---
APC_amount: 2320,48 EUR
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abstract:
- lang: eng
  text: A maximal realization of the two-dimensional Pauli operator, subject to Aharonov–Bohm
    magnetic field, is investigated. Contrary to the case of the Pauli operator with
    regular magnetic potentials, it is shown that both components of the Pauli operator
    are critical. Asymptotics of the weakly coupled eigenvalues, generated by electric
    (not necessarily self-adjoint) perturbations, are derived.
acknowledgement: Thanks belong to Johannes Ageskov and Matˇej Tuˇsek for helpful discussions
  on some technical details. M. F. would further like to acknowledge support for research
  on this paper from the European Unions Horizon 2020 research and innovation programme
  under the Marie Sklodowska-Curie Grant Agreement No. 101034413 as well as support
  by funding from Villum Fonden through the QMATH Centreof Excellence Grant No. 10059.
  D. K. was supported by the EXPRO Grant No.20-17749X of the Czech Science Foundation
  (GACR).
article_number: '2550011'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Marie
  full_name: Fialova, Marie
  id: e9c9844d-9e21-11ec-b482-f96fc09f7c4d
  last_name: Fialova
- first_name: David
  full_name: Krejčiřík, David
  last_name: Krejčiřík
citation:
  ama: Fialova M, Krejčiřík D. Virtual bound states of the Pauli operator with an
    Aharonov–Bohm potential. <i>Reviews in Mathematical Physics</i>. 2025;37(6). doi:<a
    href="https://doi.org/10.1142/S0129055X25500114">10.1142/S0129055X25500114</a>
  apa: Fialova, M., &#38; Krejčiřík, D. (2025). Virtual bound states of the Pauli
    operator with an Aharonov–Bohm potential. <i>Reviews in Mathematical Physics</i>.
    World Scientific Publishing. <a href="https://doi.org/10.1142/S0129055X25500114">https://doi.org/10.1142/S0129055X25500114</a>
  chicago: Fialova, Marie, and David Krejčiřík. “Virtual Bound States of the Pauli
    Operator with an Aharonov–Bohm Potential.” <i>Reviews in Mathematical Physics</i>.
    World Scientific Publishing, 2025. <a href="https://doi.org/10.1142/S0129055X25500114">https://doi.org/10.1142/S0129055X25500114</a>.
  ieee: M. Fialova and D. Krejčiřík, “Virtual bound states of the Pauli operator with
    an Aharonov–Bohm potential,” <i>Reviews in Mathematical Physics</i>, vol. 37,
    no. 6. World Scientific Publishing, 2025.
  ista: Fialova M, Krejčiřík D. 2025. Virtual bound states of the Pauli operator with
    an Aharonov–Bohm potential. Reviews in Mathematical Physics. 37(6), 2550011.
  mla: Fialova, Marie, and David Krejčiřík. “Virtual Bound States of the Pauli Operator
    with an Aharonov–Bohm Potential.” <i>Reviews in Mathematical Physics</i>, vol.
    37, no. 6, 2550011, World Scientific Publishing, 2025, doi:<a href="https://doi.org/10.1142/S0129055X25500114">10.1142/S0129055X25500114</a>.
  short: M. Fialova, D. Krejčiřík, Reviews in Mathematical Physics 37 (2025).
date_created: 2025-05-18T22:02:51Z
date_published: 2025-07-01T00:00:00Z
date_updated: 2026-05-06T13:03:25Z
day: '01'
ddc:
- '530'
- '510'
department:
- _id: RoSe
doi: 10.1142/S0129055X25500114
ec_funded: 1
external_id:
  arxiv:
  - '2501.17029'
  isi:
  - '001481012500001'
file:
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oa_version: Published Version
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publication: Reviews in Mathematical Physics
publication_identifier:
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  issn:
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publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
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status: public
title: Virtual bound states of the Pauli operator with an Aharonov–Bohm potential
tmp:
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type: journal_article
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OA_place: publisher
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abstract:
- lang: eng
  text: The Aharonov–Casher theorem is a result on the number of the so-called zero
    modes of a system described by the magnetic Pauli operator in R2. In this paper
    we address the same question for the Dirac operator on a flat two-dimensional
    manifold with boundary and Atiyah–Patodi–Singer boundary condition. More concretely
    we are interested in the plane and a disc with a finite number of circular holes
    cut out. We consider a smooth compactly supported magnetic field on the manifold
    and an arbitrary magnetic field inside the holes.
acknowledgement: "First and foremost I am grateful to Jan Philip Solovej for fruitful
  meetings during (and after) my PhD programme, when this work was done. Further I
  would like to thank Joshua Hunt, Anna Sisak, Jakub Löwit, Błażej Ruba, Volodymir
  Riabov, Lukas Schimmer and Georgios Koutentakis for valuable discussions. Many thanks
  belong to Rafael Benguria for hosting my visit, during which some of the work has
  been done. I am also grateful to Marina Prokhorova who first initiated the discussion
  of this project topic and to Annemarie Luger for her valuable comments during my
  PhD defence and in particular pointing out the qualitative difference in our two
  main results. I would like to acknowledge support for research on this paper from
  VILLUM FONDEN through the QMATH Centre of Excellence grant. nr. 10059. This project
  also received funding from the European Union’s Horizon 2020 research and innovation
  programme under the Marie Skłodowska-Curie grant agreement No 101034413. I am grateful
  to the two reviewers for reading carefully my manuscript and pointing out several
  issues contributing thus significantly to the readability and clarity of this paper.\r\nOpen
  access funding provided by Institute of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Marie
  full_name: Fialova, Marie
  id: e9c9844d-9e21-11ec-b482-f96fc09f7c4d
  last_name: Fialova
citation:
  ama: Fialova M. Aharonov–Casher theorems for Dirac operators on manifolds with boundary
    and APS boundary condition. <i>Annales Henri Poincare</i>. 2025;26:2859-2900.
    doi:<a href="https://doi.org/10.1007/s00023-024-01482-7">10.1007/s00023-024-01482-7</a>
  apa: Fialova, M. (2025). Aharonov–Casher theorems for Dirac operators on manifolds
    with boundary and APS boundary condition. <i>Annales Henri Poincare</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00023-024-01482-7">https://doi.org/10.1007/s00023-024-01482-7</a>
  chicago: Fialova, Marie. “Aharonov–Casher Theorems for Dirac Operators on Manifolds
    with Boundary and APS Boundary Condition.” <i>Annales Henri Poincare</i>. Springer
    Nature, 2025. <a href="https://doi.org/10.1007/s00023-024-01482-7">https://doi.org/10.1007/s00023-024-01482-7</a>.
  ieee: M. Fialova, “Aharonov–Casher theorems for Dirac operators on manifolds with
    boundary and APS boundary condition,” <i>Annales Henri Poincare</i>, vol. 26.
    Springer Nature, pp. 2859–2900, 2025.
  ista: Fialova M. 2025. Aharonov–Casher theorems for Dirac operators on manifolds
    with boundary and APS boundary condition. Annales Henri Poincare. 26, 2859–2900.
  mla: Fialova, Marie. “Aharonov–Casher Theorems for Dirac Operators on Manifolds
    with Boundary and APS Boundary Condition.” <i>Annales Henri Poincare</i>, vol.
    26, Springer Nature, 2025, pp. 2859–900, doi:<a href="https://doi.org/10.1007/s00023-024-01482-7">10.1007/s00023-024-01482-7</a>.
  short: M. Fialova, Annales Henri Poincare 26 (2025) 2859–2900.
corr_author: '1'
date_created: 2024-09-15T22:01:42Z
date_published: 2025-08-01T00:00:00Z
date_updated: 2025-09-30T10:22:14Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00023-024-01482-7
ec_funded: 1
external_id:
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  - '2304.13373'
  isi:
  - '001304370000001'
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  date_created: 2025-08-05T11:24:25Z
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intvolume: '        26'
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language:
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month: '08'
oa: 1
oa_version: Published Version
page: 2859-2900
project:
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publication: Annales Henri Poincare
publication_identifier:
  issn:
  - 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Aharonov–Casher theorems for Dirac operators on manifolds with boundary and
  APS boundary condition
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  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
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  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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...