---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22290'
abstract:
- lang: eng
  text: We introduce a multi-band BCS free energy functional and prove that for a
    multi-band superconductor the effect of inter-band coupling can only increase
    the critical temperature, irrespective of its attractive or repulsive nature and
    its strength. Further, for weak coupling and weaker inter-band coupling, we prove
    that the dependence of the increase in critical temperature on the inter-band
    coupling is (1) linear, if there are two or more equally strongly superconducting
    bands, or (2) quadratic, if there is only one dominating band.
acknowledgement: 'We would like to thank J. Lenells and R. Seiringer for their interest
  and helpful discussions, E. Babaev and Y. Yerin for useful comments about the literature,
  and the anonymous referee for their comments. J.H. gratefully acknowledges partial
  financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331 and the ERC
  Consollidator Grant “ProbQuant” (jointly with the Swiss State Secretariat for Education,
  Research and Innovation). E.L. gratefully acknowledges support from the Swedish
  Research Council, Grant No. 2023-04726. A.B.L. gratefully acknowledges partial financial
  support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as
  part of the SFB/TRR 352) and by the French State support managed by ANR under the
  France 2030 program through the MaQuI CNRS Risky and High-Impact Research programme
  (RI)^2 (grant agreement ANR-24-RRII-0001). Open access funding provided by Royal
  Institute of Technology.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
  full_name: Henheik, Sven Joscha
  id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
  last_name: Henheik
  orcid: 0000-0003-1106-327X
- first_name: Edwin
  full_name: Langmann, Edwin
  last_name: Langmann
- first_name: Asbjørn Bækgaard
  full_name: Lauritsen, Asbjørn Bækgaard
  id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
  last_name: Lauritsen
  orcid: 0000-0003-4476-2288
citation:
  ama: Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced
    critical temperatures. <i>Annales Henri Poincaré</i>. 2026. doi:<a href="https://doi.org/10.1007/s00023-026-01706-y">10.1007/s00023-026-01706-y</a>
  apa: Henheik, S. J., Langmann, E., &#38; Lauritsen, A. B. (2026). Multi-band superconductors
    have enhanced critical temperatures. <i>Annales Henri Poincaré</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s00023-026-01706-y">https://doi.org/10.1007/s00023-026-01706-y</a>
  chicago: Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band
    Superconductors Have Enhanced Critical Temperatures.” <i>Annales Henri Poincaré</i>.
    Springer Nature, 2026. <a href="https://doi.org/10.1007/s00023-026-01706-y">https://doi.org/10.1007/s00023-026-01706-y</a>.
  ieee: S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors
    have enhanced critical temperatures,” <i>Annales Henri Poincaré</i>. Springer
    Nature, 2026.
  ista: Henheik SJ, Langmann E, Lauritsen AB. 2026. Multi-band superconductors have
    enhanced critical temperatures. Annales Henri Poincaré.
  mla: Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical
    Temperatures.” <i>Annales Henri Poincaré</i>, Springer Nature, 2026, doi:<a href="https://doi.org/10.1007/s00023-026-01706-y">10.1007/s00023-026-01706-y</a>.
  short: S.J. Henheik, E. Langmann, A.B. Lauritsen, Annales Henri Poincaré (2026).
das_tickbox: '1'
dataavailabilitystatement: Data sharing is not applicable to this article as no new
  data were created or analyzed in this study.
date_created: 2026-07-13T09:42:22Z
date_published: 2026-06-29T00:00:00Z
date_updated: 2026-07-13T11:34:08Z
day: '29'
ddc:
- '500'
department:
- _id: LaEr
- _id: RoSe
doi: 10.1007/s00023-026-01706-y
ec_funded: 1
external_id:
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  - '2409.17297'
fulldoi: https://doi.org/10.1007/s00023-026-01706-y
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
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  url: https://doi.org/10.1007/s00023-026-01706-y
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
- _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b
  grant_number: I06427
  name: Mathematical Challenges in BCS Theory of Superconductivity
publication: Annales Henri Poincaré
publication_identifier:
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  issn:
  - 1424-0637
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
related_material:
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researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: not applicable
title: Multi-band superconductors have enhanced critical temperatures
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
_id: '12232'
abstract:
- lang: eng
  text: We derive a precise asymptotic formula for the density of the small singular
    values of the real Ginibre matrix ensemble shifted by a complex parameter z as
    the dimension tends to infinity. For z away from the real axis the formula coincides
    with that for the complex Ginibre ensemble we derived earlier in Cipolloni et
    al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of
    the low lying singular values we thus confirm the transition from real to complex
    Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous
    phenomenon has been well known for eigenvalues. We use the superbosonization formula
    (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the
    main contribution comes from a three dimensional saddle manifold.
acknowledgement: Open access funding provided by Swiss Federal Institute of Technology
  Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH
  Zürich Foundation.
article_processing_charge: No
article_type: original
author:
- first_name: Giorgio
  full_name: Cipolloni, Giorgio
  id: 42198EFA-F248-11E8-B48F-1D18A9856A87
  last_name: Cipolloni
  orcid: 0000-0002-4901-7992
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Dominik J
  full_name: Schröder, Dominik J
  id: 408ED176-F248-11E8-B48F-1D18A9856A87
  last_name: Schröder
  orcid: 0000-0002-2904-1856
citation:
  ama: Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the
    shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. 2022;23(11):3981-4002.
    doi:<a href="https://doi.org/10.1007/s00023-022-01188-8">10.1007/s00023-022-01188-8</a>
  apa: Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Density of small singular
    values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00023-022-01188-8">https://doi.org/10.1007/s00023-022-01188-8</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small
    Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>.
    Springer Nature, 2022. <a href="https://doi.org/10.1007/s00023-022-01188-8">https://doi.org/10.1007/s00023-022-01188-8</a>.
  ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values
    of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, vol. 23,
    no. 11. Springer Nature, pp. 3981–4002, 2022.
  ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values
    of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.
  mla: Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted
    Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>, vol. 23, no. 11, Springer
    Nature, 2022, pp. 3981–4002, doi:<a href="https://doi.org/10.1007/s00023-022-01188-8">10.1007/s00023-022-01188-8</a>.
  short: G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.
date_created: 2023-01-16T09:50:26Z
date_published: 2022-11-01T00:00:00Z
date_updated: 2023-08-04T09:33:52Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-022-01188-8
external_id:
  isi:
  - '000796323500001'
file:
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  date_created: 2023-01-27T11:06:47Z
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fulldoi: https://doi.org/10.1007/s00023-022-01188-8
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intvolume: '        23'
isi: 1
issue: '11'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 3981-4002
publication: Annales Henri Poincaré
publication_identifier:
  eissn:
  - 1424-0661
  issn:
  - 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Density of small singular values of the shifted real Ginibre ensemble
tmp:
  image: /images/cc_by.png
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  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: 23
year: '2022'
...
---
_id: '9912'
abstract:
- lang: eng
  text: "In the customary random matrix model for transport in quantum dots with M
    internal degrees of freedom coupled to a chaotic environment via \U0001D441≪\U0001D440
    channels, the density \U0001D70C of transmission eigenvalues is computed from
    a specific invariant ensemble for which explicit formula for the joint probability
    density of all eigenvalues is available. We revisit this problem in the large
    N regime allowing for (i) arbitrary ratio \U0001D719:=\U0001D441/\U0001D440≤1;
    and (ii) general distributions for the matrix elements of the Hamiltonian of the
    quantum dot. In the limit \U0001D719→0, we recover the formula for the density
    \U0001D70C that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special
    matrix ensemble. We also prove that the inverse square root singularity of the
    density at zero and full transmission in Beenakker’s formula persists for any
    \U0001D719<1 but in the borderline case \U0001D719=1 an anomalous \U0001D706−2/3
    singularity arises at zero. To access this level of generality, we develop the
    theory of global and local laws on the spectral density of a large class of noncommutative
    rational expressions in large random matrices with i.i.d. entries."
acknowledgement: The authors are very grateful to Yan Fyodorov for discussions on
  the physical background and for providing references, and to the anonymous referee
  for numerous valuable remarks.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Torben H
  full_name: Krüger, Torben H
  id: 3020C786-F248-11E8-B48F-1D18A9856A87
  last_name: Krüger
  orcid: 0000-0002-4821-3297
- first_name: Yuriy
  full_name: Nemish, Yuriy
  id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
  last_name: Nemish
  orcid: 0000-0002-7327-856X
citation:
  ama: Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative
    rational functions. <i>Annales Henri Poincaré </i>. 2021;22:4205–4269. doi:<a
    href="https://doi.org/10.1007/s00023-021-01085-6">10.1007/s00023-021-01085-6</a>
  apa: Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2021). Scattering in quantum dots
    via noncommutative rational functions. <i>Annales Henri Poincaré </i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00023-021-01085-6">https://doi.org/10.1007/s00023-021-01085-6</a>
  chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum
    Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>. Springer
    Nature, 2021. <a href="https://doi.org/10.1007/s00023-021-01085-6">https://doi.org/10.1007/s00023-021-01085-6</a>.
  ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative
    rational functions,” <i>Annales Henri Poincaré </i>, vol. 22. Springer Nature,
    pp. 4205–4269, 2021.
  ista: Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative
    rational functions. Annales Henri Poincaré . 22, 4205–4269.
  mla: Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational
    Functions.” <i>Annales Henri Poincaré </i>, vol. 22, Springer Nature, 2021, pp.
    4205–4269, doi:<a href="https://doi.org/10.1007/s00023-021-01085-6">10.1007/s00023-021-01085-6</a>.
  short: L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré  22 (2021) 4205–4269.
date_created: 2021-08-15T22:01:29Z
date_published: 2021-12-01T00:00:00Z
date_updated: 2025-04-15T08:04:59Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-021-01085-6
ec_funded: 1
external_id:
  arxiv:
  - '1911.05112'
  isi:
  - '000681531500001'
file:
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  date_updated: 2022-05-12T12:50:27Z
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isi: 1
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 4205–4269
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: 'Annales Henri Poincaré '
publication_identifier:
  eissn:
  - 1424-0661
  issn:
  - 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scattering in quantum dots via noncommutative rational functions
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: 22
year: '2021'
...
---
OA_place: publisher
OA_type: hybrid
_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.
acknowledgement: 'Open access funding provided by Institute of Science and Technology
  (IST Austria). We would like to thank Peter Pickl and Robert Seiringer for fruitful
  discussions, and the anonymous referees for their valuable comments and suggestions.
  Moreover, we would like to thank Niels Benedikter and László Erdős for helpful remarks
  about the semiclassical structure and the Schrödinger–Klein–Gordon equations. N.
  L. gratefully acknowledges financial support by the European Research Council (ERC)
  under the European Union’s Horizon 2020 research and innovation program (Grant Agreement
  No. 694227) and funding for his stay at Princeton University from the project “Effective
  One-Particle Equations for Correlated Many-Particle-(Coulomb) Systems: Derivation
  and Properties” (Project No. 318342445) of the German Research Foundation (DFG).
  S. P. gratefully acknowledges support from the German Academic Exchange Service
  (DAAD) and the National Science Foundation under Agreement No. DMS-1128155. Moreover,
  we would like to thank Princeton University and the Institute for Advanced Study
  for their hospitality. S. P. would additionally like to thank the University of
  Washington for hospitality.'
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: 2026-07-28T13:24:14Z
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
fulldoi: https://doi.org/10.1007/s00023-019-00828-w
has_accepted_license: '1'
intvolume: '        20'
isi: 1
issue: '10'
language:
- iso: eng
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
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 20
year: '2019'
...
---
_id: '2743'
abstract:
- lang: eng
  text: We consider the supersymmetric quantum mechanical system which is obtained
    by dimensionally reducing d = 6, N = 1 supersymmetric gauge theory with gauge
    group U(1) and a single charged hypermultiplet. Using the deformation method and
    ideas introduced by Porrati and Rozenberg [1], we present a detailed proof of
    the existence of a normalizable ground state for this system.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: David
  full_name: Hasler, David
  last_name: Hasler
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: 'Erdös L, Hasler D, Solovej J. Existence of the D0-D4 bound state: A detailed
    proof. <i>Annales Henri Poincare</i>. 2005;6(2):247-267. doi:<a href="https://doi.org/10.1007/s00023-005-0205-0">10.1007/s00023-005-0205-0</a>'
  apa: 'Erdös, L., Hasler, D., &#38; Solovej, J. (2005). Existence of the D0-D4 bound
    state: A detailed proof. <i>Annales Henri Poincare</i>. Birkhäuser. <a href="https://doi.org/10.1007/s00023-005-0205-0">https://doi.org/10.1007/s00023-005-0205-0</a>'
  chicago: 'Erdös, László, David Hasler, and Jan Solovej. “Existence of the D0-D4
    Bound State: A Detailed Proof.” <i>Annales Henri Poincare</i>. Birkhäuser, 2005.
    <a href="https://doi.org/10.1007/s00023-005-0205-0">https://doi.org/10.1007/s00023-005-0205-0</a>.'
  ieee: 'L. Erdös, D. Hasler, and J. Solovej, “Existence of the D0-D4 bound state:
    A detailed proof,” <i>Annales Henri Poincare</i>, vol. 6, no. 2. Birkhäuser, pp.
    247–267, 2005.'
  ista: 'Erdös L, Hasler D, Solovej J. 2005. Existence of the D0-D4 bound state: A
    detailed proof. Annales Henri Poincare. 6(2), 247–267.'
  mla: 'Erdös, László, et al. “Existence of the D0-D4 Bound State: A Detailed Proof.”
    <i>Annales Henri Poincare</i>, vol. 6, no. 2, Birkhäuser, 2005, pp. 247–67, doi:<a
    href="https://doi.org/10.1007/s00023-005-0205-0">10.1007/s00023-005-0205-0</a>.'
  short: L. Erdös, D. Hasler, J. Solovej, Annales Henri Poincare 6 (2005) 247–267.
date_created: 2018-12-11T11:59:22Z
date_published: 2005-04-01T00:00:00Z
date_updated: 2026-07-29T12:20:02Z
day: '01'
doi: 10.1007/s00023-005-0205-0
extern: '1'
external_id:
  arxiv:
  - abs/math-ph/0407020
fulldoi: https://doi.org/10.1007/s00023-005-0205-0
intvolume: '         6'
issue: '2'
language:
- iso: eng
month: '04'
oa_version: None
page: 247 - 267
publication: Annales Henri Poincare
publication_identifier:
  eissn:
  - 1424-0661
  issn:
  - 1424-0637
publication_status: published
publisher: Birkhäuser
publist_id: '4149'
status: public
title: 'Existence of the D0-D4 bound state: A detailed proof'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 6
year: '2005'
...
---
OA_place: repository
OA_type: green
_id: '2741'
abstract:
- lang: eng
  text: 'The Pauli operator describes the energy of a nonrelativistic quantum particle
    with spin 1/2 in a magnetic field and an external potential. A new Lieb-Thirring
    type inequality on the sum of the negative eigenvalues is presented. The main
    feature compared to earlier results is that in the large field regime the present
    estimate grows with the optimal (first) power of the strength of the magnetic
    field. As a byproduct of the method, we also obtain an optimal upper bound on
    the pointwise density of zero energy eigenfunctions of the Dirac operator. The
    main technical tools are: (i) a new localization scheme for the square of the
    resolvent of a general class of second order elliptic operators; (ii) a geometric
    construction of a Dirac operator with a constant magnetic field that approximates
    the original Dirac operator in a tubular neighborhood of a fixed field line. The
    errors may depend on the regularity of the magnetic field but they are uniform
    in the field strength.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: Erdös L, Solovej J. Uniform Lieb-Thirring inequality for the three-dimensional
    Pauli operator with a strong non-homogeneous magnetic field. <i>Annales Henri
    Poincare</i>. 2004;5(4):671-741. doi:<a href="https://doi.org/10.1007/s00023-004-0180-x">10.1007/s00023-004-0180-x</a>
  apa: Erdös, L., &#38; Solovej, J. (2004). Uniform Lieb-Thirring inequality for the
    three-dimensional Pauli operator with a strong non-homogeneous magnetic field.
    <i>Annales Henri Poincare</i>. Birkhäuser. <a href="https://doi.org/10.1007/s00023-004-0180-x">https://doi.org/10.1007/s00023-004-0180-x</a>
  chicago: Erdös, László, and Jan Solovej. “Uniform Lieb-Thirring Inequality for the
    Three-Dimensional Pauli Operator with a Strong Non-Homogeneous Magnetic Field.”
    <i>Annales Henri Poincare</i>. Birkhäuser, 2004. <a href="https://doi.org/10.1007/s00023-004-0180-x">https://doi.org/10.1007/s00023-004-0180-x</a>.
  ieee: L. Erdös and J. Solovej, “Uniform Lieb-Thirring inequality for the three-dimensional
    Pauli operator with a strong non-homogeneous magnetic field,” <i>Annales Henri
    Poincare</i>, vol. 5, no. 4. Birkhäuser, pp. 671–741, 2004.
  ista: Erdös L, Solovej J. 2004. Uniform Lieb-Thirring inequality for the three-dimensional
    Pauli operator with a strong non-homogeneous magnetic field. Annales Henri Poincare.
    5(4), 671–741.
  mla: Erdös, László, and Jan Solovej. “Uniform Lieb-Thirring Inequality for the Three-Dimensional
    Pauli Operator with a Strong Non-Homogeneous Magnetic Field.” <i>Annales Henri
    Poincare</i>, vol. 5, no. 4, Birkhäuser, 2004, pp. 671–741, doi:<a href="https://doi.org/10.1007/s00023-004-0180-x">10.1007/s00023-004-0180-x</a>.
  short: L. Erdös, J. Solovej, Annales Henri Poincare 5 (2004) 671–741.
date_created: 2018-12-11T11:59:21Z
date_published: 2004-08-01T00:00:00Z
date_updated: 2026-09-22T13:07:17Z
day: '01'
doi: 10.1007/s00023-004-0180-x
extern: '1'
external_id:
  arxiv:
  - '0304017'
fulldoi: https://doi.org/10.1007/s00023-004-0180-x
intvolume: '         5'
issue: '4'
language:
- iso: eng
month: '08'
oa_version: None
page: 671 - 741
publication: Annales Henri Poincare
publication_identifier:
  eissn:
  - 1424-0661
  issn:
  - 1424-0637
publication_status: published
publisher: Birkhäuser
publist_id: '4151'
status: public
title: Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with
  a strong non-homogeneous magnetic field
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 5
year: '2004'
...