---
_id: '14542'
abstract:
- lang: eng
  text: "It is a remarkable property of BCS theory that the ratio of the energy gap
    at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given
    by a universal constant, independent of the microscopic details of the fermionic
    interaction. This universality has rigorously been proven quite recently in three
    spatial dimensions and three different limiting regimes: weak coupling, low density
    and high density. The goal of this short note is to extend the universal behavior
    to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit."
acknowledgement: We thank Robert Seiringer for comments on the paper. J. H. gratefully
  acknowledges  partial  financial  support  by  the  ERC  Advanced  Grant  “RMTBeyond”No.
  101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber
  I6427.
article_number: '2360005 '
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
  full_name: Henheik, Sven Joscha
  id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
  last_name: Henheik
  orcid: 0000-0003-1106-327X
- first_name: Asbjørn Bækgaard
  full_name: Lauritsen, Asbjørn Bækgaard
  id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
  last_name: Lauritsen
  orcid: 0000-0003-4476-2288
- first_name: Barbara
  full_name: Roos, Barbara
  id: 5DA90512-D80F-11E9-8994-2E2EE6697425
  last_name: Roos
  orcid: 0000-0002-9071-5880
citation:
  ama: Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory.
    <i>Reviews in Mathematical Physics</i>. 2023. doi:<a href="https://doi.org/10.1142/s0129055x2360005x">10.1142/s0129055x2360005x</a>
  apa: Henheik, S. J., Lauritsen, A. B., &#38; Roos, B. (2023). Universality in low-dimensional
    BCS theory. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing.
    <a href="https://doi.org/10.1142/s0129055x2360005x">https://doi.org/10.1142/s0129055x2360005x</a>
  chicago: Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality
    in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>. World
    Scientific Publishing, 2023. <a href="https://doi.org/10.1142/s0129055x2360005x">https://doi.org/10.1142/s0129055x2360005x</a>.
  ieee: S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional
    BCS theory,” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing,
    2023.
  ista: Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS
    theory. Reviews in Mathematical Physics., 2360005.
  mla: Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.”
    <i>Reviews in Mathematical Physics</i>, 2360005, World Scientific Publishing,
    2023, doi:<a href="https://doi.org/10.1142/s0129055x2360005x">10.1142/s0129055x2360005x</a>.
  short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023).
date_created: 2023-11-15T23:48:14Z
date_published: 2023-10-31T00:00:00Z
date_updated: 2023-11-20T10:04:38Z
day: '31'
department:
- _id: GradSch
- _id: LaEr
- _id: RoSe
doi: 10.1142/s0129055x2360005x
ec_funded: 1
external_id:
  arxiv:
  - '2301.05621'
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1142/S0129055X2360005X
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
- _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b
  grant_number: I06427
  name: Mathematical Challenges in BCS Theory of Superconductivity
publication: Reviews in Mathematical Physics
publication_identifier:
  eissn:
  - 1793-6659
  issn:
  - 0129-055X
publication_status: epub_ahead
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Universality in low-dimensional BCS theory
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
year: '2023'
...
---
_id: '10852'
abstract:
- lang: eng
  text: ' We review old and new results on the Fröhlich polaron model. The discussion
    includes the validity of the (classical) Pekar approximation in the strong coupling
    limit, quantum corrections to this limit, as well as the divergence of the effective
    polaron mass.'
acknowledgement: This work was supported by the European Research Council (ERC) under
  the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo.
  694227).
article_number: '2060012'
article_processing_charge: No
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. The polaron at strong coupling. <i>Reviews in Mathematical Physics</i>.
    2021;33(01). doi:<a href="https://doi.org/10.1142/s0129055x20600120">10.1142/s0129055x20600120</a>
  apa: Seiringer, R. (2021). The polaron at strong coupling. <i>Reviews in Mathematical
    Physics</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/s0129055x20600120">https://doi.org/10.1142/s0129055x20600120</a>
  chicago: Seiringer, Robert. “The Polaron at Strong Coupling.” <i>Reviews in Mathematical
    Physics</i>. World Scientific Publishing, 2021. <a href="https://doi.org/10.1142/s0129055x20600120">https://doi.org/10.1142/s0129055x20600120</a>.
  ieee: R. Seiringer, “The polaron at strong coupling,” <i>Reviews in Mathematical
    Physics</i>, vol. 33, no. 01. World Scientific Publishing, 2021.
  ista: Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical
    Physics. 33(01), 2060012.
  mla: Seiringer, Robert. “The Polaron at Strong Coupling.” <i>Reviews in Mathematical
    Physics</i>, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:<a
    href="https://doi.org/10.1142/s0129055x20600120">10.1142/s0129055x20600120</a>.
  short: R. Seiringer, Reviews in Mathematical Physics 33 (2021).
date_created: 2022-03-18T08:11:34Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-09-05T16:08:02Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600120
ec_funded: 1
external_id:
  arxiv:
  - '1912.12509'
  isi:
  - '000613313200013'
intvolume: '        33'
isi: 1
issue: '01'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1912.12509
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: Reviews in Mathematical Physics
publication_identifier:
  eissn:
  - 1793-6659
  issn:
  - 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The polaron at strong coupling
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...
---
_id: '7900'
abstract:
- lang: eng
  text: Hartree–Fock theory has been justified as a mean-field approximation for fermionic
    systems. However, it suffers from some defects in predicting physical properties,
    making necessary a theory of quantum correlations. Recently, bosonization of many-body
    correlations has been rigorously justified as an upper bound on the correlation
    energy at high density with weak interactions. We review the bosonic approximation,
    deriving an effective Hamiltonian. We then show that for systems with Coulomb
    interaction this effective theory predicts collective excitations (plasmons) in
    accordance with the random phase approximation of Bohm and Pines, and with experimental
    observation.
article_number: '2060009'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Niels P
  full_name: Benedikter, Niels P
  id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
  last_name: Benedikter
  orcid: 0000-0002-1071-6091
citation:
  ama: Benedikter NP. Bosonic collective excitations in Fermi gases. <i>Reviews in
    Mathematical Physics</i>. 2021;33(1). doi:<a href="https://doi.org/10.1142/s0129055x20600090">10.1142/s0129055x20600090</a>
  apa: Benedikter, N. P. (2021). Bosonic collective excitations in Fermi gases. <i>Reviews
    in Mathematical Physics</i>. World Scientific. <a href="https://doi.org/10.1142/s0129055x20600090">https://doi.org/10.1142/s0129055x20600090</a>
  chicago: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” <i>Reviews
    in Mathematical Physics</i>. World Scientific, 2021. <a href="https://doi.org/10.1142/s0129055x20600090">https://doi.org/10.1142/s0129055x20600090</a>.
  ieee: N. P. Benedikter, “Bosonic collective excitations in Fermi gases,” <i>Reviews
    in Mathematical Physics</i>, vol. 33, no. 1. World Scientific, 2021.
  ista: Benedikter NP. 2021. Bosonic collective excitations in Fermi gases. Reviews
    in Mathematical Physics. 33(1), 2060009.
  mla: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” <i>Reviews
    in Mathematical Physics</i>, vol. 33, no. 1, 2060009, World Scientific, 2021,
    doi:<a href="https://doi.org/10.1142/s0129055x20600090">10.1142/s0129055x20600090</a>.
  short: N.P. Benedikter, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-05-28T16:47:55Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-09-05T16:07:40Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600090
ec_funded: 1
external_id:
  arxiv:
  - '1910.08190'
  isi:
  - '000613313200010'
intvolume: '        33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1910.08190
month: '01'
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: Reviews in Mathematical Physics
publication_identifier:
  eissn:
  - 1793-6659
  issn:
  - 0129-055X
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bosonic collective excitations in Fermi gases
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...