---
_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
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  creator: dernst
  date_created: 2023-12-11T12:03:12Z
  date_updated: 2023-12-11T12:03:12Z
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  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'
...
---
_id: '10879'
abstract:
- lang: eng
  text: We study effects of a bounded and compactly supported perturbation on multidimensional
    continuum random Schrödinger operators in the region of complete localisation.
    Our main emphasis is on Anderson orthogonality for random Schrödinger operators.
    Among others, we prove that Anderson orthogonality does occur for Fermi energies
    in the region of complete localisation with a non-zero probability. This partially
    confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015),
    560–565]. The spectral shift function plays an important role in our analysis
    of Anderson orthogonality. We identify it with the index of the corresponding
    pair of spectral projections and explore the consequences thereof. All our results
    rely on the main technical estimate of this paper which guarantees separate exponential
    decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b.
    Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication
    operator corresponding to the indicator function of a unit cube centred about
    a∈Rd, and f is in a suitable class of functions of bounded variation with distributional
    derivative supported in the region of complete localisation for H.
acknowledgement: M.G. was supported by the DFG under grant GE 2871/1-1.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Adrian M
  full_name: Dietlein, Adrian M
  id: 317CB464-F248-11E8-B48F-1D18A9856A87
  last_name: Dietlein
- first_name: Martin
  full_name: Gebert, Martin
  last_name: Gebert
- first_name: Peter
  full_name: Müller, Peter
  last_name: Müller
citation:
  ama: Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger
    operators with applications to Anderson orthogonality and the spectral shift function.
    <i>Journal of Spectral Theory</i>. 2019;9(3):921-965. doi:<a href="https://doi.org/10.4171/jst/267">10.4171/jst/267</a>
  apa: Dietlein, A. M., Gebert, M., &#38; Müller, P. (2019). Perturbations of continuum
    random Schrödinger operators with applications to Anderson orthogonality and the
    spectral shift function. <i>Journal of Spectral Theory</i>. European Mathematical
    Society Publishing House. <a href="https://doi.org/10.4171/jst/267">https://doi.org/10.4171/jst/267</a>
  chicago: Dietlein, Adrian M, Martin Gebert, and Peter Müller. “Perturbations of
    Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality
    and the Spectral Shift Function.” <i>Journal of Spectral Theory</i>. European
    Mathematical Society Publishing House, 2019. <a href="https://doi.org/10.4171/jst/267">https://doi.org/10.4171/jst/267</a>.
  ieee: A. M. Dietlein, M. Gebert, and P. Müller, “Perturbations of continuum random
    Schrödinger operators with applications to Anderson orthogonality and the spectral
    shift function,” <i>Journal of Spectral Theory</i>, vol. 9, no. 3. European Mathematical
    Society Publishing House, pp. 921–965, 2019.
  ista: Dietlein AM, Gebert M, Müller P. 2019. Perturbations of continuum random Schrödinger
    operators with applications to Anderson orthogonality and the spectral shift function.
    Journal of Spectral Theory. 9(3), 921–965.
  mla: Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger
    Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.”
    <i>Journal of Spectral Theory</i>, vol. 9, no. 3, European Mathematical Society
    Publishing House, 2019, pp. 921–65, doi:<a href="https://doi.org/10.4171/jst/267">10.4171/jst/267</a>.
  short: A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019)
    921–965.
date_created: 2022-03-18T12:36:42Z
date_published: 2019-03-01T00:00:00Z
date_updated: 2023-09-08T11:35:31Z
day: '01'
department:
- _id: LaEr
doi: 10.4171/jst/267
external_id:
  arxiv:
  - '1701.02956'
  isi:
  - '000484709400006'
intvolume: '         9'
isi: 1
issue: '3'
keyword:
- Random Schrödinger operators
- spectral shift function
- Anderson orthogonality
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1701.02956
month: '03'
oa: 1
oa_version: Preprint
page: 921-965
publication: Journal of Spectral Theory
publication_identifier:
  issn:
  - 1664-039X
publication_status: published
publisher: European Mathematical Society Publishing House
quality_controlled: '1'
scopus_import: '1'
status: public
title: Perturbations of continuum random Schrödinger operators with applications to
  Anderson orthogonality and the spectral shift function
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 9
year: '2019'
...