---
OA_place: publisher
OA_type: hybrid
_id: '19660'
abstract:
- lang: eng
  text: We analyze the ground state energy of N fermions in a two-dimensional box
    interacting with an impurity particle via two-body point interactions. We show
    that for weak coupling, the ground state energy is asymptotically described by
    the polaron energy, as proposed by F. Chevy in the physics literature. The polaron
    energy is the solution of a nonlinear equation involving the Green’s function
    of the free Fermi gas and the binding energy of the two-body point interaction.
    We provide quantitative error estimates that are uniform in the thermodynamic
    limit.
acknowledgement: The author would like to thank Ulrich Linden for introducing him
  to the Fermi polaron and for his valuable contributions in the early stages of this
  project. Additionally, the author is grateful to Krzysztof Myśliwy for helpful comments.
  Open access funding provided by Institute of Science and Technology (IST Austria).
article_number: '30'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: David Johannes
  full_name: Mitrouskas, David Johannes
  id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
  last_name: Mitrouskas
citation:
  ama: Mitrouskas DJ. The weakly coupled two-dimensional Fermi polaron. <i>Archive
    for Rational Mechanics and Analysis</i>. 2025;249(3). doi:<a href="https://doi.org/10.1007/s00205-025-02098-9">10.1007/s00205-025-02098-9</a>
  apa: Mitrouskas, D. J. (2025). The weakly coupled two-dimensional Fermi polaron.
    <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-025-02098-9">https://doi.org/10.1007/s00205-025-02098-9</a>
  chicago: Mitrouskas, David Johannes. “The Weakly Coupled Two-Dimensional Fermi Polaron.”
    <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2025. <a
    href="https://doi.org/10.1007/s00205-025-02098-9">https://doi.org/10.1007/s00205-025-02098-9</a>.
  ieee: D. J. Mitrouskas, “The weakly coupled two-dimensional Fermi polaron,” <i>Archive
    for Rational Mechanics and Analysis</i>, vol. 249, no. 3. Springer Nature, 2025.
  ista: Mitrouskas DJ. 2025. The weakly coupled two-dimensional Fermi polaron. Archive
    for Rational Mechanics and Analysis. 249(3), 30.
  mla: Mitrouskas, David Johannes. “The Weakly Coupled Two-Dimensional Fermi Polaron.”
    <i>Archive for Rational Mechanics and Analysis</i>, vol. 249, no. 3, 30, Springer
    Nature, 2025, doi:<a href="https://doi.org/10.1007/s00205-025-02098-9">10.1007/s00205-025-02098-9</a>.
  short: D.J. Mitrouskas, Archive for Rational Mechanics and Analysis 249 (2025).
corr_author: '1'
date_created: 2025-05-11T22:02:37Z
date_published: 2025-06-01T00:00:00Z
date_updated: 2025-09-30T12:25:19Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00205-025-02098-9
external_id:
  isi:
  - '001482770500001'
file:
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  date_created: 2025-05-12T07:27:28Z
  date_updated: 2025-05-12T07:27:28Z
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has_accepted_license: '1'
intvolume: '       249'
isi: 1
issue: '3'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The weakly coupled two-dimensional Fermi polaron
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: 249
year: '2025'
...