---
DOAJ_listed: '1'
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22970'
abstract:
- lang: eng
  text: We study the ground state of a system of N two-dimensional trapped almost-bosonic
    anyons. This setup can equivalently be viewed as bosons interacting through long-range
    magnetic potentials generated by magnetic charges carried by each particle. These
    magnetic charges are assumed to be smeared over discs of radius R—a model known
    as extended anyons. To recover the point-like anyons perspective, we consider
    the joint limit R -> 0 as N →∞. We rigorously justify the average-field approximation
    for any radius R that decays polynomially, and even for certain exponentially
    decaying R. The average-field approximation asserts that the particles behave
    like independent, identical bosons interacting through a self-consistent magnetic
    field. Our result significantly improves upon the best-known estimates from [1,
    2], and it in particular covers radii that are much smaller than the mean interparticle
    distance. The proof strategy builds on a recent work on two-dimensional attractive
    Bose gases by Junge and the author [3].
acknowledgement: The author would like to express his sincere gratitude to Nicolas
  Rougerie for introducing him to the problem, for his hospitality, and for the precious
  discussions. The author would also like to thank Douglas Lundholm and the anonymous
  referee for their precious feedback. Partial support by the Deutsche Forschungsgemeinschaft
  (DFG, German Research Foundation) through the TRR 352 Project ID 470903074 and by
  the European Research Council through the ERC CoG RAMBAS Project Nr. 101044249 is
  acknowledged. Open access funding provided by Institute of Science and Technology
  (IST Austria).
article_number: '260'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Francois L
  full_name: Visconti, Francois L
  id: 8d897387-8b69-11f1-b3df-9a1e4632e81d
  last_name: Visconti
citation:
  ama: Visconti FL. Average-field approximation for dilute almost-bosonic anyons.
    <i>Calculus of Variations and Partial Differential Equations</i>. 2026;65(9).
    doi:<a href="https://doi.org/10.1007/s00526-026-03428-9">10.1007/s00526-026-03428-9</a>
  apa: Visconti, F. L. (2026). Average-field approximation for dilute almost-bosonic
    anyons. <i>Calculus of Variations and Partial Differential Equations</i>. Springer.
    <a href="https://doi.org/10.1007/s00526-026-03428-9">https://doi.org/10.1007/s00526-026-03428-9</a>
  chicago: Visconti, Francois L. “Average-Field Approximation for Dilute Almost-Bosonic
    Anyons.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer,
    2026. <a href="https://doi.org/10.1007/s00526-026-03428-9">https://doi.org/10.1007/s00526-026-03428-9</a>.
  ieee: F. L. Visconti, “Average-field approximation for dilute almost-bosonic anyons,”
    <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no.
    9. Springer, 2026.
  ista: Visconti FL. 2026. Average-field approximation for dilute almost-bosonic anyons.
    Calculus of Variations and Partial Differential Equations. 65(9), 260.
  mla: Visconti, Francois L. “Average-Field Approximation for Dilute Almost-Bosonic
    Anyons.” <i>Calculus of Variations and Partial Differential Equations</i>, vol.
    65, no. 9, 260, Springer, 2026, doi:<a href="https://doi.org/10.1007/s00526-026-03428-9">10.1007/s00526-026-03428-9</a>.
  short: F.L. Visconti, Calculus of Variations and Partial Differential Equations
    65 (2026).
das_tickbox: '1'
dataavailabilitystatement: Data sharing not applicable to this article as no datasets
  were generated or analysed during the current study.
date_created: 2026-09-22T05:35:39Z
date_published: 2026-09-12T00:00:00Z
date_updated: 2026-10-20T14:10:55Z
day: '12'
ddc:
- '500'
doi: 10.1007/s00526-026-03428-9
extern: '1'
external_id:
  pmid:
  - '42733399'
file:
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  date_created: 2026-10-20T14:08:18Z
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fulldoi: https://doi.org/10.1007/s00526-026-03428-9
has_accepted_license: '1'
intvolume: '        65'
issue: '9'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '09'
oa: 1
oa_version: Published Version
pmid: 1
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
  eissn:
  - 1432-0835
  issn:
  - 0944-2669
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Average-field approximation for dilute almost-bosonic anyons
tmp:
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type: journal_article
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volume: 65
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...