---
_id: '1422'
abstract:
- lang: eng
  text: We study the time-dependent Bogoliubov–de-Gennes equations for generic translation-invariant
    fermionic many-body systems. For initial states that are close to thermal equilibrium
    states at temperatures near the critical temperature, we show that the magnitude
    of the order parameter stays approximately constant in time and, in particular,
    does not follow a time-dependent Ginzburg–Landau equation, which is often employed
    as a phenomenological description and predicts a decay of the order parameter
    in time. The full non-linear structure of the equations is necessary to understand
    this behavior.
acknowledgement: 'Open access funding provided by Institute of Science and Technology
  (IST Austria). '
article_processing_charge: Yes (via OA deal)
author:
- first_name: Rupert
  full_name: Frank, Rupert
  last_name: Frank
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Frank R, Hainzl C, Schlein B, Seiringer R. Incompatibility of time-dependent
    Bogoliubov–de-Gennes and Ginzburg–Landau equations. <i>Letters in Mathematical
    Physics</i>. 2016;106(7):913-923. doi:<a href="https://doi.org/10.1007/s11005-016-0847-5">10.1007/s11005-016-0847-5</a>
  apa: Frank, R., Hainzl, C., Schlein, B., &#38; Seiringer, R. (2016). Incompatibility
    of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. <i>Letters
    in Mathematical Physics</i>. Springer. <a href="https://doi.org/10.1007/s11005-016-0847-5">https://doi.org/10.1007/s11005-016-0847-5</a>
  chicago: Frank, Rupert, Christian Hainzl, Benjamin Schlein, and Robert Seiringer.
    “Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations.”
    <i>Letters in Mathematical Physics</i>. Springer, 2016. <a href="https://doi.org/10.1007/s11005-016-0847-5">https://doi.org/10.1007/s11005-016-0847-5</a>.
  ieee: R. Frank, C. Hainzl, B. Schlein, and R. Seiringer, “Incompatibility of time-dependent
    Bogoliubov–de-Gennes and Ginzburg–Landau equations,” <i>Letters in Mathematical
    Physics</i>, vol. 106, no. 7. Springer, pp. 913–923, 2016.
  ista: Frank R, Hainzl C, Schlein B, Seiringer R. 2016. Incompatibility of time-dependent
    Bogoliubov–de-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics.
    106(7), 913–923.
  mla: Frank, Rupert, et al. “Incompatibility of Time-Dependent Bogoliubov–de-Gennes
    and Ginzburg–Landau Equations.” <i>Letters in Mathematical Physics</i>, vol. 106,
    no. 7, Springer, 2016, pp. 913–23, doi:<a href="https://doi.org/10.1007/s11005-016-0847-5">10.1007/s11005-016-0847-5</a>.
  short: R. Frank, C. Hainzl, B. Schlein, R. Seiringer, Letters in Mathematical Physics
    106 (2016) 913–923.
corr_author: '1'
date_created: 2018-12-11T11:51:56Z
date_published: 2016-07-01T00:00:00Z
date_updated: 2025-09-18T14:20:53Z
day: '01'
ddc:
- '510'
- '530'
department:
- _id: RoSe
doi: 10.1007/s11005-016-0847-5
external_id:
  isi:
  - '000378844700002'
file:
- access_level: open_access
  checksum: fb404923d8ca9a1faeb949561f26cbea
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:15:57Z
  date_updated: 2020-07-14T12:44:53Z
  file_id: '5181'
  file_name: IST-2016-591-v1+1_s11005-016-0847-5.pdf
  file_size: 458968
  relation: main_file
file_date_updated: 2020-07-14T12:44:53Z
has_accepted_license: '1'
intvolume: '       106'
isi: 1
issue: '7'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 913 - 923
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P27533_N27
  name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '5785'
pubrep_id: '591'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau
  equations
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 106
year: '2016'
...