---
_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
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: 2023-11-14T13:21:01Z
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
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
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: submitted
related_material:
record:
- id: '9733'
relation: dissertation_contains
status: public
- id: '10030'
relation: dissertation_contains
status: public
- id: '12911'
relation: later_version
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: '14889'
abstract:
- lang: eng
text: We consider the Fröhlich Hamiltonian with large coupling constant α. For initial
data of Pekar product form with coherent phonon field and with the electron minimizing
the corresponding energy, we provide a norm approximation of the evolution, valid
up to times of order α2. The approximation is given in terms of a Pekar product
state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics
taking quantum fluctuations into account. This allows us to show that the Landau-Pekar
equations approximately describe the evolution of the electron- and one-phonon
reduced density matrices under the Fröhlich dynamics up to times of order α2.
acknowledgement: "Financial support by the European Union’s Horizon 2020 research
and innovation programme\r\nunder the Marie Skłodowska-Curie grant agreement No.
754411 (S.R.) and the European\r\nResearch Council under grant agreement No. 694227
(N.L. and R.S.), as well as by the SNSF\r\nEccellenza project PCEFP2 181153 (N.L.),
the NCCR SwissMAP (N.L. and B.S.) and by the\r\nDeutsche Forschungsgemeinschaft
(DFG) through the Research Training Group 1838: Spectral\r\nTheory and Dynamics
of Quantum Systems (D.M.) is gratefully acknowledged. B.S. gratefully\r\nacknowledges
financial support from the Swiss National Science Foundation through the Grant\r\n“Dynamical
and energetic properties of Bose-Einstein condensates” and from the European\r\nResearch
Council through the ERC-AdG CLaQS (grant agreement No 834782). D.M. thanks\r\nMarcel
Griesemer for helpful discussions."
article_processing_charge: No
article_type: original
author:
- first_name: Nikolai K
full_name: Leopold, Nikolai K
id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
last_name: Leopold
orcid: 0000-0002-0495-6822
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. Landau–Pekar
equations and quantum fluctuations for the dynamics of a strongly coupled polaron.
Pure and Applied Analysis. 2021;3(4):653-676. doi:10.2140/paa.2021.3.653
apa: Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., &
Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the
dynamics of a strongly coupled polaron. Pure and Applied Analysis. Mathematical
Sciences Publishers. https://doi.org/10.2140/paa.2021.3.653
chicago: Leopold, Nikolai K, David Johannes Mitrouskas, Simone Anna Elvira Rademacher,
Benjamin Schlein, and Robert Seiringer. “Landau–Pekar Equations and Quantum Fluctuations
for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis.
Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/paa.2021.3.653.
ieee: N. K. Leopold, D. J. Mitrouskas, S. A. E. Rademacher, B. Schlein, and R. Seiringer,
“Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly
coupled polaron,” Pure and Applied Analysis, vol. 3, no. 4. Mathematical
Sciences Publishers, pp. 653–676, 2021.
ista: Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. 2021. Landau–Pekar
equations and quantum fluctuations for the dynamics of a strongly coupled polaron.
Pure and Applied Analysis. 3(4), 653–676.
mla: Leopold, Nikolai K., et al. “Landau–Pekar Equations and Quantum Fluctuations
for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis,
vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:10.2140/paa.2021.3.653.
short: N.K. Leopold, D.J. Mitrouskas, S.A.E. Rademacher, B. Schlein, R. Seiringer,
Pure and Applied Analysis 3 (2021) 653–676.
date_created: 2024-01-28T23:01:43Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2024-02-05T10:02:45Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2021.3.653
ec_funded: 1
external_id:
arxiv:
- '2005.02098'
intvolume: ' 3'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2005.02098
month: '10'
oa: 1
oa_version: Preprint
page: 653-676
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Pure and Applied Analysis
publication_identifier:
eissn:
- 2578-5885
issn:
- 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly
coupled polaron
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2021'
...
---
_id: '14890'
abstract:
- lang: eng
text: We consider a system of N interacting bosons in the mean-field scaling regime
and construct corrections to the Bogoliubov dynamics that approximate the true
N-body dynamics in norm to arbitrary precision. The N-independent corrections
are given in terms of the solutions of the Bogoliubov and Hartree equations and
satisfy a generalized form of Wick's theorem. We determine the n-point correlation
functions of the excitations around the condensate, as well as the reduced densities
of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point
functions of a quasi-free state and the solution of the Hartree equation. In this
way, the complex problem of computing all n-point correlation functions for an
interacting N-body system is essentially reduced to the problem of solving the
Hartree equation and the PDEs for the Bogoliubov two-point functions.
acknowledgement: "We are grateful for the hospitality of Central China Normal University
(CCNU),\r\nwhere parts of this work were done, and thank Phan Th`anh Nam, Simone\r\nRademacher,
Robert Seiringer and Stefan Teufel for helpful discussions. L.B. gratefully acknowledges
the support by the German Research Foundation (DFG) within the Research\r\nTraining
Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and the funding\r\nfrom
the European Union’s Horizon 2020 research and innovation programme under the Marie\r\nSk
lodowska-Curie Grant Agreement No. 754411."
article_processing_charge: No
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: Peter
full_name: Pickl, Peter
last_name: Pickl
- first_name: Avy
full_name: Soffer, Avy
last_name: Soffer
citation:
ama: Bossmann L, Petrat SP, Pickl P, Soffer A. Beyond Bogoliubov dynamics. Pure
and Applied Analysis. 2021;3(4):677-726. doi:10.2140/paa.2021.3.677
apa: Bossmann, L., Petrat, S. P., Pickl, P., & Soffer, A. (2021). Beyond Bogoliubov
dynamics. Pure and Applied Analysis. Mathematical Sciences Publishers.
https://doi.org/10.2140/paa.2021.3.677
chicago: Bossmann, Lea, Sören P Petrat, Peter Pickl, and Avy Soffer. “Beyond Bogoliubov
Dynamics.” Pure and Applied Analysis. Mathematical Sciences Publishers,
2021. https://doi.org/10.2140/paa.2021.3.677.
ieee: L. Bossmann, S. P. Petrat, P. Pickl, and A. Soffer, “Beyond Bogoliubov dynamics,”
Pure and Applied Analysis, vol. 3, no. 4. Mathematical Sciences Publishers,
pp. 677–726, 2021.
ista: Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics.
Pure and Applied Analysis. 3(4), 677–726.
mla: Bossmann, Lea, et al. “Beyond Bogoliubov Dynamics.” Pure and Applied Analysis,
vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 677–726, doi:10.2140/paa.2021.3.677.
short: L. Bossmann, S.P. Petrat, P. Pickl, A. Soffer, Pure and Applied Analysis
3 (2021) 677–726.
date_created: 2024-01-28T23:01:43Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2024-02-05T09:26:31Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2021.3.677
ec_funded: 1
external_id:
arxiv:
- '1912.11004'
intvolume: ' 3'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1912.11004
month: '10'
oa: 1
oa_version: Preprint
page: 677-726
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Beyond Bogoliubov dynamics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2021'
...
---
_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.
date_created: 2021-07-27T15:48:30Z
date_published: 2021-08-20T00:00:00Z
date_updated: 2024-03-06T12:30:44Z
day: '20'
ddc:
- '515'
- '519'
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: RoSe
- _id: JaMa
doi: 10.15479/at:ista:9733
ec_funded: 1
file:
- access_level: open_access
checksum: e88bb8ca43948abe060eb2d2fa719881
content_type: application/pdf
creator: dfelicia
date_created: 2021-08-19T14:03:48Z
date_updated: 2021-09-06T09:28:56Z
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language:
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license: https://creativecommons.org/licenses/by-nd/4.0/
month: '08'
oa: 1
oa_version: Published Version
page: '180'
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 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:
- id: '9787'
relation: part_of_dissertation
status: public
- id: '9792'
relation: part_of_dissertation
status: public
- id: '9225'
relation: part_of_dissertation
status: public
- id: '9781'
relation: part_of_dissertation
status: public
- id: '9791'
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_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
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.
apa: Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (n.d.). The effective
mass problem for the Landau-Pekar equations. arXiv.
chicago: Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
“The Effective Mass Problem for the Landau-Pekar Equations.” ArXiv, n.d.
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.
short: D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, ArXiv (n.d.).
date_created: 2021-08-06T08:49:45Z
date_published: 2021-07-08T00:00:00Z
date_updated: 2024-03-06T12:30:45Z
day: '08'
ddc:
- '510'
department:
- _id: RoSe
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: submitted
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: '6649'
abstract:
- lang: eng
text: "While Hartree–Fock theory is well established as a fundamental approximation
for interacting fermions, it has been unclear how to describe corrections to it
due to many-body correlations. In this paper we start from the Hartree–Fock state
given by plane waves and introduce collective particle–hole pair excitations.
These pairs can be approximately described by a bosonic quadratic Hamiltonian.
We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type
upper bound to the ground state energy. Our result justifies the random-phase
approximation in the mean-field scaling regime, for repulsive, regular interaction
potentials.\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Niels P
full_name: Benedikter, Niels P
id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
last_name: Benedikter
orcid: 0000-0002-1071-6091
- first_name: Phan Thành
full_name: Nam, Phan Thành
last_name: Nam
- first_name: Marcello
full_name: Porta, Marcello
last_name: Porta
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Optimal upper bound
for the correlation energy of a Fermi gas in the mean-field regime. Communications
in Mathematical Physics. 2020;374:2097–2150. doi:10.1007/s00220-019-03505-5
apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R.
(2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field
regime. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03505-5
chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi
Gas in the Mean-Field Regime.” Communications in Mathematical Physics.
Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03505-5.
ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal
upper bound for the correlation energy of a Fermi gas in the mean-field regime,”
Communications in Mathematical Physics, vol. 374. Springer Nature, pp.
2097–2150, 2020.
ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper
bound for the correlation energy of a Fermi gas in the mean-field regime. Communications
in Mathematical Physics. 374, 2097–2150.
mla: Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy
of a Fermi Gas in the Mean-Field Regime.” Communications in Mathematical Physics,
vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:10.1007/s00220-019-03505-5.
short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications
in Mathematical Physics 374 (2020) 2097–2150.
date_created: 2019-07-18T13:30:04Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2023-08-17T13:51:50Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00220-019-03505-5
ec_funded: 1
external_id:
arxiv:
- '1809.01902'
isi:
- '000527910700019'
file:
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checksum: f9dd6dd615a698f1d3636c4a092fed23
content_type: application/pdf
creator: dernst
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oa_version: Published Version
page: 2097–2150
project:
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call_identifier: FWF
name: FWF Open Access Fund
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call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal upper bound for the correlation energy of a Fermi gas in the mean-field
regime
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
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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
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.
date_created: 2020-02-23T09:45:51Z
date_published: 2020-02-21T00:00:00Z
date_updated: 2023-08-18T06:37:46Z
day: '21'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s10955-020-02500-8
ec_funded: 1
external_id:
arxiv:
- '1905.06164'
isi:
- '000516342200001'
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creator: dernst
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date_updated: 2020-11-20T09:26:46Z
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language:
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month: '02'
oa: 1
oa_version: Published Version
page: 1362-1396
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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: '7790'
abstract:
- lang: eng
text: "We prove a lower bound for the free energy (per unit volume) of the two-dimensional
Bose gas in the thermodynamic limit. We show that the free energy at density \U0001D70C
and inverse temperature \U0001D6FD differs from the one of the noninteracting
system by the correction term \U0001D70B\U0001D70C\U0001D70C\U0001D6FD\U0001D6FD
. Here, is the scattering length of the interaction potential, and \U0001D6FD
is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity.
The result is valid in the dilute limit \U0001D70C and if \U0001D6FD\U0001D70C
."
article_number: e20
article_processing_charge: No
article_type: original
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- 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: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute
Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 2020;8. doi:10.1017/fms.2020.17
apa: Deuchert, A., Mayer, S., & Seiringer, R. (2020). The free energy of the
two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma.
Cambridge University Press. https://doi.org/10.1017/fms.2020.17
chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy
of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” Forum of Mathematics,
Sigma. Cambridge University Press, 2020. https://doi.org/10.1017/fms.2020.17.
ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional
dilute Bose gas. I. Lower bound,” Forum of Mathematics, Sigma, vol. 8.
Cambridge University Press, 2020.
ista: Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional
dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20.
mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose
Gas. I. Lower Bound.” Forum of Mathematics, Sigma, vol. 8, e20, Cambridge
University Press, 2020, doi:10.1017/fms.2020.17.
short: A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020).
date_created: 2020-05-03T22:00:48Z
date_published: 2020-03-14T00:00:00Z
date_updated: 2023-08-21T06:18:49Z
day: '14'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1017/fms.2020.17
ec_funded: 1
external_id:
arxiv:
- '1910.03372'
isi:
- '000527342000001'
file:
- access_level: open_access
checksum: 8a64da99d107686997876d7cad8cfe1e
content_type: application/pdf
creator: dernst
date_created: 2020-05-04T12:02:41Z
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file_id: '7797'
file_name: 2020_ForumMath_Deuchert.pdf
file_size: 692530
relation: main_file
file_date_updated: 2020-07-14T12:48:03Z
has_accepted_license: '1'
intvolume: ' 8'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- '20505094'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
record:
- id: '7524'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound
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: 8
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
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: 2023-08-22T07:47:04Z
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:
- '14359855'
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
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
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.
date_created: 2020-07-05T22:00:46Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2023-08-22T07:51:47Z
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:
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checksum: 5cbeef52caf18d0d952f17fed7b5545a
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creator: dernst
date_created: 2020-11-25T15:05:04Z
date_updated: 2020-11-25T15:05:04Z
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oa: 1
oa_version: Published Version
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project:
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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:
- '15729613'
issn:
- '00224715'
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
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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: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 181
year: '2020'
...