---
_id: '14662'
abstract:
- lang: eng
  text: "We consider a class of polaron models, including the Fröhlich model, at zero
    total\r\nmomentum, and show that at sufficiently weak coupling there are no excited
    eigenvalues below\r\nthe essential spectrum."
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Seiringer R. Absence of excited eigenvalues for Fröhlich type polaron models
    at weak coupling. <i>Journal of Spectral Theory</i>. 2023;13(3):1045-1055. doi:<a
    href="https://doi.org/10.4171/JST/469">10.4171/JST/469</a>
  apa: Seiringer, R. (2023). Absence of excited eigenvalues for Fröhlich type polaron
    models at weak coupling. <i>Journal of Spectral Theory</i>. EMS Press. <a href="https://doi.org/10.4171/JST/469">https://doi.org/10.4171/JST/469</a>
  chicago: Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron
    Models at Weak Coupling.” <i>Journal of Spectral Theory</i>. EMS Press, 2023.
    <a href="https://doi.org/10.4171/JST/469">https://doi.org/10.4171/JST/469</a>.
  ieee: R. Seiringer, “Absence of excited eigenvalues for Fröhlich type polaron models
    at weak coupling,” <i>Journal of Spectral Theory</i>, vol. 13, no. 3. EMS Press,
    pp. 1045–1055, 2023.
  ista: Seiringer R. 2023. Absence of excited eigenvalues for Fröhlich type polaron
    models at weak coupling. Journal of Spectral Theory. 13(3), 1045–1055.
  mla: Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron
    Models at Weak Coupling.” <i>Journal of Spectral Theory</i>, vol. 13, no. 3, EMS
    Press, 2023, pp. 1045–55, doi:<a href="https://doi.org/10.4171/JST/469">10.4171/JST/469</a>.
  short: R. Seiringer, Journal of Spectral Theory 13 (2023) 1045–1055.
date_created: 2023-12-10T23:00:59Z
date_published: 2023-11-25T00:00:00Z
date_updated: 2023-12-11T12:12:14Z
day: '25'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.4171/JST/469
external_id:
  arxiv:
  - '2210.17123'
file:
- access_level: open_access
  checksum: 9ce96ca87d56ea9a70d2eb9a32839f8d
  content_type: application/pdf
  creator: dernst
  date_created: 2023-12-11T12:03:12Z
  date_updated: 2023-12-11T12:03:12Z
  file_id: '14677'
  file_name: 2023_JST_Seiringer.pdf
  file_size: 201513
  relation: main_file
  success: 1
file_date_updated: 2023-12-11T12:03:12Z
has_accepted_license: '1'
intvolume: '        13'
issue: '3'
language:
- iso: eng
month: '11'
oa: 1
oa_version: None
page: 1045-1055
publication: Journal of Spectral Theory
publication_identifier:
  eissn:
  - 1664-0403
  issn:
  - 1664-039X
publication_status: published
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling
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: 13
year: '2023'
...
---
_id: '13207'
abstract:
- lang: eng
  text: We consider the linear BCS equation, determining the BCS critical temperature,
    in the presence of a boundary, where Dirichlet boundary conditions are imposed.
    In the one-dimensional case with point interactions, we prove that the critical
    temperature is strictly larger than the bulk value, at least at weak coupling.
    In particular, the Cooper-pair wave function localizes near the boundary, an effect
    that cannot be modeled by effective Neumann boundary conditions on the order parameter
    as often imposed in Ginzburg–Landau theory. We also show that the relative shift
    in critical temperature vanishes if the coupling constant either goes to zero
    or to infinity.
acknowledgement: We thank Egor Babaev for encouraging us to study this problem, and
  Rupert Frank for many fruitful discussions. scussions. Funding. Funding from the
  European Union’s Horizon 2020 research and innovation programme under the ERC grant
  agreement No. 694227 (Barbara Roos and Robert Seiringer) is gratefully acknowledged.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Barbara
  full_name: Roos, Barbara
  id: 5DA90512-D80F-11E9-8994-2E2EE6697425
  last_name: Roos
  orcid: 0000-0002-9071-5880
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Hainzl C, Roos B, Seiringer R. Boundary superconductivity in the BCS model.
    <i>Journal of Spectral Theory</i>. 2023;12(4):1507–1540. doi:<a href="https://doi.org/10.4171/JST/439">10.4171/JST/439</a>
  apa: Hainzl, C., Roos, B., &#38; Seiringer, R. (2023). Boundary superconductivity
    in the BCS model. <i>Journal of Spectral Theory</i>. EMS Press. <a href="https://doi.org/10.4171/JST/439">https://doi.org/10.4171/JST/439</a>
  chicago: Hainzl, Christian, Barbara Roos, and Robert Seiringer. “Boundary Superconductivity
    in the BCS Model.” <i>Journal of Spectral Theory</i>. EMS Press, 2023. <a href="https://doi.org/10.4171/JST/439">https://doi.org/10.4171/JST/439</a>.
  ieee: C. Hainzl, B. Roos, and R. Seiringer, “Boundary superconductivity in the BCS
    model,” <i>Journal of Spectral Theory</i>, vol. 12, no. 4. EMS Press, pp. 1507–1540,
    2023.
  ista: Hainzl C, Roos B, Seiringer R. 2023. Boundary superconductivity in the BCS
    model. Journal of Spectral Theory. 12(4), 1507–1540.
  mla: Hainzl, Christian, et al. “Boundary Superconductivity in the BCS Model.” <i>Journal
    of Spectral Theory</i>, vol. 12, no. 4, EMS Press, 2023, pp. 1507–1540, doi:<a
    href="https://doi.org/10.4171/JST/439">10.4171/JST/439</a>.
  short: C. Hainzl, B. Roos, R. Seiringer, Journal of Spectral Theory 12 (2023) 1507–1540.
date_created: 2023-07-10T16:35:45Z
date_published: 2023-05-18T00:00:00Z
date_updated: 2023-10-27T10:37:29Z
day: '18'
ddc:
- '530'
department:
- _id: GradSch
- _id: RoSe
doi: 10.4171/JST/439
ec_funded: 1
external_id:
  arxiv:
  - '2201.08090'
  isi:
  - '000997933500008'
file:
- access_level: open_access
  checksum: 5501da33be010b5c81440438287584d5
  content_type: application/pdf
  creator: alisjak
  date_created: 2023-07-11T08:19:15Z
  date_updated: 2023-07-11T08:19:15Z
  file_id: '13208'
  file_name: 2023_EMS_Hainzl.pdf
  file_size: 304619
  relation: main_file
  success: 1
file_date_updated: 2023-07-11T08:19:15Z
has_accepted_license: '1'
intvolume: '        12'
isi: 1
issue: '4'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1507–1540
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Journal of Spectral Theory
publication_identifier:
  eissn:
  - 1664-0403
  issn:
  - 1664-039X
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
  record:
  - id: '14374'
    relation: dissertation_contains
    status: public
status: public
title: Boundary superconductivity in the BCS model
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: 12
year: '2023'
...