoSe
doi: 10.1016/j.jfa.2021.109029
external_id:
arxiv:
- '1911.03187'
isi:
- '000644702800005'
intvolume: ' 281'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1911.03187
month: '04'
oa: 1
oa_version: Preprint
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: Sharp tunneling estimates for a double-well model in infinite dimension
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 281
year: '2021'
...
---
_id: '9351'
abstract:
- lang: eng
text: 'We consider the many-body quantum evolution of a factorized initial data,
in the mean-field regime. We show that fluctuations around the limiting Hartree
dynamics satisfy large deviation estimates that are consistent with central limit
theorems that have been established in the last years. '
acknowledgement: The authors gratefully acknowledge Gérard Ben Arous for suggesting
this kind of result. K.L.K. was partially supported by NSF CAREER Award DMS-125479
and a Simons Sabbatical Fellowship. S.R. acknowledges funding from the European
Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411. B. S. gratefully acknowledges partial 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. Funding 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: Kay
full_name: Kirkpatrick, Kay
last_name: Kirkpatrick
- 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
citation:
ama: Kirkpatrick K, Rademacher SAE, Schlein B. A large deviation principle in many-body
quantum dynamics. Annales Henri Poincare. 2021;22:2595-2618. doi:10.1007/s00023-021-01044-1
apa: Kirkpatrick, K., Rademacher, S. A. E., & Schlein, B. (2021). A large deviation
principle in many-body quantum dynamics. Annales Henri Poincare. Springer
Nature. https://doi.org/10.1007/s00023-021-01044-1
chicago: Kirkpatrick, Kay, Simone Anna Elvira Rademacher, and Benjamin Schlein.
“A Large Deviation Principle in Many-Body Quantum Dynamics.” Annales Henri
Poincare. Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01044-1.
ieee: K. Kirkpatrick, S. A. E. Rademacher, and B. Schlein, “A large deviation principle
in many-body quantum dynamics,” Annales Henri Poincare, vol. 22. Springer
Nature, pp. 2595–2618, 2021.
ista: Kirkpatrick K, Rademacher SAE, Schlein B. 2021. A large deviation principle
in many-body quantum dynamics. Annales Henri Poincare. 22, 2595–2618.
mla: Kirkpatrick, Kay, et al. “A Large Deviation Principle in Many-Body Quantum
Dynamics.” Annales Henri Poincare, vol. 22, Springer Nature, 2021, pp.
2595–618, doi:10.1007/s00023-021-01044-1.
short: K. Kirkpatrick, S.A.E. Rademacher, B. Schlein, Annales Henri Poincare 22
(2021) 2595–2618.
date_created: 2021-04-25T22:01:30Z
date_published: 2021-04-08T00:00:00Z
date_updated: 2025-06-12T06:39:59Z
day: '08'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00023-021-01044-1
ec_funded: 1
external_id:
arxiv:
- '2010.13754'
isi:
- '000638022600001'
pmid:
- '34776771'
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oa_version: Published Version
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call_identifier: H2020
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name: IST Austria Open Access Fund
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A large deviation principle in many-body quantum dynamics
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: 22
year: '2021'
...
---
_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
arxiv: 1
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: 2025-04-14T07:26:53Z
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
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
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).
corr_author: '1'
date_created: 2021-08-12T07:08:36Z
date_published: 2021-08-01T00:00:00Z
date_updated: 2024-10-09T21:00:48Z
day: '01'
ddc:
- '530'
department:
- _id: GradSch
- _id: RoSe
doi: 10.1063/5.0053494
external_id:
arxiv:
- '2103.07975'
isi:
- '000683960800003'
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issue: '8'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: 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: '9333'
abstract:
- lang: eng
text: We revise a previous result about the Fröhlich dynamics in the strong coupling
limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter
it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα,
where φ0 is the electron ground state of the Pekar energy functional and ξα the
associated coherent state of the phonons, can be approximated by a global phase
for times small compared to α2. In the present note we prove that a similar approximation
holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons
that is generated by an operator proportional to α−2 and quadratic in creation
and annihilation operators. Our result implies that the electron ground state
remains close to its initial state for times of order α2, while the phonon fluctuations
around the coherent state ξα can be described by a time-dependent Bogoliubov transformation.
acknowledgement: 'I thank Marcel Griesemer for many interesting discussions about
the Fröhlich polaron and also for valuable comments on this manuscript. Helpful
discussions with Nikolai Leopold and Robert Seiringer are also gratefully acknowledged.
This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG) through
the Research Training Group 1838: Spectral Theory and Dynamics of Quantum Systems.
Open Access funding enabled and organized by Projekt DEAL.'
article_number: '45'
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
citation:
ama: Mitrouskas DJ. A note on the Fröhlich dynamics in the strong coupling limit.
Letters in Mathematical Physics. 2021;111. doi:10.1007/s11005-021-01380-7
apa: Mitrouskas, D. J. (2021). A note on the Fröhlich dynamics in the strong coupling
limit. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01380-7
chicago: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong
Coupling Limit.” Letters in Mathematical Physics. Springer Nature, 2021.
https://doi.org/10.1007/s11005-021-01380-7.
ieee: D. J. Mitrouskas, “A note on the Fröhlich dynamics in the strong coupling
limit,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021.
ista: Mitrouskas DJ. 2021. A note on the Fröhlich dynamics in the strong coupling
limit. Letters in Mathematical Physics. 111, 45.
mla: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong
Coupling Limit.” Letters in Mathematical Physics, vol. 111, 45, Springer
Nature, 2021, doi:10.1007/s11005-021-01380-7.
short: D.J. Mitrouskas, Letters in Mathematical Physics 111 (2021).
date_created: 2021-04-18T22:01:41Z
date_published: 2021-04-05T00:00:00Z
date_updated: 2026-04-02T13:58:00Z
day: '05'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-021-01380-7
external_id:
isi:
- '000637359300002'
file:
- access_level: open_access
checksum: be56c0845a43c0c5c772ee0b5053f7d7
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creator: dernst
date_created: 2021-04-19T10:40:01Z
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has_accepted_license: '1'
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language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
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: A note on the Fröhlich dynamics in the strong coupling limit
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 111
year: '2021'
...
---
_id: '9318'
abstract:
- lang: eng
text: We consider a system of N bosons in the mean-field scaling regime for a class
of interactions including the repulsive Coulomb potential. We derive an asymptotic
expansion of the low-energy eigenstates and the corresponding energies, which
provides corrections to Bogoliubov theory to any order in 1/N.
acknowledgement: The first author gratefully acknowledges funding from the European
Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie
Grant Agreement No. 754411. The third author was supported by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No. 694227).
article_number: e28
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lea
full_name: Bossmann, Lea
id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
last_name: Bossmann
orcid: 0000-0002-6854-1343
- first_name: Sören P
full_name: Petrat, Sören P
id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
last_name: Petrat
orcid: 0000-0002-9166-5889
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Bossmann L, Petrat SP, Seiringer R. Asymptotic expansion of low-energy excitations
for weakly interacting bosons. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.22
apa: Bossmann, L., Petrat, S. P., & Seiringer, R. (2021). Asymptotic expansion
of low-energy excitations for weakly interacting bosons. Forum of Mathematics,
Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.22
chicago: Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion
of Low-Energy Excitations for Weakly Interacting Bosons.” Forum of Mathematics,
Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.22.
ieee: L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy
excitations for weakly interacting bosons,” Forum of Mathematics, Sigma,
vol. 9. Cambridge University Press, 2021.
ista: Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy
excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28.
mla: Bossmann, Lea, et al. “Asymptotic Expansion of Low-Energy Excitations for Weakly
Interacting Bosons.” Forum of Mathematics, Sigma, vol. 9, e28, Cambridge
University Press, 2021, doi:10.1017/fms.2021.22.
short: L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).
date_created: 2021-04-11T22:01:15Z
date_published: 2021-03-26T00:00:00Z
date_updated: 2026-04-02T14:02:29Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1017/fms.2021.22
ec_funded: 1
external_id:
isi:
- '000634006900001'
file:
- access_level: open_access
checksum: 17a3e6786d1e930cf0c14a880a6d7e92
content_type: application/pdf
creator: dernst
date_created: 2021-04-12T07:15:58Z
date_updated: 2021-04-12T07:15:58Z
file_id: '9319'
file_name: 2021_ForumMath_Bossmann.pdf
file_size: 883851
relation: main_file
success: 1
file_date_updated: 2021-04-12T07:15:58Z
has_accepted_license: '1'
intvolume: ' 9'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
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: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Asymptotic expansion of low-energy excitations 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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 9
year: '2021'
...
---
_id: '9256'
abstract:
- lang: eng
text: We consider the ferromagnetic quantum Heisenberg model in one dimension, for
any spin S≥1/2. We give upper and lower bounds on the free energy, proving that
at low temperature it is asymptotically equal to the one of an ideal Bose gas
of magnons, as predicted by the spin-wave approximation. The trial state used
in the upper bound yields an analogous estimate also in the case of two spatial
dimensions, which is believed to be sharp at low temperature.
acknowledgement: "The work of MN was supported by the National Science Centre (NCN)
Project Nr. 2016/21/D/ST1/02430. The work of RS was supported by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No. 694227).\r\nOpen access funding provided by Institute of Science
and Technology (IST Austria)."
article_number: '31'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Napiórkowski MM, Seiringer R. Free energy asymptotics of the quantum Heisenberg
spin chain. Letters in Mathematical Physics. 2021;111(2). doi:10.1007/s11005-021-01375-4
apa: Napiórkowski, M. M., & Seiringer, R. (2021). Free energy asymptotics of
the quantum Heisenberg spin chain. Letters in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s11005-021-01375-4
chicago: Napiórkowski, Marcin M, and Robert Seiringer. “Free Energy Asymptotics
of the Quantum Heisenberg Spin Chain.” Letters in Mathematical Physics.
Springer Nature, 2021. https://doi.org/10.1007/s11005-021-01375-4.
ieee: M. M. Napiórkowski and R. Seiringer, “Free energy asymptotics of the quantum
Heisenberg spin chain,” Letters in Mathematical Physics, vol. 111, no.
2. Springer Nature, 2021.
ista: Napiórkowski MM, Seiringer R. 2021. Free energy asymptotics of the quantum
Heisenberg spin chain. Letters in Mathematical Physics. 111(2), 31.
mla: Napiórkowski, Marcin M., and Robert Seiringer. “Free Energy Asymptotics of
the Quantum Heisenberg Spin Chain.” Letters in Mathematical Physics, vol.
111, no. 2, 31, Springer Nature, 2021, doi:10.1007/s11005-021-01375-4.
short: M.M. Napiórkowski, R. Seiringer, Letters in Mathematical Physics 111 (2021).
date_created: 2021-03-21T23:01:19Z
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title: Free energy asymptotics of the quantum Heisenberg spin chain
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abstract:
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text: This thesis is the result of the research carried out by the author during
his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich
polaron model, specifically to its regime of strong coupling. This model, which
is rigorously introduced and discussed in the introduction, has been of great
interest in condensed matter physics and field theory for more than eighty years.
It is used to describe an electron interacting with the atoms of a solid material
(the strength of this interaction is modeled by the presence of a coupling constant
α in the Hamiltonian of the system). The particular regime examined here, which
is mathematically described by considering the limit α →∞, displays many interesting
features related to the emergence of classical behavior, which allows for a simplified
effective description of the system under analysis. The properties, the range
of validity and a quantitative analysis of the precision of such classical approximations
are the main object of the present work. We specify our investigation to the study
of the ground state energy of the system, its dynamics and its effective mass.
For each of these problems, we provide in the introduction an overview of the
previously known results and a detailed account of the original contributions
by the author.
alternative_title:
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author:
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full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
citation:
ama: Feliciangeli D. The polaron at strong coupling. 2021. doi:10.15479/at:ista:9733
apa: Feliciangeli, D. (2021). The polaron at strong coupling. Institute of
Science and Technology Austria. https://doi.org/10.15479/at:ista:9733
chicago: Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science
and Technology Austria, 2021. https://doi.org/10.15479/at:ista:9733.
ieee: D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and
Technology Austria, 2021.
ista: Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science
and Technology Austria.
mla: Feliciangeli, Dario. The Polaron at Strong Coupling. Institute of Science
and Technology Austria, 2021, doi:10.15479/at:ista:9733.
short: D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and
Technology Austria, 2021.
corr_author: '1'
date_created: 2021-07-27T15:48:30Z
date_published: 2021-08-20T00:00:00Z
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issn:
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publisher: Institute of Science and Technology Austria
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id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
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title: The polaron at strong coupling
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...
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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: 2026-04-08T06:59:49Z
day: '11'
ddc:
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department:
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doi: 10.1007/s11005-020-01350-5
ec_funded: 1
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creator: dernst
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date_updated: 2021-03-09T11:44:34Z
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file_name: 2021_LettersMathPhysics_Feliciangeli.pdf
file_size: 391205
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language:
- iso: eng
month: '02'
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
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name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
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publisher: Springer Nature
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title: Persistence of the spectral gap for the Landau–Pekar equations
tmp:
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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
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 111
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...
---
_id: '9792'
abstract:
- lang: eng
text: 'This paper establishes new connections between many-body quantum systems,
One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport
(OT), by interpreting the problem of computing the ground-state energy of a finite
dimensional composite quantum system at positive temperature as a non-commutative
entropy regularized Optimal Transport problem. We develop a new approach to fully
characterize the dual-primal solutions in such non-commutative setting. The mathematical
formalism is particularly relevant in quantum chemistry: numerical realizations
of the many-electron ground state energy can be computed via a non-commutative
version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness
of this algorithm, which, to our best knowledge, were unknown even in the two
marginal case. Our methods are based on careful a priori estimates in the dual
problem, which we believe to be of independent interest. Finally, the above results
are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions
are enforced on the problem.'
acknowledgement: 'This work started when A.G. was visiting the Erwin Schrödinger Institute
and then continued when D.F. and L.P visited the Theoretical Chemistry Department
of the Vrije Universiteit Amsterdam. The authors thanks the hospitality of both
places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions
and literature suggestions in the early state of the project. Finally, the authors
also thanks J. Maas and R. Seiringer for their feedback and useful comments to a
first draft of the article. L.P. acknowledges support by the Austrian Science Fund
(FWF), grants No W1245 and NoF65. D.F acknowledges support by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreements No 716117 and No 694227). A.G. acknowledges funding by the European
Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942].'
article_number: '2106.11217'
article_processing_charge: No
arxiv: 1
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
- first_name: Augusto
full_name: Gerolin, Augusto
last_name: Gerolin
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal
transport approach to quantum composite systems at positive temperature. arXiv.
doi:10.48550/arXiv.2106.11217
apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (n.d.). A non-commutative
entropic optimal transport approach to quantum composite systems at positive temperature.
arXiv. https://doi.org/10.48550/arXiv.2106.11217
chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative
Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2106.11217.
ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic
optimal transport approach to quantum composite systems at positive temperature,”
arXiv. .
ista: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal
transport approach to quantum composite systems at positive temperature. arXiv,
2106.11217.
mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach
to Quantum Composite Systems at Positive Temperature.” ArXiv, 2106.11217,
doi:10.48550/arXiv.2106.11217.
short: D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.).
date_created: 2021-08-06T09:07:12Z
date_published: 2021-07-21T00:00:00Z
date_updated: 2026-04-08T07:00:03Z
day: '21'
ddc:
- '510'
department:
- _id: RoSe
- _id: JaMa
doi: 10.48550/arXiv.2106.11217
ec_funded: 1
external_id:
arxiv:
- '2106.11217'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.48550/arXiv.2106.11217
month: '07'
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
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
related_material:
record:
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relation: later_version
status: public
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relation: dissertation_contains
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relation: dissertation_contains
status: public
status: public
title: A non-commutative entropic optimal transport approach to quantum composite
systems at positive temperature
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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
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: 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. doi:10.48550/arXiv.2101.12566'
apa: 'Feliciangeli, D., & Seiringer, R. (n.d.). The strongly coupled polaron
on the torus: Quantum corrections to the Pekar asymptotics. arXiv. https://doi.org/10.48550/arXiv.2101.12566'
chicago: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron
on the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, n.d.
https://doi.org/10.48550/arXiv.2101.12566.'
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,
doi:10.48550/arXiv.2101.12566.'
short: D. Feliciangeli, R. Seiringer, ArXiv (n.d.).
corr_author: '1'
date_created: 2021-08-06T08:25:57Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2026-04-08T06:59:49Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.48550/arXiv.2101.12566
ec_funded: 1
external_id:
arxiv:
- '2101.12566'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
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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: draft
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
OA_place: repository
_id: '9791'
abstract:
- lang: eng
text: We provide a definition of the effective mass for the classical polaron described
by the Landau-Pekar 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 Landau
and Pekar.
acknowledgement: We thank Herbert Spohn for helpful comments. 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..
article_number: '2107.03720 '
article_processing_charge: No
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. arXiv. doi:10.48550/arXiv.2107.03720
apa: Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (n.d.). The effective
mass problem for the Landau-Pekar equations. arXiv. https://doi.org/10.48550/arXiv.2107.03720
chicago: Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
“The Effective Mass Problem for the Landau-Pekar Equations.” ArXiv, n.d.
https://doi.org/10.48550/arXiv.2107.03720.
ieee: D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass
problem for the Landau-Pekar equations,” arXiv. .
ista: Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for
the Landau-Pekar equations. arXiv, 2107.03720.
mla: Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar
Equations.” ArXiv, 2107.03720, doi:10.48550/arXiv.2107.03720.
short: D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, ArXiv (n.d.).
corr_author: '1'
date_created: 2021-08-06T08:49:45Z
date_published: 2021-07-08T00:00:00Z
date_updated: 2026-04-08T06:59:49Z
day: '08'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.48550/arXiv.2107.03720
ec_funded: 1
external_id:
arxiv:
- '2107.03720'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2107.03720
month: '07'
oa: 1
oa_version: Preprint
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: arXiv
publication_status: draft
related_material:
record:
- id: '10755'
relation: later_version
status: public
- id: '9733'
relation: dissertation_contains
status: public
status: public
title: The effective mass problem for the Landau-Pekar equations
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9005'
abstract:
- lang: eng
text: Studies on the experimental realization of two-dimensional anyons in terms
of quasiparticles have been restricted, so far, to only anyons on the plane. It
is known, however, that the geometry and topology of space can have significant
effects on quantum statistics for particles moving on it. Here, we have undertaken
the first step toward realizing the emerging fractional statistics for particles
restricted to move on the sphere instead of on the plane. We show that such a
model arises naturally in the context of quantum impurity problems. In particular,
we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic
or fermionic molecules immersed in a quantum many-particle environment can coincide
with the anyonic spectrum on the sphere. This paves the way toward the experimental
realization of anyons on the sphere using molecular impurities. Furthermore, since
a change in the alignment of the molecules corresponds to the exchange of the
particles on the sphere, such a realization reveals a novel type of exclusion
principle for molecular impurities, which could also be of use as a powerful technique
to measure the statistics parameter. Finally, our approach opens up a simple numerical
route to investigate the spectra of many anyons on the sphere. Accordingly, we
present the spectrum of two anyons on the sphere in the presence of a Dirac monopole
field.
acknowledgement: "We are grateful to A. Ghazaryan for valuable discussions and also
thank the anonymous referees for comments. D.L. acknowledges financial support from
the G¨oran Gustafsson Foundation (grant no. 1804) and LMU Munich. M.L. gratefully
acknowledges financial support\r\nby the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (grant agreements
No 801770)."
article_number: '015301'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Morris
full_name: Brooks, Morris
id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
last_name: Brooks
orcid: 0000-0002-6249-0928
- first_name: Mikhail
full_name: Lemeshko, Mikhail
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
- first_name: D.
full_name: Lundholm, D.
last_name: Lundholm
- first_name: Enderalp
full_name: Yakaboylu, Enderalp
id: 38CB71F6-F248-11E8-B48F-1D18A9856A87
last_name: Yakaboylu
orcid: 0000-0001-5973-0874
citation:
ama: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Molecular impurities as a realization
of anyons on the two-sphere. Physical Review Letters. 2021;126(1). doi:10.1103/PhysRevLett.126.015301
apa: Brooks, M., Lemeshko, M., Lundholm, D., & Yakaboylu, E. (2021). Molecular
impurities as a realization of anyons on the two-sphere. Physical Review Letters.
American Physical Society. https://doi.org/10.1103/PhysRevLett.126.015301
chicago: Brooks, Morris, Mikhail Lemeshko, D. Lundholm, and Enderalp Yakaboylu.
“Molecular Impurities as a Realization of Anyons on the Two-Sphere.” Physical
Review Letters. American Physical Society, 2021. https://doi.org/10.1103/PhysRevLett.126.015301.
ieee: M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Molecular impurities
as a realization of anyons on the two-sphere,” Physical Review Letters,
vol. 126, no. 1. American Physical Society, 2021.
ista: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Molecular impurities
as a realization of anyons on the two-sphere. Physical Review Letters. 126(1),
015301.
mla: Brooks, Morris, et al. “Molecular Impurities as a Realization of Anyons on
the Two-Sphere.” Physical Review Letters, vol. 126, no. 1, 015301, American
Physical Society, 2021, doi:10.1103/PhysRevLett.126.015301.
short: M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Physical Review Letters
126 (2021).
date_created: 2021-01-17T23:01:10Z
date_published: 2021-01-08T00:00:00Z
date_updated: 2026-04-16T08:20:53Z
day: '08'
department:
- _id: MiLe
- _id: RoSe
doi: 10.1103/PhysRevLett.126.015301
ec_funded: 1
external_id:
arxiv:
- '2009.05948'
isi:
- '000606325000003'
pmid:
- '33480760'
intvolume: ' 126'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2009.05948
month: '01'
oa: 1
oa_version: Preprint
pmid: 1
project:
- _id: 2688CF98-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '801770'
name: 'Angulon: physics and applications of a new quasiparticle'
publication: Physical Review Letters
publication_identifier:
eissn:
- 1079-7114
issn:
- 0031-9007
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
related_material:
link:
- description: News on IST Homepage
relation: press_release
url: https://ist.ac.at/en/news/dancing-molecules-and-two-dimensional-particles/
record:
- id: '12390'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Molecular impurities as a realization of anyons on the two-sphere
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 126
year: '2021'
...
---
_id: '14891'
abstract:
- lang: eng
text: We give the first mathematically rigorous justification of the local density
approximation in density functional theory. We provide a quantitative estimate
on the difference between the grand-canonical Levy–Lieb energy of a given density
(the lowest possible energy of all quantum states having this density) and the
integral over the uniform electron gas energy of this density. The error involves
gradient terms and justifies the use of the local density approximation in the
situation where the density is very flat on sufficiently large regions in space.
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. The local density approximation in density
functional theory. Pure and Applied Analysis. 2020;2(1):35-73. doi:10.2140/paa.2020.2.35
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2020). The local density approximation
in density functional theory. Pure and Applied Analysis. Mathematical Sciences
Publishers. https://doi.org/10.2140/paa.2020.2.35
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “ The Local Density
Approximation in Density Functional Theory.” Pure and Applied Analysis.
Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/paa.2020.2.35.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “ The local density approximation
in density functional theory,” Pure and Applied Analysis, vol. 2, no. 1.
Mathematical Sciences Publishers, pp. 35–73, 2020.
ista: Lewin M, Lieb EH, Seiringer R. 2020. The local density approximation in density
functional theory. Pure and Applied Analysis. 2(1), 35–73.
mla: Lewin, Mathieu, et al. “ The Local Density Approximation in Density Functional
Theory.” Pure and Applied Analysis, vol. 2, no. 1, Mathematical Sciences
Publishers, 2020, pp. 35–73, doi:10.2140/paa.2020.2.35.
short: M. Lewin, E.H. Lieb, R. Seiringer, Pure and Applied Analysis 2 (2020) 35–73.
corr_author: '1'
date_created: 2024-01-28T23:01:44Z
date_published: 2020-01-01T00:00:00Z
date_updated: 2024-10-09T21:08:02Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2020.2.35
external_id:
arxiv:
- '1903.04046'
intvolume: ' 2'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1903.04046
month: '01'
oa: 1
oa_version: Preprint
page: 35-73
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: ' The local density approximation in density functional theory'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2020'
...
---
_id: '15072'
abstract:
- lang: eng
text: The interaction among fundamental particles in nature leads to many interesting
effects in quantum statistical mechanics; examples include superconductivity for
charged systems and superfluidity in cold gases. It is a huge challenge for mathematical
physics to understand the collective behavior of systems containing a large number
of particles, emerging from known microscopic interactions. In this workshop we
brought together researchers working on different aspects of many-body quantum
mechanics to discuss recent developments, exchange ideas and propose new challenges
and research directions.
article_processing_charge: No
article_type: original
author:
- first_name: Christian
full_name: Hainzl, Christian
last_name: Hainzl
- 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
- first_name: Simone
full_name: Warzel, Simone
last_name: Warzel
citation:
ama: Hainzl C, Schlein B, Seiringer R, Warzel S. Many-body quantum systems. Oberwolfach
Reports. 2020;16(3):2541-2603. doi:10.4171/owr/2019/41
apa: Hainzl, C., Schlein, B., Seiringer, R., & Warzel, S. (2020). Many-body
quantum systems. Oberwolfach Reports. European Mathematical Society. https://doi.org/10.4171/owr/2019/41
chicago: Hainzl, Christian, Benjamin Schlein, Robert Seiringer, and Simone Warzel.
“Many-Body Quantum Systems.” Oberwolfach Reports. European Mathematical
Society, 2020. https://doi.org/10.4171/owr/2019/41.
ieee: C. Hainzl, B. Schlein, R. Seiringer, and S. Warzel, “Many-body quantum systems,”
Oberwolfach Reports, vol. 16, no. 3. European Mathematical Society, pp.
2541–2603, 2020.
ista: Hainzl C, Schlein B, Seiringer R, Warzel S. 2020. Many-body quantum systems.
Oberwolfach Reports. 16(3), 2541–2603.
mla: Hainzl, Christian, et al. “Many-Body Quantum Systems.” Oberwolfach Reports,
vol. 16, no. 3, European Mathematical Society, 2020, pp. 2541–603, doi:10.4171/owr/2019/41.
short: C. Hainzl, B. Schlein, R. Seiringer, S. Warzel, Oberwolfach Reports 16 (2020)
2541–2603.
date_created: 2024-03-04T11:46:12Z
date_published: 2020-09-10T00:00:00Z
date_updated: 2024-03-12T12:02:00Z
day: '10'
department:
- _id: RoSe
doi: 10.4171/owr/2019/41
intvolume: ' 16'
issue: '3'
language:
- iso: eng
month: '09'
oa_version: None
page: 2541-2603
publication: Oberwolfach Reports
publication_identifier:
issn:
- 1660-8933
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
status: public
title: Many-body quantum systems
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 16
year: '2020'
...