---
_id: '6788'
abstract:
- lang: eng
  text: We consider the Nelson model with ultraviolet cutoff, which describes the
    interaction between non-relativistic particles and a positive or zero mass quantized
    scalar field. We take the non-relativistic particles to obey Fermi statistics
    and discuss the time evolution in a mean-field limit of many fermions. In this
    case, the limit is known to be also a semiclassical limit. We prove convergence
    in terms of reduced density matrices of the many-body state to a tensor product
    of a Slater determinant with semiclassical structure and a coherent state, which
    evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Nikolai K
  full_name: Leopold, Nikolai K
  id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
  last_name: Leopold
  orcid: 0000-0002-0495-6822
- first_name: Sören P
  full_name: Petrat, Sören P
  id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
  last_name: Petrat
  orcid: 0000-0002-9166-5889
citation:
  ama: Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions.
    <i>Annales Henri Poincare</i>. 2019;20(10):3471–3508. doi:<a href="https://doi.org/10.1007/s00023-019-00828-w">10.1007/s00023-019-00828-w</a>
  apa: Leopold, N. K., &#38; Petrat, S. P. (2019). Mean-field dynamics for the Nelson
    model with fermions. <i>Annales Henri Poincare</i>. Springer Nature. <a href="https://doi.org/10.1007/s00023-019-00828-w">https://doi.org/10.1007/s00023-019-00828-w</a>
  chicago: Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson
    Model with Fermions.” <i>Annales Henri Poincare</i>. Springer Nature, 2019. <a
    href="https://doi.org/10.1007/s00023-019-00828-w">https://doi.org/10.1007/s00023-019-00828-w</a>.
  ieee: N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model
    with fermions,” <i>Annales Henri Poincare</i>, vol. 20, no. 10. Springer Nature,
    pp. 3471–3508, 2019.
  ista: Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with
    fermions. Annales Henri Poincare. 20(10), 3471–3508.
  mla: Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson
    Model with Fermions.” <i>Annales Henri Poincare</i>, vol. 20, no. 10, Springer
    Nature, 2019, pp. 3471–3508, doi:<a href="https://doi.org/10.1007/s00023-019-00828-w">10.1007/s00023-019-00828-w</a>.
  short: N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 3471–3508.
corr_author: '1'
date_created: 2019-08-11T21:59:21Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00023-019-00828-w
ec_funded: 1
external_id:
  arxiv:
  - '1807.06781'
  isi:
  - '000487036900008'
file:
- access_level: open_access
  checksum: b6dbf0d837d809293d449adf77138904
  content_type: application/pdf
  creator: dernst
  date_created: 2019-08-12T12:05:58Z
  date_updated: 2020-07-14T12:47:40Z
  file_id: '6801'
  file_name: 2019_AnnalesHenriPoincare_Leopold.pdf
  file_size: 681139
  relation: main_file
file_date_updated: 2020-07-14T12:47:40Z
has_accepted_license: '1'
intvolume: '        20'
isi: 1
issue: '10'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '10'
oa: 1
oa_version: Published Version
page: 3471–3508
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Annales Henri Poincare
publication_identifier:
  eissn:
  - 1424-0661
  issn:
  - 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mean-field dynamics for the Nelson model with fermions
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: 20
year: '2019'
...