---
_id: '1889'
abstract:
- lang: eng
  text: We study translation-invariant quasi-free states for a system of fermions
    with two-particle interactions. The associated energy functional is similar to
    the BCS functional but also includes direct and exchange energies. We show that
    for suitable short-range interactions, these latter terms only lead to a renormalization
    of the chemical potential, with the usual properties of the BCS functional left
    unchanged. Our analysis thus represents a rigorous justification of part of the
    BCS approximation. We give bounds on the critical temperature below which the
    system displays superfluidity.
acknowledgement: We would like to thank Max Lein and Andreas Deuchert for valuable
  suggestions and remarks. Partial financial support by the NSERC (R.S.) is gratefully
  acknowledged.
article_number: '1450012'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gerhard
  full_name: Bräunlich, Gerhard
  last_name: Bräunlich
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Bräunlich G, Hainzl C, Seiringer R. Translation-invariant quasi-free states
    for fermionic systems and the BCS approximation. <i>Reviews in Mathematical Physics</i>.
    2014;26(7). doi:<a href="https://doi.org/10.1142/S0129055X14500123">10.1142/S0129055X14500123</a>
  apa: Bräunlich, G., Hainzl, C., &#38; Seiringer, R. (2014). Translation-invariant
    quasi-free states for fermionic systems and the BCS approximation. <i>Reviews
    in Mathematical Physics</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/S0129055X14500123">https://doi.org/10.1142/S0129055X14500123</a>
  chicago: Bräunlich, Gerhard, Christian Hainzl, and Robert Seiringer. “Translation-Invariant
    Quasi-Free States for Fermionic Systems and the BCS Approximation.” <i>Reviews
    in Mathematical Physics</i>. World Scientific Publishing, 2014. <a href="https://doi.org/10.1142/S0129055X14500123">https://doi.org/10.1142/S0129055X14500123</a>.
  ieee: G. Bräunlich, C. Hainzl, and R. Seiringer, “Translation-invariant quasi-free
    states for fermionic systems and the BCS approximation,” <i>Reviews in Mathematical
    Physics</i>, vol. 26, no. 7. World Scientific Publishing, 2014.
  ista: Bräunlich G, Hainzl C, Seiringer R. 2014. Translation-invariant quasi-free
    states for fermionic systems and the BCS approximation. Reviews in Mathematical
    Physics. 26(7), 1450012.
  mla: Bräunlich, Gerhard, et al. “Translation-Invariant Quasi-Free States for Fermionic
    Systems and the BCS Approximation.” <i>Reviews in Mathematical Physics</i>, vol.
    26, no. 7, 1450012, World Scientific Publishing, 2014, doi:<a href="https://doi.org/10.1142/S0129055X14500123">10.1142/S0129055X14500123</a>.
  short: G. Bräunlich, C. Hainzl, R. Seiringer, Reviews in Mathematical Physics 26
    (2014).
date_created: 2018-12-11T11:54:33Z
date_published: 2014-08-01T00:00:00Z
date_updated: 2025-09-29T13:07:59Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/S0129055X14500123
external_id:
  arxiv:
  - '1305.5135'
  isi:
  - '000341933500002'
intvolume: '        26'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1305.5135
month: '08'
oa: 1
oa_version: Submitted Version
publication: Reviews in Mathematical Physics
publication_status: published
publisher: World Scientific Publishing
publist_id: '5206'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Translation-invariant quasi-free states for fermionic systems and the BCS approximation
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 26
year: '2014'
...