---
_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
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isi:
- '000634006900001'
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month: '03'
oa: 1
oa_version: Published Version
project:
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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)
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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
date_published: 2021-03-09T00:00:00Z
date_updated: 2026-04-02T14:06:48Z
day: '09'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-021-01375-4
external_id:
isi:
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pmid:
- '33785980'
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oa: 1
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publication: Letters in Mathematical Physics
publication_identifier:
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issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
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title: Free energy asymptotics of the quantum Heisenberg spin chain
tmp:
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
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type: journal_article
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year: '2021'
...
---
OA_place: publisher
_id: '9733'
abstract:
- lang: eng
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:
- ISTA Thesis
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
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
date_updated: 2026-04-08T06:59:50Z
day: '20'
ddc:
- '515'
- '519'
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: RoSe
- _id: JaMa
doi: 10.15479/at:ista:9733
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page: '180'
project:
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call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
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relation: part_of_dissertation
status: public
- id: '9792'
relation: part_of_dissertation
status: public
- id: '9791'
relation: part_of_dissertation
status: public
- id: '9781'
relation: part_of_dissertation
status: public
- id: '9225'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: The polaron at strong coupling
tmp:
image: /image/cc_by_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
short: CC BY-ND (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
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: 2026-04-08T06:59:49Z
day: '11'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-020-01350-5
ec_funded: 1
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isi:
- '000617195700001'
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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
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has_accepted_license: '1'
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isi: 1
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
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_identifier:
eissn:
- 1573-0530
issn:
- 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
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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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 111
year: '2021'
...
---
_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
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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)
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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:
- 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: 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'
...
---
_id: '8042'
abstract:
- lang: eng
text: We consider systems of N bosons in a box of volume one, interacting through
a repulsive two-body potential of the form κN3β−1V(Nβx). For all 0<β<1, and for
sufficiently small coupling constant κ>0, we establish the validity of Bogolyubov
theory, identifying the ground state energy and the low-lying excitation spectrum
up to errors that vanish in the limit of large N.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
full_name: Boccato, Chiara
id: 342E7E22-F248-11E8-B48F-1D18A9856A87
last_name: Boccato
- first_name: Christian
full_name: Brennecke, Christian
last_name: Brennecke
- first_name: Serena
full_name: Cenatiempo, Serena
last_name: Cenatiempo
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
citation:
ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. The excitation spectrum of
Bose gases interacting through singular potentials. Journal of the European
Mathematical Society. 2020;22(7):2331-2403. doi:10.4171/JEMS/966
apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2020). The excitation
spectrum of Bose gases interacting through singular potentials. Journal of
the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/966
chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
“The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.”
Journal of the European Mathematical Society. European Mathematical Society,
2020. https://doi.org/10.4171/JEMS/966.
ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “The excitation spectrum
of Bose gases interacting through singular potentials,” Journal of the European
Mathematical Society, vol. 22, no. 7. European Mathematical Society, pp. 2331–2403,
2020.
ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. The excitation spectrum
of Bose gases interacting through singular potentials. Journal of the European
Mathematical Society. 22(7), 2331–2403.
mla: Boccato, Chiara, et al. “The Excitation Spectrum of Bose Gases Interacting
through Singular Potentials.” Journal of the European Mathematical Society,
vol. 22, no. 7, European Mathematical Society, 2020, pp. 2331–403, doi:10.4171/JEMS/966.
short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Journal of the European
Mathematical Society 22 (2020) 2331–2403.
date_created: 2020-06-29T07:59:35Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2025-07-10T11:55:02Z
day: '01'
department:
- _id: RoSe
doi: 10.4171/JEMS/966
external_id:
arxiv:
- '1704.04819'
isi:
- '000548174700006'
intvolume: ' 22'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1704.04819
month: '07'
oa: 1
oa_version: Preprint
page: 2331-2403
publication: Journal of the European Mathematical Society
publication_identifier:
issn:
- 1435-9855
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: The excitation spectrum of Bose gases interacting through singular potentials
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 22
year: '2020'
...
---
_id: '8091'
abstract:
- lang: eng
text: In the setting of the fractional quantum Hall effect we study the effects
of strong, repulsive two-body interaction potentials of short range. We prove
that Haldane’s pseudo-potential operators, including their pre-factors, emerge
as mathematically rigorous limits of such interactions when the range of the potential
tends to zero while its strength tends to infinity. In a common approach the interaction
potential is expanded in angular momentum eigenstates in the lowest Landau level,
which amounts to taking the pre-factors to be the moments of the potential. Such
a procedure is not appropriate for very strong interactions, however, in particular
not in the case of hard spheres. We derive the formulas valid in the short-range
case, which involve the scattering lengths of the interaction potential in different
angular momentum channels rather than its moments. Our results hold for bosons
and fermions alike and generalize previous results in [6], which apply to bosons
in the lowest angular momentum channel. Our main theorem asserts the convergence
in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after
appropriate energy scalings, to Hamiltonians with contact interactions in the
lowest Landau level.
acknowledgement: "Open access funding provided by Institute of Science and Technology
(IST Austria).\r\nThe work of R.S. was supported by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No 694227). J.Y. gratefully acknowledges hospitality at the LPMMC
Grenoble and valuable discussions with Alessandro Olgiati and Nicolas Rougerie. "
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems
with short-range interactions. Journal of Statistical Physics. 2020;181:448-464.
doi:10.1007/s10955-020-02586-0
apa: Seiringer, R., & Yngvason, J. (2020). Emergence of Haldane pseudo-potentials
in systems with short-range interactions. Journal of Statistical Physics.
Springer. https://doi.org/10.1007/s10955-020-02586-0
chicago: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials
in Systems with Short-Range Interactions.” Journal of Statistical Physics.
Springer, 2020. https://doi.org/10.1007/s10955-020-02586-0.
ieee: R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems
with short-range interactions,” Journal of Statistical Physics, vol. 181.
Springer, pp. 448–464, 2020.
ista: Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems
with short-range interactions. Journal of Statistical Physics. 181, 448–464.
mla: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials
in Systems with Short-Range Interactions.” Journal of Statistical Physics,
vol. 181, Springer, 2020, pp. 448–64, doi:10.1007/s10955-020-02586-0.
short: R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464.
corr_author: '1'
date_created: 2020-07-05T22:00:46Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2025-07-10T11:55:04Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s10955-020-02586-0
ec_funded: 1
external_id:
arxiv:
- '2001.07144'
isi:
- '000543030000002'
file:
- access_level: open_access
checksum: 5cbeef52caf18d0d952f17fed7b5545a
content_type: application/pdf
creator: dernst
date_created: 2020-11-25T15:05:04Z
date_updated: 2020-11-25T15:05:04Z
file_id: '8812'
file_name: 2020_JourStatPhysics_Seiringer.pdf
file_size: 404778
relation: main_file
success: 1
file_date_updated: 2020-11-25T15:05:04Z
has_accepted_license: '1'
intvolume: ' 181'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 448-464
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: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Emergence of Haldane pseudo-potentials in systems with short-range interactions
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: 181
year: '2020'
...
---
_id: '8130'
abstract:
- lang: eng
text: We study the dynamics of a system of N interacting bosons in a disc-shaped
trap, which is realised by an external potential that confines the bosons in one
spatial dimension to an interval of length of order ε. The interaction is non-negative
and scaled in such a way that its scattering length is of order ε/N, while its
range is proportional to (ε/N)β with scaling parameter β∈(0,1]. We consider the
simultaneous limit (N,ε)→(∞,0) and assume that the system initially exhibits Bose–Einstein
condensation. We prove that condensation is preserved by the N-body dynamics,
where the time-evolved condensate wave function is the solution of a two-dimensional
non-linear equation. The strength of the non-linearity depends on the scaling
parameter β. For β∈(0,1), we obtain a cubic defocusing non-linear Schrödinger
equation, while the choice β=1 yields a Gross–Pitaevskii equation featuring the
scattering length of the interaction. In both cases, the coupling parameter depends
on the confining potential.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). I thank Stefan Teufel for helpful remarks and for his involvement
in the closely related joint project [10]. Helpful discussions with Serena Cenatiempo
and Nikolai Leopold are gratefully acknowledged. This work was supported by the
German Research Foundation within the Research Training Group 1838 “Spectral Theory
and Dynamics of Quantum Systems” and has received funding from the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
full_name: Bossmann, Lea
id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
last_name: Bossmann
orcid: 0000-0002-6854-1343
citation:
ama: Bossmann L. Derivation of the 2d Gross–Pitaevskii equation for strongly confined
3d Bosons. Archive for Rational Mechanics and Analysis. 2020;238(11):541-606.
doi:10.1007/s00205-020-01548-w
apa: Bossmann, L. (2020). Derivation of the 2d Gross–Pitaevskii equation for strongly
confined 3d Bosons. Archive for Rational Mechanics and Analysis. Springer
Nature. https://doi.org/10.1007/s00205-020-01548-w
chicago: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly
Confined 3d Bosons.” Archive for Rational Mechanics and Analysis. Springer
Nature, 2020. https://doi.org/10.1007/s00205-020-01548-w.
ieee: L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly
confined 3d Bosons,” Archive for Rational Mechanics and Analysis, vol.
238, no. 11. Springer Nature, pp. 541–606, 2020.
ista: Bossmann L. 2020. Derivation of the 2d Gross–Pitaevskii equation for strongly
confined 3d Bosons. Archive for Rational Mechanics and Analysis. 238(11), 541–606.
mla: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly
Confined 3d Bosons.” Archive for Rational Mechanics and Analysis, vol.
238, no. 11, Springer Nature, 2020, pp. 541–606, doi:10.1007/s00205-020-01548-w.
short: L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.
corr_author: '1'
date_created: 2020-07-18T15:06:35Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2025-04-14T07:44:05Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-020-01548-w
ec_funded: 1
external_id:
arxiv:
- '1907.04547'
isi:
- '000550164400001'
file:
- access_level: open_access
checksum: cc67a79a67bef441625fcb1cd031db3d
content_type: application/pdf
creator: dernst
date_created: 2020-12-02T08:50:38Z
date_updated: 2020-12-02T08:50:38Z
file_id: '8826'
file_name: 2020_ArchiveRatMech_Bossmann.pdf
file_size: 942343
relation: main_file
success: 1
file_date_updated: 2020-12-02T08:50:38Z
has_accepted_license: '1'
intvolume: ' 238'
isi: 1
issue: '11'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 541-606
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
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 2d Gross–Pitaevskii equation for strongly confined 3d 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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 238
year: '2020'
...
---
_id: '8134'
abstract:
- lang: eng
text: We prove an upper bound on the free energy of a two-dimensional homogeneous
Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the
free energy per unit volume differs from the one of the non-interacting system
by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]2+) to leading order, where a is the scattering
length of the two-body interaction potential, ρ is the density, β is the inverse
temperature, and βc is the inverse Berezinskii–Kosterlitz–Thouless critical temperature
for superfluidity. In combination with the corresponding matching lower bound
proved by Deuchert et al. [Forum Math. Sigma 8, e20 (2020)], this shows equality
in the asymptotic expansion.
article_number: '061901'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Simon
full_name: Mayer, Simon
id: 30C4630A-F248-11E8-B48F-1D18A9856A87
last_name: Mayer
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas.
II. Upper bound. Journal of Mathematical Physics. 2020;61(6). doi:10.1063/5.0005950
apa: Mayer, S., & Seiringer, R. (2020). The free energy of the two-dimensional
dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. AIP
Publishing. https://doi.org/10.1063/5.0005950
chicago: Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional
Dilute Bose Gas. II. Upper Bound.” Journal of Mathematical Physics. AIP
Publishing, 2020. https://doi.org/10.1063/5.0005950.
ieee: S. Mayer and R. Seiringer, “The free energy of the two-dimensional dilute
Bose gas. II. Upper bound,” Journal of Mathematical Physics, vol. 61, no.
6. AIP Publishing, 2020.
ista: Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute
Bose gas. II. Upper bound. Journal of Mathematical Physics. 61(6), 061901.
mla: Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional
Dilute Bose Gas. II. Upper Bound.” Journal of Mathematical Physics, vol.
61, no. 6, 061901, AIP Publishing, 2020, doi:10.1063/5.0005950.
short: S. Mayer, R. Seiringer, Journal of Mathematical Physics 61 (2020).
corr_author: '1'
date_created: 2020-07-19T22:00:59Z
date_published: 2020-06-22T00:00:00Z
date_updated: 2025-07-10T11:55:05Z
day: '22'
department:
- _id: RoSe
doi: 10.1063/5.0005950
ec_funded: 1
external_id:
arxiv:
- '2002.08281'
isi:
- '000544595100001'
intvolume: ' 61'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2002.08281
month: '06'
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 Mathematical Physics
publication_identifier:
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The free energy of the two-dimensional dilute Bose gas. II. Upper bound
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 61
year: '2020'
...
---
_id: '8769'
abstract:
- lang: eng
text: One of the hallmarks of quantum statistics, tightly entwined with the concept
of topological phases of matter, is the prediction of anyons. Although anyons
are predicted to be realized in certain fractional quantum Hall systems, they
have not yet been unambiguously detected in experiment. Here we introduce a simple
quantum impurity model, where bosonic or fermionic impurities turn into anyons
as a consequence of their interaction with the surrounding many-particle bath.
A cloud of phonons dresses each impurity in such a way that it effectively attaches
fluxes or vortices to it and thereby converts it into an Abelian anyon. The corresponding
quantum impurity model, first, provides a different approach to the numerical
solution of the many-anyon problem, along with a concrete perspective of anyons
as emergent quasiparticles built from composite bosons or fermions. More importantly,
the model paves the way toward realizing anyons using impurities in crystal lattices
as well as ultracold gases. In particular, we consider two heavy electrons interacting
with a two-dimensional lattice crystal in a magnetic field, and show that when
the impurity-bath system is rotated at the cyclotron frequency, impurities behave
as anyons as a consequence of the angular momentum exchange between the impurities
and the bath. A possible experimental realization is proposed by identifying the
statistics parameter in terms of the mean-square distance of the impurities and
the magnetization of the impurity-bath system, both of which are accessible to
experiment. Another proposed application is impurities immersed in a two-dimensional
weakly interacting Bose gas.
acknowledgement: "We are grateful to M. Correggi, A. Deuchert, and P. Schmelcher for
valuable discussions. We also thank the anonymous referees for helping to clarify
a few important points in the experimental realization. A.G. acknowledges support
by the European Unions Horizon 2020 research and innovation program under the Marie
Skłodowska-Curie grant agreement\r\nNo 754411. D.L. acknowledges financial support
from the Goran Gustafsson Foundation (grant no. 1804) and LMU Munich. R.S., M.L.,
and N.R. gratefully acknowledge financial support by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreements No 694227, No 801770, and No 758620, respectively)."
article_number: '144109'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Enderalp
full_name: Yakaboylu, Enderalp
id: 38CB71F6-F248-11E8-B48F-1D18A9856A87
last_name: Yakaboylu
orcid: 0000-0001-5973-0874
- first_name: Areg
full_name: Ghazaryan, Areg
id: 4AF46FD6-F248-11E8-B48F-1D18A9856A87
last_name: Ghazaryan
orcid: 0000-0001-9666-3543
- first_name: D.
full_name: Lundholm, D.
last_name: Lundholm
- first_name: N.
full_name: Rougerie, N.
last_name: Rougerie
- first_name: Mikhail
full_name: Lemeshko, Mikhail
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Yakaboylu E, Ghazaryan A, Lundholm D, Rougerie N, Lemeshko M, Seiringer R.
Quantum impurity model for anyons. Physical Review B. 2020;102(14). doi:10.1103/physrevb.102.144109
apa: Yakaboylu, E., Ghazaryan, A., Lundholm, D., Rougerie, N., Lemeshko, M., &
Seiringer, R. (2020). Quantum impurity model for anyons. Physical Review B.
American Physical Society. https://doi.org/10.1103/physrevb.102.144109
chicago: Yakaboylu, Enderalp, Areg Ghazaryan, D. Lundholm, N. Rougerie, Mikhail
Lemeshko, and Robert Seiringer. “Quantum Impurity Model for Anyons.” Physical
Review B. American Physical Society, 2020. https://doi.org/10.1103/physrevb.102.144109.
ieee: E. Yakaboylu, A. Ghazaryan, D. Lundholm, N. Rougerie, M. Lemeshko, and R.
Seiringer, “Quantum impurity model for anyons,” Physical Review B, vol.
102, no. 14. American Physical Society, 2020.
ista: Yakaboylu E, Ghazaryan A, Lundholm D, Rougerie N, Lemeshko M, Seiringer R.
2020. Quantum impurity model for anyons. Physical Review B. 102(14), 144109.
mla: Yakaboylu, Enderalp, et al. “Quantum Impurity Model for Anyons.” Physical
Review B, vol. 102, no. 14, 144109, American Physical Society, 2020, doi:10.1103/physrevb.102.144109.
short: E. Yakaboylu, A. Ghazaryan, D. Lundholm, N. Rougerie, M. Lemeshko, R. Seiringer,
Physical Review B 102 (2020).
date_created: 2020-11-18T07:34:17Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2025-04-14T07:26:54Z
day: '01'
department:
- _id: MiLe
- _id: RoSe
doi: 10.1103/physrevb.102.144109
ec_funded: 1
external_id:
arxiv:
- '1912.07890'
isi:
- '000582563300001'
intvolume: ' 102'
isi: 1
issue: '14'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1912.07890
month: '10'
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
- _id: 2688CF98-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '801770'
name: 'Angulon: physics and applications of a new quasiparticle'
publication: Physical Review B
publication_identifier:
eissn:
- 2469-9969
issn:
- 2469-9950
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantum impurity model for anyons
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 102
year: '2020'
...
---
_id: '6906'
abstract:
- lang: eng
text: We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime.
We show that low-energy states exhibit complete Bose–Einstein condensation with
an optimal bound on the number of orthogonal excitations. This extends recent
results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing
the assumption of small interaction potential.
acknowledgement: "We would like to thank P. T. Nam and R. Seiringer for several useful
discussions and\r\nfor suggesting us to use the localization techniques from [9].
C. Boccato has received funding from the\r\nEuropean Research Council (ERC) under
the programme Horizon 2020 (Grant Agreement 694227). B. Schlein gratefully acknowledges
support from the NCCR SwissMAP and from the Swiss National Foundation of Science
(Grant No. 200020_1726230) through the SNF Grant “Dynamical and energetic properties
of Bose–Einstein condensates”."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
full_name: Boccato, Chiara
id: 342E7E22-F248-11E8-B48F-1D18A9856A87
last_name: Boccato
- first_name: Christian
full_name: Brennecke, Christian
last_name: Brennecke
- first_name: Serena
full_name: Cenatiempo, Serena
last_name: Cenatiempo
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
citation:
ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. Optimal rate for Bose-Einstein
condensation in the Gross-Pitaevskii regime. Communications in Mathematical
Physics. 2020;376:1311-1395. doi:10.1007/s00220-019-03555-9
apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2020). Optimal
rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. Communications
in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-019-03555-9
chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
“Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.”
Communications in Mathematical Physics. Springer, 2020. https://doi.org/10.1007/s00220-019-03555-9.
ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Optimal rate for
Bose-Einstein condensation in the Gross-Pitaevskii regime,” Communications
in Mathematical Physics, vol. 376. Springer, pp. 1311–1395, 2020.
ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. Optimal rate for Bose-Einstein
condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics.
376, 1311–1395.
mla: Boccato, Chiara, et al. “Optimal Rate for Bose-Einstein Condensation in the
Gross-Pitaevskii Regime.” Communications in Mathematical Physics, vol.
376, Springer, 2020, pp. 1311–95, doi:10.1007/s00220-019-03555-9.
short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical
Physics 376 (2020) 1311–1395.
date_created: 2019-09-24T17:30:59Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00220-019-03555-9
ec_funded: 1
external_id:
arxiv:
- '1812.03086'
isi:
- '000536053300012'
intvolume: ' 376'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1812.03086
month: '06'
oa: 1
oa_version: Preprint
page: 1311-1395
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 376
year: '2020'
...
---
_id: '7235'
abstract:
- lang: eng
text: We consider the Fröhlich model of a polaron, and show that its effective mass
diverges in thestrong coupling limit.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). Financial support through the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme (Grant Agreement
No. 694227; R.S.) is gratefully acknowledged.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- 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: Lieb EH, Seiringer R. Divergence of the effective mass of a polaron in the
strong coupling limit. Journal of Statistical Physics. 2020;180:23-33.
doi:10.1007/s10955-019-02322-3
apa: Lieb, E. H., & Seiringer, R. (2020). Divergence of the effective mass of
a polaron in the strong coupling limit. Journal of Statistical Physics.
Springer Nature. https://doi.org/10.1007/s10955-019-02322-3
chicago: Lieb, Elliott H., and Robert Seiringer. “Divergence of the Effective Mass
of a Polaron in the Strong Coupling Limit.” Journal of Statistical Physics.
Springer Nature, 2020. https://doi.org/10.1007/s10955-019-02322-3.
ieee: E. H. Lieb and R. Seiringer, “Divergence of the effective mass of a polaron
in the strong coupling limit,” Journal of Statistical Physics, vol. 180.
Springer Nature, pp. 23–33, 2020.
ista: Lieb EH, Seiringer R. 2020. Divergence of the effective mass of a polaron
in the strong coupling limit. Journal of Statistical Physics. 180, 23–33.
mla: Lieb, Elliott H., and Robert Seiringer. “Divergence of the Effective Mass of
a Polaron in the Strong Coupling Limit.” Journal of Statistical Physics,
vol. 180, Springer Nature, 2020, pp. 23–33, doi:10.1007/s10955-019-02322-3.
short: E.H. Lieb, R. Seiringer, Journal of Statistical Physics 180 (2020) 23–33.
corr_author: '1'
date_created: 2020-01-07T09:42:03Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2025-04-14T07:27:01Z
day: '01'
ddc:
- '510'
- '530'
department:
- _id: RoSe
doi: 10.1007/s10955-019-02322-3
ec_funded: 1
external_id:
isi:
- '000556199700003'
file:
- access_level: open_access
checksum: 1e67bee6728592f7bdcea2ad2d9366dc
content_type: application/pdf
creator: dernst
date_created: 2020-11-19T11:13:55Z
date_updated: 2020-11-19T11:13:55Z
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language:
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month: '09'
oa: 1
oa_version: Published Version
page: 23-33
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: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Divergence of the effective mass of a polaron 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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 180
year: '2020'
...
---
_id: '7508'
abstract:
- lang: eng
text: In this paper, we introduce a novel method for deriving higher order corrections
to the mean-field description of the dynamics of interacting bosons. More precisely,
we consider the dynamics of N d-dimensional bosons for large N. The bosons initially
form a Bose–Einstein condensate and interact with each other via a pair potential
of the form (N−1)−1Ndβv(Nβ·)forβ∈[0,14d). We derive a sequence of N-body functions
which approximate the true many-body dynamics in L2(RdN)-norm to arbitrary precision
in powers of N−1. The approximating functions are constructed as Duhamel expansions
of finite order in terms of the first quantised analogue of a Bogoliubov time
evolution.
acknowledgement: "Open access funding provided by Institute of Science and Technology
(IST Austria).\r\nL.B. gratefully acknowledges the support by the German Research
Foundation (DFG) within the Research Training Group 1838 “Spectral Theory and Dynamics
of Quantum Systems”, and wishes to thank Stefan Teufel, Sören Petrat and Marcello
Porta for helpful discussions. This project has received funding from the European
Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411. N.P. gratefully acknowledges support from NSF grant
DMS-1516228 and DMS-1840314. P.P.’s research was funded by DFG Grant no. PI 1114/3-1.
Part of this work was done when N.P. and P.P. were visiting CCNU, Wuhan. N.P. and
P.P. thank A.S. for his hospitality at CCNU."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
full_name: Bossmann, Lea
id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
last_name: Bossmann
orcid: 0000-0002-6854-1343
- first_name: Nataša
full_name: Pavlović, Nataša
last_name: Pavlović
- first_name: Peter
full_name: Pickl, Peter
last_name: Pickl
- first_name: Avy
full_name: Soffer, Avy
last_name: Soffer
citation:
ama: Bossmann L, Pavlović N, Pickl P, Soffer A. Higher order corrections to the
mean-field description of the dynamics of interacting bosons. Journal of Statistical
Physics. 2020;178:1362-1396. doi:10.1007/s10955-020-02500-8
apa: Bossmann, L., Pavlović, N., Pickl, P., & Soffer, A. (2020). Higher order
corrections to the mean-field description of the dynamics of interacting bosons.
Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-020-02500-8
chicago: Bossmann, Lea, Nataša Pavlović, Peter Pickl, and Avy Soffer. “Higher Order
Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.”
Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-020-02500-8.
ieee: L. Bossmann, N. Pavlović, P. Pickl, and A. Soffer, “Higher order corrections
to the mean-field description of the dynamics of interacting bosons,” Journal
of Statistical Physics, vol. 178. Springer Nature, pp. 1362–1396, 2020.
ista: Bossmann L, Pavlović N, Pickl P, Soffer A. 2020. Higher order corrections
to the mean-field description of the dynamics of interacting bosons. Journal of
Statistical Physics. 178, 1362–1396.
mla: Bossmann, Lea, et al. “Higher Order Corrections to the Mean-Field Description
of the Dynamics of Interacting Bosons.” Journal of Statistical Physics,
vol. 178, Springer Nature, 2020, pp. 1362–96, doi:10.1007/s10955-020-02500-8.
short: L. Bossmann, N. Pavlović, P. Pickl, A. Soffer, Journal of Statistical Physics
178 (2020) 1362–1396.
corr_author: '1'
date_created: 2020-02-23T09:45:51Z
date_published: 2020-02-21T00:00:00Z
date_updated: 2025-04-14T07:44:03Z
day: '21'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s10955-020-02500-8
ec_funded: 1
external_id:
arxiv:
- '1905.06164'
isi:
- '000516342200001'
file:
- access_level: open_access
checksum: 643e230bf147e64d9cdb3f6cc573679d
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T09:26:46Z
date_updated: 2020-11-20T09:26:46Z
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file_name: 2020_JournStatPhysics_Bossmann.pdf
file_size: 576726
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file_date_updated: 2020-11-20T09:26:46Z
has_accepted_license: '1'
intvolume: ' 178'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 1362-1396
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Higher order corrections to the mean-field description of the dynamics of interacting
bosons
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 178
year: '2020'
...
---
_id: '7611'
abstract:
- lang: eng
text: We consider a system of N bosons in the limit N→∞, interacting through singular
potentials. For initial data exhibiting Bose–Einstein condensation, the many-body
time evolution is well approximated through a quadratic fluctuation dynamics around
a cubic nonlinear Schrödinger equation of the condensate wave function. We show
that these fluctuations satisfy a (multi-variate) central limit theorem.
acknowledgement: "Simone Rademacher acknowledges partial support from the NCCR SwissMAP.
This project has received\r\nfunding from the European Union’s Horizon 2020 research
and innovation program under the Marie\r\nSkłodowska-Curie Grant Agreement No. 754411.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria).\r\nS.R.
would like to thank Benjamin Schlein for many fruitful discussions."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
citation:
ama: Rademacher SAE. Central limit theorem for Bose gases interacting through singular
potentials. Letters in Mathematical Physics. 2020;110:2143-2174. doi:10.1007/s11005-020-01286-w
apa: Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting
through singular potentials. Letters in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s11005-020-01286-w
chicago: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
through Singular Potentials.” Letters in Mathematical Physics. Springer
Nature, 2020. https://doi.org/10.1007/s11005-020-01286-w.
ieee: S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through
singular potentials,” Letters in Mathematical Physics, vol. 110. Springer
Nature, pp. 2143–2174, 2020.
ista: Rademacher SAE. 2020. Central limit theorem for Bose gases interacting through
singular potentials. Letters in Mathematical Physics. 110, 2143–2174.
mla: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
through Singular Potentials.” Letters in Mathematical Physics, vol. 110,
Springer Nature, 2020, pp. 2143–74, doi:10.1007/s11005-020-01286-w.
short: S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174.
corr_author: '1'
date_created: 2020-03-23T11:11:47Z
date_published: 2020-03-12T00:00:00Z
date_updated: 2025-04-14T07:44:03Z
day: '12'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-020-01286-w
ec_funded: 1
external_id:
isi:
- '000551556000006'
file:
- access_level: open_access
checksum: 3bdd41f10ad947b67a45b98f507a7d4a
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creator: dernst
date_created: 2020-11-20T12:04:26Z
date_updated: 2020-11-20T12:04:26Z
file_id: '8784'
file_name: 2020_LettersMathPhysics_Rademacher.pdf
file_size: 478683
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success: 1
file_date_updated: 2020-11-20T12:04:26Z
has_accepted_license: '1'
intvolume: ' 110'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 2143-2174
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
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: Central limit theorem for Bose gases interacting through singular potentials
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 110
year: '2020'
...
---
_id: '7650'
abstract:
- lang: eng
text: We consider a dilute, homogeneous Bose gas at positive temperature. The system
is investigated in the Gross–Pitaevskii limit, where the scattering length a is
so small that the interaction energy is of the same order of magnitude as the
spectral gap of the Laplacian, and for temperatures that are comparable to the
critical temperature of the ideal gas. We show that the difference between the
specific free energy of the interacting system and the one of the ideal gas is
to leading order given by 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system
and ϱ0 is the expected condensate density of the ideal gas. Additionally, we show
that the one-particle density matrix of any approximate minimizer of the Gibbs
free energy functional is to leading order given by the one of the ideal gas.
This in particular proves Bose–Einstein condensation with critical temperature
given by the one of the ideal gas to leading order. One key ingredient of our
proof is a novel use of the Gibbs variational principle that goes hand in hand
with the c-number substitution.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). It is a pleasure to thank Jakob Yngvason for helpful discussions.
Financial support by the European Research Council (ERC) under the European Union’sHorizon
2020 research and innovation programme (Grant Agreement No. 694227) is gratefully
acknowledged. A. D. acknowledges funding from the European Union’s Horizon 2020
research and innovation programme under the Marie Sklodowska-Curie Grant Agreement
No. 836146.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- 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. Gross-Pitaevskii limit of a homogeneous Bose gas at
positive temperature. Archive for Rational Mechanics and Analysis. 2020;236(6):1217-1271.
doi:10.1007/s00205-020-01489-4
apa: Deuchert, A., & Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous
Bose gas at positive temperature. Archive for Rational Mechanics and Analysis.
Springer Nature. https://doi.org/10.1007/s00205-020-01489-4
chicago: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous
Bose Gas at Positive Temperature.” Archive for Rational Mechanics and Analysis.
Springer Nature, 2020. https://doi.org/10.1007/s00205-020-01489-4.
ieee: A. Deuchert and R. Seiringer, “Gross-Pitaevskii limit of a homogeneous Bose
gas at positive temperature,” Archive for Rational Mechanics and Analysis,
vol. 236, no. 6. Springer Nature, pp. 1217–1271, 2020.
ista: Deuchert A, Seiringer R. 2020. Gross-Pitaevskii limit of a homogeneous Bose
gas at positive temperature. Archive for Rational Mechanics and Analysis. 236(6),
1217–1271.
mla: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous
Bose Gas at Positive Temperature.” Archive for Rational Mechanics and Analysis,
vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:10.1007/s00205-020-01489-4.
short: A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236
(2020) 1217–1271.
corr_author: '1'
date_created: 2020-04-08T15:18:03Z
date_published: 2020-03-09T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
day: '09'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-020-01489-4
ec_funded: 1
external_id:
arxiv:
- '1901.11363'
isi:
- '000519415000001'
file:
- access_level: open_access
checksum: b645fb64bfe95bbc05b3eea374109a9c
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T13:17:42Z
date_updated: 2020-11-20T13:17:42Z
file_id: '8785'
file_name: 2020_ArchRatMechanicsAnalysis_Deuchert.pdf
file_size: 704633
relation: main_file
success: 1
file_date_updated: 2020-11-20T13:17:42Z
has_accepted_license: '1'
intvolume: ' 236'
isi: 1
issue: '6'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 1217-1271
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
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: Gross-Pitaevskii limit of a homogeneous Bose gas 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: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 236
year: '2020'
...