---
_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'
...