---
_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:
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has_accepted_license: '1'
intvolume: '        55'
issue: '1'
language:
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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:
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scopus_import: '1'
status: public
title: The effective mass problem for the Landau-Pekar equations
tmp:
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2022'
...
---
_id: '11917'
abstract:
- lang: eng
  text: We study the many-body dynamics of an initially factorized bosonic wave function
    in the mean-field regime. We prove large deviation estimates for the fluctuations
    around the condensate. We derive an upper bound extending a recent result to more
    general interactions. Furthermore, we derive a new lower bound which agrees with
    the upper bound in leading order.
acknowledgement: "The authors thank Gérard Ben Arous for pointing out the question
  of a lower bound. Funding from the European Union’s Horizon 2020 research and innovation
  programme under the ERC Grant Agreement No. 694227 (R.S.) and under the Marie Skłodowska-Curie
  Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.\r\nOpen access funding
  provided by IST Austria."
article_number: '9'
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
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Rademacher SAE, Seiringer R. Large deviation estimates for weakly interacting
    bosons. <i>Journal of Statistical Physics</i>. 2022;188. doi:<a href="https://doi.org/10.1007/s10955-022-02940-4">10.1007/s10955-022-02940-4</a>
  apa: Rademacher, S. A. E., &#38; Seiringer, R. (2022). Large deviation estimates
    for weakly interacting bosons. <i>Journal of Statistical Physics</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s10955-022-02940-4">https://doi.org/10.1007/s10955-022-02940-4</a>
  chicago: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation
    Estimates for Weakly Interacting Bosons.” <i>Journal of Statistical Physics</i>.
    Springer Nature, 2022. <a href="https://doi.org/10.1007/s10955-022-02940-4">https://doi.org/10.1007/s10955-022-02940-4</a>.
  ieee: S. A. E. Rademacher and R. Seiringer, “Large deviation estimates for weakly
    interacting bosons,” <i>Journal of Statistical Physics</i>, vol. 188. Springer
    Nature, 2022.
  ista: Rademacher SAE, Seiringer R. 2022. Large deviation estimates for weakly interacting
    bosons. Journal of Statistical Physics. 188, 9.
  mla: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates
    for Weakly Interacting Bosons.” <i>Journal of Statistical Physics</i>, vol. 188,
    9, Springer Nature, 2022, doi:<a href="https://doi.org/10.1007/s10955-022-02940-4">10.1007/s10955-022-02940-4</a>.
  short: S.A.E. Rademacher, R. Seiringer, Journal of Statistical Physics 188 (2022).
date_created: 2022-08-18T07:23:26Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-08-03T12:55:58Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s10955-022-02940-4
ec_funded: 1
external_id:
  isi:
  - '000805175000001'
file:
- access_level: open_access
  checksum: 44418cb44f07fa21ed3907f85abf7f39
  content_type: application/pdf
  creator: dernst
  date_created: 2022-08-18T08:09:00Z
  date_updated: 2022-08-18T08:09:00Z
  file_id: '11922'
  file_name: 2022_JournalStatisticalPhysics_Rademacher.pdf
  file_size: 483481
  relation: main_file
  success: 1
file_date_updated: 2022-08-18T08:09:00Z
has_accepted_license: '1'
intvolume: '       188'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '07'
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 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: Large deviation estimates for weakly interacting bosons
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 188
year: '2022'
...
---
_id: '12083'
abstract:
- lang: eng
  text: We consider the many-body time evolution of weakly interacting bosons in the
    mean field regime for initial coherent states. We show that bounded k-particle
    operators, corresponding to dependent random variables, satisfy both a law of
    large numbers and a central limit theorem.
acknowledgement: S.R. would like to thank Robert Seiringer and Benedikt Stufler for
  helpful discussions. Funding from the European Union’s Horizon 2020 Research and
  Innovation Program under the ERC grant (Grant Agreement No. 694227) and under the
  Marie Skłodowska-Curie grant (Agreement No. 754411) is acknowledged.
article_number: '081902'
article_processing_charge: No
article_type: original
arxiv: 1
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. Dependent random variables in quantum dynamics. <i>Journal
    of Mathematical Physics</i>. 2022;63(8). doi:<a href="https://doi.org/10.1063/5.0086712">10.1063/5.0086712</a>
  apa: Rademacher, S. A. E. (2022). Dependent random variables in quantum dynamics.
    <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href="https://doi.org/10.1063/5.0086712">https://doi.org/10.1063/5.0086712</a>
  chicago: Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum
    Dynamics.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href="https://doi.org/10.1063/5.0086712">https://doi.org/10.1063/5.0086712</a>.
  ieee: S. A. E. Rademacher, “Dependent random variables in quantum dynamics,” <i>Journal
    of Mathematical Physics</i>, vol. 63, no. 8. AIP Publishing, 2022.
  ista: Rademacher SAE. 2022. Dependent random variables in quantum dynamics. Journal
    of Mathematical Physics. 63(8), 081902.
  mla: Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.”
    <i>Journal of Mathematical Physics</i>, vol. 63, no. 8, 081902, AIP Publishing,
    2022, doi:<a href="https://doi.org/10.1063/5.0086712">10.1063/5.0086712</a>.
  short: S.A.E. Rademacher, Journal of Mathematical Physics 63 (2022).
date_created: 2022-09-11T22:01:56Z
date_published: 2022-08-25T00:00:00Z
date_updated: 2023-08-03T13:57:19Z
day: '25'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1063/5.0086712
ec_funded: 1
external_id:
  arxiv:
  - '2112.04817'
  isi:
  - '000844402500001'
file:
- access_level: open_access
  checksum: e6fb0cf3f0327739c5e69a2cfc4020eb
  content_type: application/pdf
  creator: dernst
  date_created: 2022-09-12T07:35:34Z
  date_updated: 2022-09-12T07:35:34Z
  file_id: '12089'
  file_name: 2022_JourMathPhysics_Rademacher.pdf
  file_size: 4552261
  relation: main_file
  success: 1
file_date_updated: 2022-09-12T07:35:34Z
has_accepted_license: '1'
intvolume: '        63'
isi: 1
issue: '8'
language:
- iso: eng
month: '08'
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 Mathematical Physics
publication_identifier:
  issn:
  - 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dependent random variables in quantum dynamics
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2022'
...
---
_id: '10738'
abstract:
- lang: eng
  text: We prove an adiabatic theorem for the Landau–Pekar equations. This allows
    us to derive new results on the accuracy of their use as effective equations for
    the time evolution generated by the Fröhlich Hamiltonian with large coupling constant
    α. In particular, we show that the time evolution of Pekar product states with
    coherent phonon field and the electron being trapped by the phonons is well approximated
    by the Landau–Pekar equations until times short compared to α2.
acknowledgement: "N. L. and R. S. gratefully acknowledge financial support by the
  European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research
  and innovation programme (grant\r\nagreement No 694227). B. S. acknowledges support
  from the Swiss National Science Foundation (grant 200020_172623) and from the NCCR
  SwissMAP. N. L. would like to thank\r\nAndreas Deuchert and David Mitrouskas for
  interesting discussions. B. S. and R. S. would\r\nlike to thank Rupert Frank for
  stimulating discussions about the time-evolution of a polaron.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nikolai K
  full_name: Leopold, Nikolai K
  id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
  last_name: Leopold
  orcid: 0000-0002-0495-6822
- first_name: Simone Anna Elvira
  full_name: Rademacher, Simone Anna Elvira
  id: 856966FE-A408-11E9-977E-802DE6697425
  last_name: Rademacher
  orcid: 0000-0001-5059-4466
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: 'Leopold NK, Rademacher SAE, Schlein B, Seiringer R.  The Landau–Pekar equations:
    Adiabatic theorem and accuracy. <i>Analysis and PDE</i>. 2021;14(7):2079-2100.
    doi:<a href="https://doi.org/10.2140/APDE.2021.14.2079">10.2140/APDE.2021.14.2079</a>'
  apa: 'Leopold, N. K., Rademacher, S. A. E., Schlein, B., &#38; Seiringer, R. (2021).  The
    Landau–Pekar equations: Adiabatic theorem and accuracy. <i>Analysis and PDE</i>.
    Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/APDE.2021.14.2079">https://doi.org/10.2140/APDE.2021.14.2079</a>'
  chicago: 'Leopold, Nikolai K, Simone Anna Elvira Rademacher, Benjamin Schlein, and
    Robert Seiringer. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.”
    <i>Analysis and PDE</i>. Mathematical Sciences Publishers, 2021. <a href="https://doi.org/10.2140/APDE.2021.14.2079">https://doi.org/10.2140/APDE.2021.14.2079</a>.'
  ieee: 'N. K. Leopold, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “ The Landau–Pekar
    equations: Adiabatic theorem and accuracy,” <i>Analysis and PDE</i>, vol. 14,
    no. 7. Mathematical Sciences Publishers, pp. 2079–2100, 2021.'
  ista: 'Leopold NK, Rademacher SAE, Schlein B, Seiringer R. 2021.  The Landau–Pekar
    equations: Adiabatic theorem and accuracy. Analysis and PDE. 14(7), 2079–2100.'
  mla: 'Leopold, Nikolai K., et al. “ The Landau–Pekar Equations: Adiabatic Theorem
    and Accuracy.” <i>Analysis and PDE</i>, vol. 14, no. 7, Mathematical Sciences
    Publishers, 2021, pp. 2079–100, doi:<a href="https://doi.org/10.2140/APDE.2021.14.2079">10.2140/APDE.2021.14.2079</a>.'
  short: N.K. Leopold, S.A.E. Rademacher, B. Schlein, R. Seiringer, Analysis and PDE
    14 (2021) 2079–2100.
date_created: 2022-02-06T23:01:33Z
date_published: 2021-11-10T00:00:00Z
date_updated: 2023-10-17T11:26:45Z
day: '10'
department:
- _id: RoSe
doi: 10.2140/APDE.2021.14.2079
ec_funded: 1
external_id:
  arxiv:
  - '1904.12532'
  isi:
  - '000733976600004'
intvolume: '        14'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1904.12532
month: '11'
oa: 1
oa_version: Preprint
page: 2079-2100
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Analysis and PDE
publication_identifier:
  eissn:
  - 1948-206X
  issn:
  - 2157-5045
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' The Landau–Pekar equations: Adiabatic theorem and accuracy'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2021'
...
---
_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
arxiv: 1
author:
- first_name: Nikolai K
  full_name: Leopold, Nikolai K
  id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
  last_name: Leopold
  orcid: 0000-0002-0495-6822
- first_name: David Johannes
  full_name: Mitrouskas, David Johannes
  id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
  last_name: Mitrouskas
- first_name: 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.
    <i>Pure and Applied Analysis</i>. 2021;3(4):653-676. doi:<a href="https://doi.org/10.2140/paa.2021.3.653">10.2140/paa.2021.3.653</a>
  apa: Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., &#38;
    Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the
    dynamics of a strongly coupled polaron. <i>Pure and Applied Analysis</i>. Mathematical
    Sciences Publishers. <a href="https://doi.org/10.2140/paa.2021.3.653">https://doi.org/10.2140/paa.2021.3.653</a>
  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.” <i>Pure and Applied Analysis</i>.
    Mathematical Sciences Publishers, 2021. <a href="https://doi.org/10.2140/paa.2021.3.653">https://doi.org/10.2140/paa.2021.3.653</a>.
  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,” <i>Pure and Applied Analysis</i>, 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.” <i>Pure and Applied Analysis</i>,
    vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:<a href="https://doi.org/10.2140/paa.2021.3.653">10.2140/paa.2021.3.653</a>.
  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
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department:
- _id: RoSe
doi: 10.2140/paa.2021.3.653
ec_funded: 1
external_id:
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  - '2005.02098'
intvolume: '         3'
issue: '4'
language:
- iso: eng
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  url: https://doi.org/10.48550/arXiv.2005.02098
month: '10'
oa: 1
oa_version: Preprint
page: 653-676
project:
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  grant_number: '754411'
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- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
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  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Pure and Applied Analysis
publication_identifier:
  eissn:
  - 2578-5885
  issn:
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publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
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title: Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly
  coupled polaron
type: journal_article
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year: '2021'
...
---
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abstract:
- lang: eng
  text: "The Landau–Pekar equations describe the dynamics of a strongly coupled polaron.\r\nHere,
    we provide a class of initial data for which the associated effective Hamiltonian\r\nhas
    a uniform spectral gap for all times. For such initial data, this allows us to
    extend the\r\nresults on the adiabatic theorem for the Landau–Pekar equations
    and their derivation\r\nfrom the Fröhlich model obtained in previous works to
    larger times."
acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation
  programme under the ERC Grant Agreement No 694227 (D.F. and R.S.) and under the
  Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.
  Open Access funding provided by Institute of Science and Technology (IST Austria)
article_number: '19'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Dario
  full_name: Feliciangeli, Dario
  id: 41A639AA-F248-11E8-B48F-1D18A9856A87
  last_name: Feliciangeli
  orcid: 0000-0003-0754-8530
- first_name: Simone Anna Elvira
  full_name: Rademacher, Simone Anna Elvira
  id: 856966FE-A408-11E9-977E-802DE6697425
  last_name: Rademacher
  orcid: 0000-0001-5059-4466
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Feliciangeli D, Rademacher SAE, Seiringer R. Persistence of the spectral gap
    for the Landau–Pekar equations. <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:
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doi: 10.1007/s11005-020-01350-5
ec_funded: 1
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  - '000617195700001'
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  grant_number: '694227'
  name: Analysis of quantum many-body systems
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publication: Letters in Mathematical Physics
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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title: Persistence of the spectral gap for the Landau–Pekar equations
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...
---
_id: '9351'
abstract:
- lang: eng
  text: 'We consider the many-body quantum evolution of a factorized initial data,
    in the mean-field regime. We show that fluctuations around the limiting Hartree
    dynamics satisfy large deviation estimates that are consistent with central limit
    theorems that have been established in the last years. '
acknowledgement: The authors gratefully acknowledge Gérard Ben Arous for suggesting
  this kind of result. K.L.K. was partially supported by NSF CAREER Award DMS-125479
  and a Simons Sabbatical Fellowship. S.R. acknowledges funding from the European
  Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  Grant Agreement No. 754411. B. S. gratefully acknowledges partial support from the
  NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical
  and energetic properties of Bose–Einstein condensates” and from the European Research
  Council through the ERC-AdG CLaQS. Funding Open access funding provided by Institute
  of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Kay
  full_name: Kirkpatrick, Kay
  last_name: Kirkpatrick
- first_name: Simone Anna Elvira
  full_name: Rademacher, Simone Anna Elvira
  id: 856966FE-A408-11E9-977E-802DE6697425
  last_name: Rademacher
  orcid: 0000-0001-5059-4466
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
citation:
  ama: Kirkpatrick K, Rademacher SAE, Schlein B. A large deviation principle in many-body
    quantum dynamics. <i>Annales Henri Poincare</i>. 2021;22:2595-2618. doi:<a href="https://doi.org/10.1007/s00023-021-01044-1">10.1007/s00023-021-01044-1</a>
  apa: Kirkpatrick, K., Rademacher, S. A. E., &#38; Schlein, B. (2021). A large deviation
    principle in many-body quantum dynamics. <i>Annales Henri Poincare</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00023-021-01044-1">https://doi.org/10.1007/s00023-021-01044-1</a>
  chicago: Kirkpatrick, Kay, Simone Anna Elvira Rademacher, and Benjamin Schlein.
    “A Large Deviation Principle in Many-Body Quantum Dynamics.” <i>Annales Henri
    Poincare</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s00023-021-01044-1">https://doi.org/10.1007/s00023-021-01044-1</a>.
  ieee: K. Kirkpatrick, S. A. E. Rademacher, and B. Schlein, “A large deviation principle
    in many-body quantum dynamics,” <i>Annales Henri Poincare</i>, vol. 22. Springer
    Nature, pp. 2595–2618, 2021.
  ista: Kirkpatrick K, Rademacher SAE, Schlein B. 2021. A large deviation principle
    in many-body quantum dynamics. Annales Henri Poincare. 22, 2595–2618.
  mla: Kirkpatrick, Kay, et al. “A Large Deviation Principle in Many-Body Quantum
    Dynamics.” <i>Annales Henri Poincare</i>, vol. 22, Springer Nature, 2021, pp.
    2595–618, doi:<a href="https://doi.org/10.1007/s00023-021-01044-1">10.1007/s00023-021-01044-1</a>.
  short: K. Kirkpatrick, S.A.E. Rademacher, B. Schlein, Annales Henri Poincare 22
    (2021) 2595–2618.
date_created: 2021-04-25T22:01:30Z
date_published: 2021-04-08T00:00:00Z
date_updated: 2023-08-08T13:14:40Z
day: '08'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00023-021-01044-1
ec_funded: 1
external_id:
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  - '2010.13754'
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  - '000638022600001'
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month: '04'
oa: 1
oa_version: Published Version
page: 2595-2618
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: Annales Henri Poincare
publication_identifier:
  issn:
  - 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A large deviation principle in many-body quantum dynamics
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user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
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...
---
_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
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- _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
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title: The effective mass problem for the Landau-Pekar equations
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_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. <i>Letters in Mathematical Physics</i>. 2020;110:2143-2174. doi:<a
    href="https://doi.org/10.1007/s11005-020-01286-w">10.1007/s11005-020-01286-w</a>
  apa: Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting
    through singular potentials. <i>Letters in Mathematical Physics</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s11005-020-01286-w">https://doi.org/10.1007/s11005-020-01286-w</a>
  chicago: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
    through Singular Potentials.” <i>Letters in Mathematical Physics</i>. Springer
    Nature, 2020. <a href="https://doi.org/10.1007/s11005-020-01286-w">https://doi.org/10.1007/s11005-020-01286-w</a>.
  ieee: S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through
    singular potentials,” <i>Letters in Mathematical Physics</i>, 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.” <i>Letters in Mathematical Physics</i>, vol. 110,
    Springer Nature, 2020, pp. 2143–74, doi:<a href="https://doi.org/10.1007/s11005-020-01286-w">10.1007/s11005-020-01286-w</a>.
  short: S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174.
date_created: 2020-03-23T11:11:47Z
date_published: 2020-03-12T00:00:00Z
date_updated: 2023-09-05T15:14:50Z
day: '12'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-020-01286-w
ec_funded: 1
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  isi:
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oa: 1
oa_version: Published Version
page: 2143-2174
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- _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
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...