---
_id: '12911'
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 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 thank 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. The authors also thank J. Maas and
  R. Seiringer for their feedback and useful comments to a first draft of the article.
  Finally, we acknowledge the high quality review done by the anonymous referee of
  our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.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 HORIZON EUROPE European Research Council
  under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of
  his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences
  and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges
  support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the
  Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813."
article_number: '109963'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dario
  full_name: Feliciangeli, Dario
  id: 41A639AA-F248-11E8-B48F-1D18A9856A87
  last_name: Feliciangeli
  orcid: 0000-0003-0754-8530
- first_name: 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. <i>Journal
    of Functional Analysis</i>. 2023;285(4). doi:<a href="https://doi.org/10.1016/j.jfa.2023.109963">10.1016/j.jfa.2023.109963</a>
  apa: Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (2023). A non-commutative
    entropic optimal transport approach to quantum composite systems at positive temperature.
    <i>Journal of Functional Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jfa.2023.109963">https://doi.org/10.1016/j.jfa.2023.109963</a>
  chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative
    Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.”
    <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href="https://doi.org/10.1016/j.jfa.2023.109963">https://doi.org/10.1016/j.jfa.2023.109963</a>.
  ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic
    optimal transport approach to quantum composite systems at positive temperature,”
    <i>Journal of Functional Analysis</i>, vol. 285, no. 4. Elsevier, 2023.
  ista: Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal
    transport approach to quantum composite systems at positive temperature. Journal
    of Functional Analysis. 285(4), 109963.
  mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach
    to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional
    Analysis</i>, vol. 285, no. 4, 109963, Elsevier, 2023, doi:<a href="https://doi.org/10.1016/j.jfa.2023.109963">10.1016/j.jfa.2023.109963</a>.
  short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis
    285 (2023).
date_created: 2023-05-07T22:01:02Z
date_published: 2023-08-15T00:00:00Z
date_updated: 2023-11-14T13:21:01Z
day: '15'
department:
- _id: RoSe
- _id: JaMa
doi: 10.1016/j.jfa.2023.109963
ec_funded: 1
external_id:
  arxiv:
  - '2106.11217'
  isi:
  - '000990804300001'
intvolume: '       285'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2106.11217
month: '08'
oa: 1
oa_version: Preprint
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: 260482E2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: ' F06504'
  name: Taming Complexity in Partial Di erential Systems
publication: Journal of Functional Analysis
publication_identifier:
  eissn:
  - 1096-0783
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
  record:
  - id: '9792'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: A non-commutative entropic optimal transport approach to quantum composite
  systems at positive temperature
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 285
year: '2023'
...
---
_id: '10755'
abstract:
- lang: eng
  text: We provide a definition of the effective mass for the classical polaron described
    by the Landau–Pekar (LP) equations. It is based on a novel variational principle,
    minimizing the energy functional over states with given (initial) velocity. The
    resulting formula for the polaron's effective mass agrees with the prediction
    by LP (1948 J. Exp. Theor. Phys. 18 419–423).
acknowledgement: "We thank Herbert Spohn for helpful comments. Funding from the European
  Union’s Horizon\r\n2020 research and innovation programme under the ERC Grant Agreement
  No. 694227\r\n(DF and RS) and under the Marie Skłodowska-Curie Grant Agreement No.
  754411 (SR) is\r\ngratefully acknowledged."
article_number: '015201'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Dario
  full_name: Feliciangeli, Dario
  id: 41A639AA-F248-11E8-B48F-1D18A9856A87
  last_name: Feliciangeli
  orcid: 0000-0003-0754-8530
- first_name: Simone Anna Elvira
  full_name: Rademacher, Simone Anna Elvira
  id: 856966FE-A408-11E9-977E-802DE6697425
  last_name: Rademacher
  orcid: 0000-0001-5059-4466
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: 'Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for
    the Landau-Pekar equations. <i>Journal of Physics A: Mathematical and Theoretical</i>.
    2022;55(1). doi:<a href="https://doi.org/10.1088/1751-8121/ac3947">10.1088/1751-8121/ac3947</a>'
  apa: 'Feliciangeli, D., Rademacher, S. A. E., &#38; Seiringer, R. (2022). The effective
    mass problem for the Landau-Pekar equations. <i>Journal of Physics A: Mathematical
    and Theoretical</i>. IOP Publishing. <a href="https://doi.org/10.1088/1751-8121/ac3947">https://doi.org/10.1088/1751-8121/ac3947</a>'
  chicago: 'Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
    “The Effective Mass Problem for the Landau-Pekar Equations.” <i>Journal of Physics
    A: Mathematical and Theoretical</i>. IOP Publishing, 2022. <a href="https://doi.org/10.1088/1751-8121/ac3947">https://doi.org/10.1088/1751-8121/ac3947</a>.'
  ieee: 'D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass
    problem for the Landau-Pekar equations,” <i>Journal of Physics A: Mathematical
    and Theoretical</i>, vol. 55, no. 1. IOP Publishing, 2022.'
  ista: 'Feliciangeli D, Rademacher SAE, Seiringer R. 2022. The effective mass problem
    for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical.
    55(1), 015201.'
  mla: 'Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar
    Equations.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55,
    no. 1, 015201, IOP Publishing, 2022, doi:<a href="https://doi.org/10.1088/1751-8121/ac3947">10.1088/1751-8121/ac3947</a>.'
  short: 'D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Journal of Physics A:
    Mathematical and Theoretical 55 (2022).'
date_created: 2022-02-13T23:01:35Z
date_published: 2022-01-19T00:00:00Z
date_updated: 2024-03-06T12:30:44Z
day: '19'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1088/1751-8121/ac3947
ec_funded: 1
external_id:
  arxiv:
  - '2107.03720'
file:
- access_level: open_access
  checksum: 0875e562705563053d6dd98fba4d8578
  content_type: application/pdf
  creator: dernst
  date_created: 2022-02-14T08:20:19Z
  date_updated: 2022-02-14T08:20:19Z
  file_id: '10757'
  file_name: 2022_JournalPhysicsA_Feliciangeli.pdf
  file_size: 1132380
  relation: main_file
  success: 1
file_date_updated: 2022-02-14T08:20:19Z
has_accepted_license: '1'
intvolume: '        55'
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
  eissn:
  - 1751-8121
  issn:
  - 1751-8113
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
related_material:
  record:
  - id: '9791'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: The effective mass problem for the Landau-Pekar equations
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2022'
...
---
_id: '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. <i>Letters in Mathematical Physics</i>. 2021;111.
    doi:<a href="https://doi.org/10.1007/s11005-020-01350-5">10.1007/s11005-020-01350-5</a>
  apa: Feliciangeli, D., Rademacher, S. A. E., &#38; Seiringer, R. (2021). Persistence
    of the spectral gap for the Landau–Pekar equations. <i>Letters in Mathematical
    Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-020-01350-5">https://doi.org/10.1007/s11005-020-01350-5</a>
  chicago: Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
    “Persistence of the Spectral Gap for the Landau–Pekar Equations.” <i>Letters in
    Mathematical Physics</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s11005-020-01350-5">https://doi.org/10.1007/s11005-020-01350-5</a>.
  ieee: D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “Persistence of the
    spectral gap for the Landau–Pekar equations,” <i>Letters in Mathematical Physics</i>,
    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.” <i>Letters in Mathematical Physics</i>, vol. 111, 19, Springer Nature,
    2021, doi:<a href="https://doi.org/10.1007/s11005-020-01350-5">10.1007/s11005-020-01350-5</a>.
  short: D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Letters in Mathematical
    Physics 111 (2021).
date_created: 2021-03-07T23:01:25Z
date_published: 2021-02-11T00:00:00Z
date_updated: 2023-09-07T13:30:11Z
day: '11'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-020-01350-5
ec_funded: 1
external_id:
  isi:
  - '000617195700001'
file:
- access_level: open_access
  checksum: ffbfe1aad623bce7ff529c207e343b53
  content_type: application/pdf
  creator: dernst
  date_created: 2021-03-09T11:44:34Z
  date_updated: 2021-03-09T11:44:34Z
  file_id: '9232'
  file_name: 2021_LettersMathPhysics_Feliciangeli.pdf
  file_size: 391205
  relation: main_file
  success: 1
file_date_updated: 2021-03-09T11:44:34Z
has_accepted_license: '1'
intvolume: '       111'
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:
  - '15730530'
  issn:
  - '03779017'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  record:
  - id: '9733'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Persistence of the spectral gap for the Landau–Pekar equations
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 111
year: '2021'
...
---
_id: '10224'
abstract:
- lang: eng
  text: We investigate the Fröhlich polaron model on a three-dimensional torus, and
    give a proof of the second-order quantum corrections to its ground-state energy
    in the strong-coupling limit. Compared to previous work in the confined case,
    the translational symmetry (and its breaking in the Pekar approximation) makes
    the analysis substantially more challenging.
acknowledgement: "Funding from the European Union’s Horizon 2020 research and innovation
  programme under the ERC grant agreement No 694227 is gratefully acknowledged. We
  would also like to thank Rupert Frank for many helpful discussions, especially related
  to the Gross coordinate transformation defined in Def. 4.7.\r\nOpen access funding
  provided by Institute of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
article_type: original
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. <i>Archive for Rational Mechanics and Analysis</i>.
    2021;242(3):1835–1906. doi:<a href="https://doi.org/10.1007/s00205-021-01715-7">10.1007/s00205-021-01715-7</a>'
  apa: 'Feliciangeli, D., &#38; Seiringer, R. (2021). The strongly coupled polaron
    on the torus: Quantum corrections to the Pekar asymptotics. <i>Archive for Rational
    Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-021-01715-7">https://doi.org/10.1007/s00205-021-01715-7</a>'
  chicago: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron
    on the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>Archive for Rational
    Mechanics and Analysis</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s00205-021-01715-7">https://doi.org/10.1007/s00205-021-01715-7</a>.'
  ieee: 'D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus:
    Quantum corrections to the Pekar asymptotics,” <i>Archive for Rational Mechanics
    and Analysis</i>, vol. 242, no. 3. Springer Nature, pp. 1835–1906, 2021.'
  ista: 'Feliciangeli D, Seiringer R. 2021. The strongly coupled polaron on the torus:
    Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and
    Analysis. 242(3), 1835–1906.'
  mla: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on
    the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>Archive for Rational
    Mechanics and Analysis</i>, vol. 242, no. 3, Springer Nature, 2021, pp. 1835–1906,
    doi:<a href="https://doi.org/10.1007/s00205-021-01715-7">10.1007/s00205-021-01715-7</a>.'
  short: D. Feliciangeli, R. Seiringer, Archive for Rational Mechanics and Analysis
    242 (2021) 1835–1906.
date_created: 2021-11-07T23:01:26Z
date_published: 2021-10-25T00:00:00Z
date_updated: 2023-08-14T10:32:19Z
day: '25'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00205-021-01715-7
ec_funded: 1
external_id:
  arxiv:
  - '2101.12566'
  isi:
  - '000710850600001'
file:
- access_level: open_access
  checksum: 672e9c21b20f1a50854b7c821edbb92f
  content_type: application/pdf
  creator: alisjak
  date_created: 2021-12-14T08:35:42Z
  date_updated: 2021-12-14T08:35:42Z
  file_id: '10544'
  file_name: 2021_Springer_Feliciangeli.pdf
  file_size: 990529
  relation: main_file
  success: 1
file_date_updated: 2021-12-14T08:35:42Z
has_accepted_license: '1'
intvolume: '       242'
isi: 1
issue: '3'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1835–1906
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  record:
  - id: '9787'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: 'The strongly coupled polaron on the torus: Quantum corrections to the Pekar
  asymptotics'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 242
year: '2021'
...
---
_id: '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:<a href="https://doi.org/10.15479/at:ista:9733">10.15479/at:ista:9733</a>
  apa: Feliciangeli, D. (2021). <i>The polaron at strong coupling</i>. Institute of
    Science and Technology Austria. <a href="https://doi.org/10.15479/at:ista:9733">https://doi.org/10.15479/at:ista:9733</a>
  chicago: Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science
    and Technology Austria, 2021. <a href="https://doi.org/10.15479/at:ista:9733">https://doi.org/10.15479/at:ista:9733</a>.
  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. <i>The Polaron at Strong Coupling</i>. Institute of Science
    and Technology Austria, 2021, doi:<a href="https://doi.org/10.15479/at:ista:9733">10.15479/at:ista:9733</a>.
  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
  file_id: '9944'
  file_name: Thesis_FeliciangeliA.pdf
  file_size: 1958710
  relation: main_file
- access_level: closed
  checksum: 72810843abee83705853505b3f8348aa
  content_type: application/octet-stream
  creator: dfelicia
  date_created: 2021-08-19T14:06:35Z
  date_updated: 2022-03-10T12:13:57Z
  file_id: '9945'
  file_name: thesis.7z
  file_size: 3771669
  relation: source_file
file_date_updated: 2022-03-10T12:13:57Z
has_accepted_license: '1'
language:
- iso: eng
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: '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. <i>arXiv</i>.'
  apa: 'Feliciangeli, D., &#38; Seiringer, R. (n.d.). The strongly coupled polaron
    on the torus: Quantum corrections to the Pekar asymptotics. <i>arXiv</i>.'
  chicago: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron
    on the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>ArXiv</i>, n.d.'
  ieee: 'D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus:
    Quantum corrections to the Pekar asymptotics,” <i>arXiv</i>. .'
  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.” <i>ArXiv</i>, 2101.12566.'
  short: D. Feliciangeli, R. Seiringer, ArXiv (n.d.).
date_created: 2021-08-06T08:25:57Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-09-07T13:30:10Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
ec_funded: 1
external_id:
  arxiv:
  - '2101.12566'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2101.12566
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: arXiv
publication_status: submitted
related_material:
  record:
  - id: '10224'
    relation: later_version
    status: public
  - id: '9733'
    relation: dissertation_contains
    status: public
status: public
title: 'The strongly coupled polaron on the torus: Quantum corrections to the Pekar
  asymptotics'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: preprint
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
year: '2021'
...
---
_id: '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. <i>arXiv</i>.
  apa: Feliciangeli, D., Rademacher, S. A. E., &#38; Seiringer, R. (n.d.). The effective
    mass problem for the Landau-Pekar equations. <i>arXiv</i>.
  chicago: Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
    “The Effective Mass Problem for the Landau-Pekar Equations.” <i>ArXiv</i>, n.d.
  ieee: D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass
    problem for the Landau-Pekar equations,” <i>arXiv</i>. .
  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.” <i>ArXiv</i>, 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: '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. <i>arXiv</i>.
    doi:<a href="https://doi.org/10.48550/arXiv.2106.11217">10.48550/arXiv.2106.11217</a>
  apa: Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (n.d.). A non-commutative
    entropic optimal transport approach to quantum composite systems at positive temperature.
    <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2106.11217">https://doi.org/10.48550/arXiv.2106.11217</a>
  chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative
    Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.”
    <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2106.11217">https://doi.org/10.48550/arXiv.2106.11217</a>.
  ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic
    optimal transport approach to quantum composite systems at positive temperature,”
    <i>arXiv</i>. .
  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.” <i>ArXiv</i>, 2106.11217,
    doi:<a href="https://doi.org/10.48550/arXiv.2106.11217">10.48550/arXiv.2106.11217</a>.
  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
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: '9781'
abstract:
- lang: eng
  text: We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers,
    and a quadratic lower bound in terms of the distance to the minimizer. The latter
    follows from nondegeneracy of the Hessian at the minimum.
acknowledgement: We are grateful for the hospitality at the Mittag-Leffler Institute,
  where part of this work has been done. The work of the authors was supported by
  the European Research Council (ERC)under the European Union's Horizon 2020 research
  and innovation programme grant 694227.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dario
  full_name: Feliciangeli, Dario
  id: 41A639AA-F248-11E8-B48F-1D18A9856A87
  last_name: Feliciangeli
  orcid: 0000-0003-0754-8530
- first_name: 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. Uniqueness and nondegeneracy of minimizers of
    the Pekar functional on a ball. <i>SIAM Journal on Mathematical Analysis</i>.
    2020;52(1):605-622. doi:<a href="https://doi.org/10.1137/19m126284x">10.1137/19m126284x</a>
  apa: Feliciangeli, D., &#38; Seiringer, R. (2020). Uniqueness and nondegeneracy
    of minimizers of the Pekar functional on a ball. <i>SIAM Journal on Mathematical
    Analysis</i>. Society for Industrial &#38; Applied Mathematics . <a href="https://doi.org/10.1137/19m126284x">https://doi.org/10.1137/19m126284x</a>
  chicago: Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy
    of Minimizers of the Pekar Functional on a Ball.” <i>SIAM Journal on Mathematical
    Analysis</i>. Society for Industrial &#38; Applied Mathematics , 2020. <a href="https://doi.org/10.1137/19m126284x">https://doi.org/10.1137/19m126284x</a>.
  ieee: D. Feliciangeli and R. Seiringer, “Uniqueness and nondegeneracy of minimizers
    of the Pekar functional on a ball,” <i>SIAM Journal on Mathematical Analysis</i>,
    vol. 52, no. 1. Society for Industrial &#38; Applied Mathematics , pp. 605–622,
    2020.
  ista: Feliciangeli D, Seiringer R. 2020. Uniqueness and nondegeneracy of minimizers
    of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 52(1),
    605–622.
  mla: Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of
    Minimizers of the Pekar Functional on a Ball.” <i>SIAM Journal on Mathematical
    Analysis</i>, vol. 52, no. 1, Society for Industrial &#38; Applied Mathematics
    , 2020, pp. 605–22, doi:<a href="https://doi.org/10.1137/19m126284x">10.1137/19m126284x</a>.
  short: D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020)
    605–622.
date_created: 2021-08-06T07:34:16Z
date_published: 2020-02-12T00:00:00Z
date_updated: 2023-09-07T13:30:11Z
day: '12'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1137/19m126284x
ec_funded: 1
external_id:
  arxiv:
  - '1904.08647 '
  isi:
  - '000546967700022'
has_accepted_license: '1'
intvolume: '        52'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Analysis
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1904.08647
month: '02'
oa: 1
oa_version: Preprint
page: 605-622
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
  eissn:
  - 1095-7154
  issn:
  - 0036-1410
publication_status: published
publisher: 'Society for Industrial & Applied Mathematics '
quality_controlled: '1'
related_material:
  record:
  - id: '9733'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball
tmp:
  image: /images/cc_by_nc_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 52
year: '2020'
...