---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '19548'
abstract:
- lang: eng
  text: "We consider the BCS energy gap „.T / (essentially given by „.T / \x19 \x81.T;
    p\x16/,\r\nthe BCS order parameter) at all temperatures 0 \x14 T \x14 Tc up to
    the critical one, Tc, and show\r\nthat, in the limit of weak coupling, the ratio
    „.T /=Tc is given by a universal function of the relative temperature T =Tc. On
    the one hand, this recovers a recent result by Langmann and Triola\r\n[Phys. Rev.
    B 108 (2023), no. 10, article no. 104503] on three-dimensional s-wave superconductors
    for temperatures bounded uniformly away from Tc. On the other hand, our result
    lifts these\r\nrestrictions, as we consider arbitrary spatial dimensions d 2 ¹1;
    2; 3º, discuss superconductors\r\nwith non-zero angular momentum (primarily in
    two dimensions), and treat the perhaps physically most interesting (due to the
    occurrence of the superconducting phase transition) regime of\r\ntemperatures
    close to Tc.\r\n\r\n​\r\n ."
acknowledgement: "We thank Andreas Deuchert, Christian Hainzl, Edwin Langmann, Marius
  Lemm, Robert Seiringer, and Jan Philip Solovej for helpful discussions,\r\nand Edwin
  Langmann and Robert Seiringer for valuable comments on an earlier version of the
  manuscript.\r\nFunding. Joscha Henheik gratefully acknowledges partial financial
  support by the\r\nERC Advanced Grant “RMTBeyond” No. 101020331. Asbjørn Bækgaard
  Lauritsen\r\ngratefully acknowledges partial financial support by the Austrian Science
  Fund (FWF)\r\nthrough grant DOI 10.55776/I6427 (as part of the SFB/TRR 352).\r\n"
article_processing_charge: No
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
citation:
  ama: Henheik SJ, Lauritsen AB. Universal behavior of the BCS energy gap. <i>Journal
    of Spectral Theory</i>. 2025;15(1):305–352. doi:<a href="https://doi.org/10.4171/JST/540">10.4171/JST/540</a>
  apa: Henheik, S. J., &#38; Lauritsen, A. B. (2025). Universal behavior of the BCS
    energy gap. <i>Journal of Spectral Theory</i>. EMS Press. <a href="https://doi.org/10.4171/JST/540">https://doi.org/10.4171/JST/540</a>
  chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior
    of the BCS Energy Gap.” <i>Journal of Spectral Theory</i>. EMS Press, 2025. <a
    href="https://doi.org/10.4171/JST/540">https://doi.org/10.4171/JST/540</a>.
  ieee: S. J. Henheik and A. B. Lauritsen, “Universal behavior of the BCS energy gap,”
    <i>Journal of Spectral Theory</i>, vol. 15, no. 1. EMS Press, pp. 305–352, 2025.
  ista: Henheik SJ, Lauritsen AB. 2025. Universal behavior of the BCS energy gap.
    Journal of Spectral Theory. 15(1), 305–352.
  mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of
    the BCS Energy Gap.” <i>Journal of Spectral Theory</i>, vol. 15, no. 1, EMS Press,
    2025, pp. 305–352, doi:<a href="https://doi.org/10.4171/JST/540">10.4171/JST/540</a>.
  short: S.J. Henheik, A.B. Lauritsen, Journal of Spectral Theory 15 (2025) 305–352.
corr_author: '1'
date_created: 2025-04-11T09:19:28Z
date_published: 2025-01-09T00:00:00Z
date_updated: 2026-04-07T12:37:11Z
day: '09'
ddc:
- '500'
department:
- _id: LaEr
- _id: RoSe
doi: 10.4171/JST/540
ec_funded: 1
external_id:
  arxiv:
  - '2312.11310'
  isi:
  - '001438931600009'
file:
- access_level: open_access
  checksum: f49e06e8dba819f7ad52a202e287ebca
  content_type: application/pdf
  creator: cchlebak
  date_created: 2025-04-11T09:13:31Z
  date_updated: 2025-04-11T09:13:31Z
  file_id: '19549'
  file_name: Henheik_JSpectralTheory_2025.pdf
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file_date_updated: 2025-04-11T09:13:31Z
has_accepted_license: '1'
intvolume: '        15'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 305–352
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: Journal of Spectral Theory
publication_identifier:
  eissn:
  - 1664-0403
publication_status: published
publisher: EMS Press
quality_controlled: '1'
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    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Universal behavior of the BCS energy gap
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: 15
year: '2025'
...