---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20925'
abstract:
- lang: eng
  text: 'We prove normal typicality and dynamical typicality for a (centered) random
    block-band matrix model with block-dependent variances. A key feature of our model
    is that we achieve intermediate equilibration times, an aspect that has not been
    proven rigorously in any model before. Our proof builds on recently established
    concentration estimates for products of resolvents of Wigner type random matrices
    (Erdős and Riabov in Commun Math Phys 405(12): 282, 2024) and an intricate analysis
    of the deterministic approximation.'
acknowledgement: L.E. and J.H. are supported by the ERC Advanced Grant “RMTBeyond”
  No. 101020331. Moreover, J.H. acknowledges (partial) financial support by the ERC
  Consolidator Grant “ProbQuant” (jointly with the Swiss State Secretariat for Education,
  Research and Innovation). C.V. was (partially) supported by the German Academic
  Scholarship Foundation and the Deutsche Forschungsgemeinschaft (DFG, German Research
  Foundation) – TRR 352 – Project-ID 470903074. Moreover, C.V. acknowledges (partial)
  financial support by the ERC Starting Grant “FermiMath" No. 101040991 and the ERC
  Consolidator Grant “RAMBAS” No. 10104424, funded by the European Union. Open access
  funding provided by Institute of Science and Technology (IST Austria).
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- 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: Cornelia
  full_name: Vogel, Cornelia
  id: 1cd0554a-ea28-11f0-9f40-ff76440883cd
  last_name: Vogel
citation:
  ama: Erdös L, Henheik SJ, Vogel C. Normal typicality and dynamical typicality for
    a random block-band matrix model. <i>Letters in Mathematical Physics</i>. 2025;116.
    doi:<a href="https://doi.org/10.1007/s11005-025-02037-5">10.1007/s11005-025-02037-5</a>
  apa: Erdös, L., Henheik, S. J., &#38; Vogel, C. (2025). Normal typicality and dynamical
    typicality for a random block-band matrix model. <i>Letters in Mathematical Physics</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s11005-025-02037-5">https://doi.org/10.1007/s11005-025-02037-5</a>
  chicago: Erdös, László, Sven Joscha Henheik, and Cornelia Vogel. “Normal Typicality
    and Dynamical Typicality for a Random Block-Band Matrix Model.” <i>Letters in
    Mathematical Physics</i>. Springer Nature, 2025. <a href="https://doi.org/10.1007/s11005-025-02037-5">https://doi.org/10.1007/s11005-025-02037-5</a>.
  ieee: L. Erdös, S. J. Henheik, and C. Vogel, “Normal typicality and dynamical typicality
    for a random block-band matrix model,” <i>Letters in Mathematical Physics</i>,
    vol. 116. Springer Nature, 2025.
  ista: Erdös L, Henheik SJ, Vogel C. 2025. Normal typicality and dynamical typicality
    for a random block-band matrix model. Letters in Mathematical Physics. 116, 5.
  mla: Erdös, László, et al. “Normal Typicality and Dynamical Typicality for a Random
    Block-Band Matrix Model.” <i>Letters in Mathematical Physics</i>, vol. 116, 5,
    Springer Nature, 2025, doi:<a href="https://doi.org/10.1007/s11005-025-02037-5">10.1007/s11005-025-02037-5</a>.
  short: L. Erdös, S.J. Henheik, C. Vogel, Letters in Mathematical Physics 116 (2025).
corr_author: '1'
date_created: 2026-01-04T23:01:33Z
date_published: 2025-12-26T00:00:00Z
date_updated: 2026-01-05T11:22:25Z
day: '26'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s11005-025-02037-5
ec_funded: 1
external_id:
  pmid:
  - '41459414'
has_accepted_license: '1'
intvolume: '       116'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s11005-025-02037-5
month: '12'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Normal typicality and dynamical typicality for a random block-band matrix model
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: 116
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '13226'
abstract:
- lang: eng
  text: We consider the ground state and the low-energy excited states of a system
    of N identical bosons with interactions in the mean-field scaling regime. For
    the ground state, we derive a weak Edgeworth expansion for the fluctuations of
    bounded one-body operators, which yields corrections to a central limit theorem
    to any order in 1/N−−√. For suitable excited states, we show that the limiting
    distribution is a polynomial times a normal distribution, and that higher-order
    corrections are given by an Edgeworth-type expansion.
acknowledgement: "It is a pleasure to thank Martin Kolb, Simone Rademacher, Robert
  Seiringer and Stefan Teufel for helpful discussions. Moreover, we thank the referee
  for many constructive comments. L.B. gratefully acknowledges funding from the German
  Research Foundation within the Munich Center of Quantum Science and Technology (EXC
  2111) and from the European Union’s Horizon 2020 research and innovation programme
  under the Marie Skłodowska-Curie Grant Agreement No. 754411. We thank the Mathematical
  Research Institute Oberwolfach, where part of this work was done, for their hospitality.\r\nOpen
  Access funding enabled and organized by Projekt DEAL."
article_number: '77'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
  full_name: Bossmann, Lea
  id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
  last_name: Bossmann
  orcid: 0000-0002-6854-1343
- 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: Bossmann L, Petrat SP. Weak Edgeworth expansion for the mean-field Bose gas.
    <i>Letters in Mathematical Physics</i>. 2023;113(4). doi:<a href="https://doi.org/10.1007/s11005-023-01698-4">10.1007/s11005-023-01698-4</a>
  apa: Bossmann, L., &#38; Petrat, S. P. (2023). Weak Edgeworth expansion for the
    mean-field Bose gas. <i>Letters in Mathematical Physics</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s11005-023-01698-4">https://doi.org/10.1007/s11005-023-01698-4</a>
  chicago: Bossmann, Lea, and Sören P Petrat. “Weak Edgeworth Expansion for the Mean-Field
    Bose Gas.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s11005-023-01698-4">https://doi.org/10.1007/s11005-023-01698-4</a>.
  ieee: L. Bossmann and S. P. Petrat, “Weak Edgeworth expansion for the mean-field
    Bose gas,” <i>Letters in Mathematical Physics</i>, vol. 113, no. 4. Springer Nature,
    2023.
  ista: Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose
    gas. Letters in Mathematical Physics. 113(4), 77.
  mla: Bossmann, Lea, and Sören P. Petrat. “Weak Edgeworth Expansion for the Mean-Field
    Bose Gas.” <i>Letters in Mathematical Physics</i>, vol. 113, no. 4, 77, Springer
    Nature, 2023, doi:<a href="https://doi.org/10.1007/s11005-023-01698-4">10.1007/s11005-023-01698-4</a>.
  short: L. Bossmann, S.P. Petrat, Letters in Mathematical Physics 113 (2023).
corr_author: '1'
date_created: 2023-07-16T22:01:08Z
date_published: 2023-07-03T00:00:00Z
date_updated: 2025-06-25T06:20:15Z
day: '03'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-023-01698-4
ec_funded: 1
external_id:
  arxiv:
  - '2208.00199'
  isi:
  - '001022878900002'
file:
- access_level: open_access
  checksum: 995c902a989a6769fd3db456cfd41111
  content_type: application/pdf
  creator: dernst
  date_created: 2025-06-25T06:20:02Z
  date_updated: 2025-06-25T06:20:02Z
  file_id: '19898'
  file_name: 2023_LettersMathPhysics_Bossmann.pdf
  file_size: 586698
  relation: main_file
  success: 1
file_date_updated: 2025-06-25T06:20:02Z
has_accepted_license: '1'
intvolume: '       113'
isi: 1
issue: '4'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weak Edgeworth expansion for the mean-field Bose gas
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: 113
year: '2023'
...
---
_id: '12246'
abstract:
- lang: eng
  text: The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of
    a classical system of N identical charges only in terms of their one-particle
    density. We prove here a new estimate on the best constant in this inequality.
    Numerical evaluation provides the value 1.58, which is a significant improvement
    to the previously known value 1.64. The best constant has recently been shown
    to be larger than 1.44. In a second part, we prove that the constant can be reduced
    to 1.25 when the inequality is restricted to Hartree–Fock states. This is the
    first proof that the exchange term is always much lower than the full indirect
    Coulomb energy.
acknowledgement: We would like to thank David Gontier for useful advice on the numerical
  simulations. This project has received funding from the European Research Council
  (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant
  Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful
  for the hospitality of the Institut Henri Poincaré in Paris, where part of this
  work was done.
article_number: '92'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
  full_name: Lewin, Mathieu
  last_name: Lewin
- first_name: Elliott H.
  full_name: Lieb, Elliott H.
  last_name: Lieb
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Lewin M, Lieb EH, Seiringer R. Improved Lieb–Oxford bound on the indirect and
    exchange energies. <i>Letters in Mathematical Physics</i>. 2022;112(5). doi:<a
    href="https://doi.org/10.1007/s11005-022-01584-5">10.1007/s11005-022-01584-5</a>
  apa: Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2022). Improved Lieb–Oxford bound
    on the indirect and exchange energies. <i>Letters in Mathematical Physics</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s11005-022-01584-5">https://doi.org/10.1007/s11005-022-01584-5</a>
  chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford
    Bound on the Indirect and Exchange Energies.” <i>Letters in Mathematical Physics</i>.
    Springer Nature, 2022. <a href="https://doi.org/10.1007/s11005-022-01584-5">https://doi.org/10.1007/s11005-022-01584-5</a>.
  ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the
    indirect and exchange energies,” <i>Letters in Mathematical Physics</i>, vol.
    112, no. 5. Springer Nature, 2022.
  ista: Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect
    and exchange energies. Letters in Mathematical Physics. 112(5), 92.
  mla: Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange
    Energies.” <i>Letters in Mathematical Physics</i>, vol. 112, no. 5, 92, Springer
    Nature, 2022, doi:<a href="https://doi.org/10.1007/s11005-022-01584-5">10.1007/s11005-022-01584-5</a>.
  short: M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022).
date_created: 2023-01-16T09:53:54Z
date_published: 2022-09-15T00:00:00Z
date_updated: 2025-04-14T07:26:59Z
day: '15'
department:
- _id: RoSe
doi: 10.1007/s11005-022-01584-5
ec_funded: 1
external_id:
  arxiv:
  - '2203.12473'
  isi:
  - '000854762600001'
intvolume: '       112'
isi: 1
issue: '5'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2203.12473
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Improved Lieb–Oxford bound on the indirect and exchange energies
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 112
year: '2022'
...
---
_id: '10642'
abstract:
- lang: eng
  text: Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized
    but otherwise arbitrary perturbations of weakly interacting quantum spin systems
    with uniformly gapped on-site terms change the ground state of such a system only
    locally, even if they close the spectral gap. We call this a strong version of
    the local perturbations perturb locally (LPPL) principle which is known to hold
    for much more general gapped systems, but only for perturbations that do not close
    the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle
    to Hamiltonians that have the appropriate structure of gapped on-site terms and
    weak interactions only locally in some region of space. While our results are
    technically corollaries to a theorem of Yarotsky, we expect that the paradigm
    of systems with a locally gapped ground state that is completely insensitive to
    the form of the Hamiltonian elsewhere extends to other situations and has important
    physical consequences.
acknowledgement: J. H. acknowledges partial financial support by the ERC Advanced
  Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for
  very helpful comments and discussions and Jürg Fröhlich for references to the literature.
  Open Access funding enabled and organized by Projekt DEAL.
article_number: '9'
article_processing_charge: No
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: Stefan
  full_name: Teufel, Stefan
  last_name: Teufel
- first_name: Tom
  full_name: Wessel, Tom
  last_name: Wessel
citation:
  ama: Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally
    gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical
    Physics</i>. 2022;112(1). doi:<a href="https://doi.org/10.1007/s11005-021-01494-y">10.1007/s11005-021-01494-y</a>
  apa: Henheik, S. J., Teufel, S., &#38; Wessel, T. (2022). Local stability of ground
    states in locally gapped and weakly interacting quantum spin systems. <i>Letters
    in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-021-01494-y">https://doi.org/10.1007/s11005-021-01494-y</a>
  chicago: Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of
    Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.”
    <i>Letters in Mathematical Physics</i>. Springer Nature, 2022. <a href="https://doi.org/10.1007/s11005-021-01494-y">https://doi.org/10.1007/s11005-021-01494-y</a>.
  ieee: S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states
    in locally gapped and weakly interacting quantum spin systems,” <i>Letters in
    Mathematical Physics</i>, vol. 112, no. 1. Springer Nature, 2022.
  ista: Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in
    locally gapped and weakly interacting quantum spin systems. Letters in Mathematical
    Physics. 112(1), 9.
  mla: Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped
    and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>,
    vol. 112, no. 1, 9, Springer Nature, 2022, doi:<a href="https://doi.org/10.1007/s11005-021-01494-y">10.1007/s11005-021-01494-y</a>.
  short: S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).
date_created: 2022-01-18T16:18:25Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2026-04-07T12:37:10Z
day: '18'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11005-021-01494-y
ec_funded: 1
external_id:
  arxiv:
  - '2106.13780'
  isi:
  - '000744930400001'
  pmid:
  - '35125630'
file:
- access_level: open_access
  checksum: 7e8e69b76e892c305071a4736131fe18
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  date_created: 2022-01-19T09:41:14Z
  date_updated: 2022-01-19T09:41:14Z
  file_id: '10647'
  file_name: 2022_LettersMathPhys_Henheik.pdf
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  relation: main_file
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has_accepted_license: '1'
intvolume: '       112'
isi: 1
issue: '1'
keyword:
- mathematical physics
- statistical and nonlinear physics
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  record:
  - id: '19540'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Local stability of ground states in locally gapped and weakly interacting quantum
  spin systems
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: 112
year: '2022'
...
---
_id: '9121'
abstract:
- lang: eng
  text: "We show that the energy gap for the BCS gap equation is\r\nΞ=μ(8e−2+o(1))exp(π2μ−−√a)\r\nin
    the low density limit μ→0. Together with the similar result for the critical temperature
    by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in
    the low density limit, the ratio of the energy gap and critical temperature is
    a universal constant independent of the interaction potential V. The results hold
    for a class of potentials with negative scattering length a and no bound states."
acknowledgement: "Most of this work was done as part of the author’s master’s thesis.
  The author would like to thank Jan Philip Solovej for his supervision of this process.\r\nOpen
  Access funding provided by Institute of Science and Technology (IST Austria)"
article_number: '20'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- 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: Lauritsen AB. The BCS energy gap at low density. <i>Letters in Mathematical
    Physics</i>. 2021;111. doi:<a href="https://doi.org/10.1007/s11005-021-01358-5">10.1007/s11005-021-01358-5</a>
  apa: Lauritsen, A. B. (2021). The BCS energy gap at low density. <i>Letters in Mathematical
    Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-021-01358-5">https://doi.org/10.1007/s11005-021-01358-5</a>
  chicago: Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” <i>Letters
    in Mathematical Physics</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s11005-021-01358-5">https://doi.org/10.1007/s11005-021-01358-5</a>.
  ieee: A. B. Lauritsen, “The BCS energy gap at low density,” <i>Letters in Mathematical
    Physics</i>, vol. 111. Springer Nature, 2021.
  ista: Lauritsen AB. 2021. The BCS energy gap at low density. Letters in Mathematical
    Physics. 111, 20.
  mla: Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” <i>Letters
    in Mathematical Physics</i>, vol. 111, 20, Springer Nature, 2021, doi:<a href="https://doi.org/10.1007/s11005-021-01358-5">10.1007/s11005-021-01358-5</a>.
  short: A.B. Lauritsen, Letters in Mathematical Physics 111 (2021).
date_created: 2021-02-15T09:27:14Z
date_published: 2021-02-12T00:00:00Z
date_updated: 2025-04-15T06:53:09Z
day: '12'
ddc:
- '510'
department:
- _id: GradSch
doi: 10.1007/s11005-021-01358-5
external_id:
  isi:
  - '000617531900001'
file:
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  date_created: 2021-02-15T09:31:07Z
  date_updated: 2021-02-15T09:31:07Z
  file_id: '9122'
  file_name: 2021_LettersMathPhysics_Lauritsen.pdf
  file_size: 329332
  relation: main_file
  success: 1
file_date_updated: 2021-02-15T09:31:07Z
has_accepted_license: '1'
intvolume: '       111'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The BCS energy gap at low density
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 111
year: '2021'
...
---
_id: '9333'
abstract:
- lang: eng
  text: We revise a previous result about the Fröhlich dynamics in the strong coupling
    limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter
    it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα,
    where φ0 is the electron ground state of the Pekar energy functional and ξα the
    associated coherent state of the phonons, can be approximated by a global phase
    for times small compared to α2. In the present note we prove that a similar approximation
    holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons
    that is generated by an operator proportional to α−2 and quadratic in creation
    and annihilation operators. Our result implies that the electron ground state
    remains close to its initial state for times of order α2, while the phonon fluctuations
    around the coherent state ξα can be described by a time-dependent Bogoliubov transformation.
acknowledgement: 'I thank Marcel Griesemer for many interesting discussions about
  the Fröhlich polaron and also for valuable comments on this manuscript. Helpful
  discussions with Nikolai Leopold and Robert Seiringer are also gratefully acknowledged.
  This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG) through
  the Research Training Group 1838: Spectral Theory and Dynamics of Quantum Systems.
  Open Access funding enabled and organized by Projekt DEAL.'
article_number: '45'
article_processing_charge: No
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. A note on the Fröhlich dynamics in the strong coupling limit.
    <i>Letters in Mathematical Physics</i>. 2021;111. doi:<a href="https://doi.org/10.1007/s11005-021-01380-7">10.1007/s11005-021-01380-7</a>
  apa: Mitrouskas, D. J. (2021). A note on the Fröhlich dynamics in the strong coupling
    limit. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-021-01380-7">https://doi.org/10.1007/s11005-021-01380-7</a>
  chicago: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong
    Coupling Limit.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2021.
    <a href="https://doi.org/10.1007/s11005-021-01380-7">https://doi.org/10.1007/s11005-021-01380-7</a>.
  ieee: D. J. Mitrouskas, “A note on the Fröhlich dynamics in the strong coupling
    limit,” <i>Letters in Mathematical Physics</i>, vol. 111. Springer Nature, 2021.
  ista: Mitrouskas DJ. 2021. A note on the Fröhlich dynamics in the strong coupling
    limit. Letters in Mathematical Physics. 111, 45.
  mla: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong
    Coupling Limit.” <i>Letters in Mathematical Physics</i>, vol. 111, 45, Springer
    Nature, 2021, doi:<a href="https://doi.org/10.1007/s11005-021-01380-7">10.1007/s11005-021-01380-7</a>.
  short: D.J. Mitrouskas, Letters in Mathematical Physics 111 (2021).
date_created: 2021-04-18T22:01:41Z
date_published: 2021-04-05T00:00:00Z
date_updated: 2026-04-02T13:58:00Z
day: '05'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-021-01380-7
external_id:
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  - '000637359300002'
file:
- access_level: open_access
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intvolume: '       111'
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language:
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oa_version: Published Version
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A note on the Fröhlich dynamics in the strong coupling limit
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  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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 111
year: '2021'
...
---
_id: '9256'
abstract:
- lang: eng
  text: We consider the ferromagnetic quantum Heisenberg model in one dimension, for
    any spin S≥1/2. We give upper and lower bounds on the free energy, proving that
    at low temperature it is asymptotically equal to the one of an ideal Bose gas
    of magnons, as predicted by the spin-wave approximation. The trial state used
    in the upper bound yields an analogous estimate also in the case of two spatial
    dimensions, which is believed to be sharp at low temperature.
acknowledgement: "The work of MN was supported by the National Science Centre (NCN)
  Project Nr. 2016/21/D/ST1/02430. The work of RS was supported by the European Research
  Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
  (Grant Agreement No. 694227).\r\nOpen access funding provided by Institute of Science
  and Technology (IST Austria)."
article_number: '31'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Napiórkowski MM, Seiringer R. Free energy asymptotics of the quantum Heisenberg
    spin chain. <i>Letters in Mathematical Physics</i>. 2021;111(2). doi:<a href="https://doi.org/10.1007/s11005-021-01375-4">10.1007/s11005-021-01375-4</a>
  apa: Napiórkowski, M. M., &#38; Seiringer, R. (2021). Free energy asymptotics of
    the quantum Heisenberg spin chain. <i>Letters in Mathematical Physics</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s11005-021-01375-4">https://doi.org/10.1007/s11005-021-01375-4</a>
  chicago: Napiórkowski, Marcin M, and Robert Seiringer. “Free Energy Asymptotics
    of the Quantum Heisenberg Spin Chain.” <i>Letters in Mathematical Physics</i>.
    Springer Nature, 2021. <a href="https://doi.org/10.1007/s11005-021-01375-4">https://doi.org/10.1007/s11005-021-01375-4</a>.
  ieee: M. M. Napiórkowski and R. Seiringer, “Free energy asymptotics of the quantum
    Heisenberg spin chain,” <i>Letters in Mathematical Physics</i>, vol. 111, no.
    2. Springer Nature, 2021.
  ista: Napiórkowski MM, Seiringer R. 2021. Free energy asymptotics of the quantum
    Heisenberg spin chain. Letters in Mathematical Physics. 111(2), 31.
  mla: Napiórkowski, Marcin M., and Robert Seiringer. “Free Energy Asymptotics of
    the Quantum Heisenberg Spin Chain.” <i>Letters in Mathematical Physics</i>, vol.
    111, no. 2, 31, Springer Nature, 2021, doi:<a href="https://doi.org/10.1007/s11005-021-01375-4">10.1007/s11005-021-01375-4</a>.
  short: M.M. Napiórkowski, R. Seiringer, Letters in Mathematical Physics 111 (2021).
date_created: 2021-03-21T23:01:19Z
date_published: 2021-03-09T00:00:00Z
date_updated: 2026-04-02T14:06:48Z
day: '09'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-021-01375-4
external_id:
  isi:
  - '000626837400001'
  pmid:
  - '33785980'
file:
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  file_name: 2021_LettersMathPhysics_Napiorkowski.pdf
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intvolume: '       111'
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month: '03'
oa: 1
oa_version: Published Version
pmid: 1
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Free energy asymptotics of the quantum Heisenberg spin chain
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 111
year: '2021'
...
---
_id: '9225'
abstract:
- lang: eng
  text: "The Landau–Pekar equations describe the dynamics of a strongly coupled polaron.\r\nHere,
    we provide a class of initial data for which the associated effective Hamiltonian\r\nhas
    a uniform spectral gap for all times. For such initial data, this allows us to
    extend the\r\nresults on the adiabatic theorem for the Landau–Pekar equations
    and their derivation\r\nfrom the Fröhlich model obtained in previous works to
    larger times."
acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation
  programme under the ERC Grant Agreement No 694227 (D.F. and R.S.) and under the
  Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.
  Open Access funding provided by Institute of Science and Technology (IST Austria)
article_number: '19'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Dario
  full_name: Feliciangeli, Dario
  id: 41A639AA-F248-11E8-B48F-1D18A9856A87
  last_name: Feliciangeli
  orcid: 0000-0003-0754-8530
- first_name: Simone Anna Elvira
  full_name: Rademacher, Simone Anna Elvira
  id: 856966FE-A408-11E9-977E-802DE6697425
  last_name: Rademacher
  orcid: 0000-0001-5059-4466
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Feliciangeli D, Rademacher SAE, Seiringer R. Persistence of the spectral gap
    for the Landau–Pekar equations. <i>Letters in Mathematical Physics</i>. 2021;111.
    doi:<a href="https://doi.org/10.1007/s11005-020-01350-5">10.1007/s11005-020-01350-5</a>
  apa: Feliciangeli, D., Rademacher, S. A. E., &#38; Seiringer, R. (2021). Persistence
    of the spectral gap for the Landau–Pekar equations. <i>Letters in Mathematical
    Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-020-01350-5">https://doi.org/10.1007/s11005-020-01350-5</a>
  chicago: Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
    “Persistence of the Spectral Gap for the Landau–Pekar Equations.” <i>Letters in
    Mathematical Physics</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s11005-020-01350-5">https://doi.org/10.1007/s11005-020-01350-5</a>.
  ieee: D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “Persistence of the
    spectral gap for the Landau–Pekar equations,” <i>Letters in Mathematical Physics</i>,
    vol. 111. Springer Nature, 2021.
  ista: Feliciangeli D, Rademacher SAE, Seiringer R. 2021. Persistence of the spectral
    gap for the Landau–Pekar equations. Letters in Mathematical Physics. 111, 19.
  mla: Feliciangeli, Dario, et al. “Persistence of the Spectral Gap for the Landau–Pekar
    Equations.” <i>Letters in Mathematical Physics</i>, vol. 111, 19, Springer Nature,
    2021, doi:<a href="https://doi.org/10.1007/s11005-020-01350-5">10.1007/s11005-020-01350-5</a>.
  short: D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Letters in Mathematical
    Physics 111 (2021).
date_created: 2021-03-07T23:01:25Z
date_published: 2021-02-11T00:00:00Z
date_updated: 2026-04-08T06:59:49Z
day: '11'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-020-01350-5
ec_funded: 1
external_id:
  isi:
  - '000617195700001'
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  date_updated: 2021-03-09T11:44:34Z
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  file_name: 2021_LettersMathPhysics_Feliciangeli.pdf
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  success: 1
file_date_updated: 2021-03-09T11:44:34Z
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intvolume: '       111'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
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  - id: '9733'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Persistence of the spectral gap for the Landau–Pekar equations
tmp:
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  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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 111
year: '2021'
...
---
_id: '7611'
abstract:
- lang: eng
  text: We consider a system of N bosons in the limit N→∞, interacting through singular
    potentials. For initial data exhibiting Bose–Einstein condensation, the many-body
    time evolution is well approximated through a quadratic fluctuation dynamics around
    a cubic nonlinear Schrödinger equation of the condensate wave function. We show
    that these fluctuations satisfy a (multi-variate) central limit theorem.
acknowledgement: "Simone Rademacher acknowledges partial support from the NCCR SwissMAP.
  This project has received\r\nfunding from the European Union’s Horizon 2020 research
  and innovation program under the Marie\r\nSkłodowska-Curie Grant Agreement No. 754411.\r\nOpen
  access funding provided by Institute of Science and Technology (IST Austria).\r\nS.R.
  would like to thank Benjamin Schlein for many fruitful discussions."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Simone Anna Elvira
  full_name: Rademacher, Simone Anna Elvira
  id: 856966FE-A408-11E9-977E-802DE6697425
  last_name: Rademacher
  orcid: 0000-0001-5059-4466
citation:
  ama: Rademacher SAE. Central limit theorem for Bose gases interacting through singular
    potentials. <i>Letters in Mathematical Physics</i>. 2020;110:2143-2174. doi:<a
    href="https://doi.org/10.1007/s11005-020-01286-w">10.1007/s11005-020-01286-w</a>
  apa: Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting
    through singular potentials. <i>Letters in Mathematical Physics</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s11005-020-01286-w">https://doi.org/10.1007/s11005-020-01286-w</a>
  chicago: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
    through Singular Potentials.” <i>Letters in Mathematical Physics</i>. Springer
    Nature, 2020. <a href="https://doi.org/10.1007/s11005-020-01286-w">https://doi.org/10.1007/s11005-020-01286-w</a>.
  ieee: S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through
    singular potentials,” <i>Letters in Mathematical Physics</i>, vol. 110. Springer
    Nature, pp. 2143–2174, 2020.
  ista: Rademacher SAE. 2020. Central limit theorem for Bose gases interacting through
    singular potentials. Letters in Mathematical Physics. 110, 2143–2174.
  mla: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
    through Singular Potentials.” <i>Letters in Mathematical Physics</i>, vol. 110,
    Springer Nature, 2020, pp. 2143–74, doi:<a href="https://doi.org/10.1007/s11005-020-01286-w">10.1007/s11005-020-01286-w</a>.
  short: S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174.
corr_author: '1'
date_created: 2020-03-23T11:11:47Z
date_published: 2020-03-12T00:00:00Z
date_updated: 2025-04-14T07:44:03Z
day: '12'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-020-01286-w
ec_funded: 1
external_id:
  isi:
  - '000551556000006'
file:
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  checksum: 3bdd41f10ad947b67a45b98f507a7d4a
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  date_created: 2020-11-20T12:04:26Z
  date_updated: 2020-11-20T12:04:26Z
  file_id: '8784'
  file_name: 2020_LettersMathPhysics_Rademacher.pdf
  file_size: 478683
  relation: main_file
  success: 1
file_date_updated: 2020-11-20T12:04:26Z
has_accepted_license: '1'
intvolume: '       110'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 2143-2174
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Central limit theorem for Bose gases interacting through singular potentials
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 110
year: '2020'
...
---
_id: '7618'
abstract:
- lang: eng
  text: 'This short note aims to study quantum Hellinger distances investigated recently
    by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis
    on barycenters. We introduce the family of generalized quantum Hellinger divergences
    that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando
    mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to
    the family of maximal quantum f-divergences, and hence are jointly convex, and
    satisfy the data processing inequality. We derive a characterization of the barycenter
    of finitely many positive definite operators for these generalized quantum Hellinger
    divergences. We note that the characterization of the barycenter as the weighted
    multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true
    in the case of commuting operators, but it is not correct in the general case. '
acknowledgement: "J. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum
  Grant for Quantum\r\nInformation Theory, No. 96 141, and by the Hungarian National
  Research, Development and Innovation\r\nOffice (NKFIH) via Grants Nos. K119442,
  K124152 and KH129601. D. Virosztek was supported by the\r\nISTFELLOW program of
  the Institute of Science and Technology Austria (Project Code IC1027FELL01),\r\nby
  the European Union’s Horizon 2020 research and innovation program under the Marie\r\nSklodowska-Curie
  Grant Agreement No. 846294, and partially supported by the Hungarian National\r\nResearch,
  Development and Innovation Office (NKFIH) via Grants Nos. K124152 and KH129601.\r\nWe
  are grateful to Milán Mosonyi for drawing our attention to Ref.’s [6,14,15,17,\r\n20,21],
  for comments on earlier versions of this paper, and for several discussions on the
  topic. We are\r\nalso grateful to Miklós Pálfia for several discussions; to László
  Erdös for his essential suggestions on the\r\nstructure and highlights of this paper,
  and for his comments on earlier versions; and to the anonymous\r\nreferee for his/her
  valuable comments and suggestions."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jozsef
  full_name: Pitrik, Jozsef
  last_name: Pitrik
- first_name: Daniel
  full_name: Virosztek, Daniel
  id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
  last_name: Virosztek
  orcid: 0000-0003-1109-5511
citation:
  ama: Pitrik J, Virosztek D. Quantum Hellinger distances revisited. <i>Letters in
    Mathematical Physics</i>. 2020;110(8):2039-2052. doi:<a href="https://doi.org/10.1007/s11005-020-01282-0">10.1007/s11005-020-01282-0</a>
  apa: Pitrik, J., &#38; Virosztek, D. (2020). Quantum Hellinger distances revisited.
    <i>Letters in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-020-01282-0">https://doi.org/10.1007/s11005-020-01282-0</a>
  chicago: Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.”
    <i>Letters in Mathematical Physics</i>. Springer Nature, 2020. <a href="https://doi.org/10.1007/s11005-020-01282-0">https://doi.org/10.1007/s11005-020-01282-0</a>.
  ieee: J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” <i>Letters
    in Mathematical Physics</i>, vol. 110, no. 8. Springer Nature, pp. 2039–2052,
    2020.
  ista: Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters
    in Mathematical Physics. 110(8), 2039–2052.
  mla: Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.”
    <i>Letters in Mathematical Physics</i>, vol. 110, no. 8, Springer Nature, 2020,
    pp. 2039–52, doi:<a href="https://doi.org/10.1007/s11005-020-01282-0">10.1007/s11005-020-01282-0</a>.
  short: J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052.
corr_author: '1'
date_created: 2020-03-25T15:57:48Z
date_published: 2020-08-01T00:00:00Z
date_updated: 2025-10-09T08:23:15Z
day: '01'
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- _id: LaEr
doi: 10.1007/s11005-020-01282-0
ec_funded: 1
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publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
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title: Quantum Hellinger distances revisited
type: journal_article
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year: '2020'
...
---
_id: '1198'
abstract:
- lang: eng
  text: We consider a model of fermions interacting via point interactions, defined
    via a certain weighted Dirichlet form. While for two particles the interaction
    corresponds to infinite scattering length, the presence of further particles effectively
    decreases the interaction strength. We show that the model becomes trivial in
    the thermodynamic limit, in the sense that the free energy density at any given
    particle density and temperature agrees with the corresponding expression for
    non-interacting particles.
acknowledgement: 'Open access funding provided by Institute of Science and Technology
  (IST Austria). '
article_processing_charge: Yes (via OA deal)
author:
- first_name: Thomas
  full_name: Moser, Thomas
  id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87
  last_name: Moser
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Moser T, Seiringer R. Triviality of a model of particles with point interactions
    in the thermodynamic limit. <i>Letters in Mathematical Physics</i>. 2017;107(3):533-552.
    doi:<a href="https://doi.org/10.1007/s11005-016-0915-x">10.1007/s11005-016-0915-x</a>
  apa: Moser, T., &#38; Seiringer, R. (2017). Triviality of a model of particles with
    point interactions in the thermodynamic limit. <i>Letters in Mathematical Physics</i>.
    Springer. <a href="https://doi.org/10.1007/s11005-016-0915-x">https://doi.org/10.1007/s11005-016-0915-x</a>
  chicago: Moser, Thomas, and Robert Seiringer. “Triviality of a Model of Particles
    with Point Interactions in the Thermodynamic Limit.” <i>Letters in Mathematical
    Physics</i>. Springer, 2017. <a href="https://doi.org/10.1007/s11005-016-0915-x">https://doi.org/10.1007/s11005-016-0915-x</a>.
  ieee: T. Moser and R. Seiringer, “Triviality of a model of particles with point
    interactions in the thermodynamic limit,” <i>Letters in Mathematical Physics</i>,
    vol. 107, no. 3. Springer, pp. 533–552, 2017.
  ista: Moser T, Seiringer R. 2017. Triviality of a model of particles with point
    interactions in the thermodynamic limit. Letters in Mathematical Physics. 107(3),
    533–552.
  mla: Moser, Thomas, and Robert Seiringer. “Triviality of a Model of Particles with
    Point Interactions in the Thermodynamic Limit.” <i>Letters in Mathematical Physics</i>,
    vol. 107, no. 3, Springer, 2017, pp. 533–52, doi:<a href="https://doi.org/10.1007/s11005-016-0915-x">10.1007/s11005-016-0915-x</a>.
  short: T. Moser, R. Seiringer, Letters in Mathematical Physics 107 (2017) 533–552.
date_created: 2018-12-11T11:50:40Z
date_published: 2017-03-01T00:00:00Z
date_updated: 2026-04-16T10:06:46Z
day: '01'
ddc:
- '510'
- '539'
department:
- _id: RoSe
doi: 10.1007/s11005-016-0915-x
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  - '000394280200007'
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month: '03'
oa: 1
oa_version: Published Version
page: ' 533 - 552'
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P27533_N27
  name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_identifier:
  issn:
  - 0377-9017
publication_status: published
publisher: Springer
publist_id: '6152'
pubrep_id: '723'
quality_controlled: '1'
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  - id: '52'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Triviality of a model of particles with point interactions in the thermodynamic
  limit
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
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---
_id: '2346'
abstract:
- lang: eng
  text: By means of a generalization of the Fefferman - de la Llave decomposition
    we derive a general lower bound on the interaction energy of one-dimensional quantum
    systems. We apply this result to a specific class of lowest Landau band wave functions.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Hainzl C, Seiringer R. Bounds on one-dimensional exchange energies with application
    to lowest Landau band quantum mechanics. <i>Letters in Mathematical Physics</i>.
    2001;55(2):133-142. doi:<a href="https://doi.org/10.1023/A:1010951905548">10.1023/A:1010951905548</a>
  apa: Hainzl, C., &#38; Seiringer, R. (2001). Bounds on one-dimensional exchange
    energies with application to lowest Landau band quantum mechanics. <i>Letters
    in Mathematical Physics</i>. Springer. <a href="https://doi.org/10.1023/A:1010951905548">https://doi.org/10.1023/A:1010951905548</a>
  chicago: Hainzl, Christian, and Robert Seiringer. “Bounds on One-Dimensional Exchange
    Energies with Application to Lowest Landau Band Quantum Mechanics.” <i>Letters
    in Mathematical Physics</i>. Springer, 2001. <a href="https://doi.org/10.1023/A:1010951905548">https://doi.org/10.1023/A:1010951905548</a>.
  ieee: C. Hainzl and R. Seiringer, “Bounds on one-dimensional exchange energies with
    application to lowest Landau band quantum mechanics,” <i>Letters in Mathematical
    Physics</i>, vol. 55, no. 2. Springer, pp. 133–142, 2001.
  ista: Hainzl C, Seiringer R. 2001. Bounds on one-dimensional exchange energies with
    application to lowest Landau band quantum mechanics. Letters in Mathematical Physics.
    55(2), 133–142.
  mla: Hainzl, Christian, and Robert Seiringer. “Bounds on One-Dimensional Exchange
    Energies with Application to Lowest Landau Band Quantum Mechanics.” <i>Letters
    in Mathematical Physics</i>, vol. 55, no. 2, Springer, 2001, pp. 133–42, doi:<a
    href="https://doi.org/10.1023/A:1010951905548">10.1023/A:1010951905548</a>.
  short: C. Hainzl, R. Seiringer, Letters in Mathematical Physics 55 (2001) 133–142.
date_created: 2018-12-11T11:57:07Z
date_published: 2001-02-01T00:00:00Z
date_updated: 2023-05-30T12:44:05Z
day: '01'
doi: 10.1023/A:1010951905548
extern: '1'
external_id:
  arxiv:
  - cond-mat/0102118
intvolume: '        55'
issue: '2'
language:
- iso: eng
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- open_access: '1'
  url: http://arxiv.org/abs/cond-mat/0102118
month: '02'
oa: 1
oa_version: Published Version
page: 133 - 142
publication: Letters in Mathematical Physics
publication_identifier:
  issn:
  - 0377-9017
publication_status: published
publisher: Springer
publist_id: '4581'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bounds on one-dimensional exchange energies with application to lowest Landau
  band quantum mechanics
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 55
year: '2001'
...
---
_id: '2723'
abstract:
- lang: eng
  text: 'The ground-state density of the Pauli operator in the case of a nonconstant
    magnetic field with constant direction is studied. It is shown that in the large
    field limit, the naturally rescaled ground-state density function is bounded from
    above by the megnetic field, and under some additional conditions, the limit density
    function is equal to the magnetic field. A restatement of this result yields an
    estimate on the density of complex orthogonal polynomials with respect to a fairly
    general weight function. We also prove a special case of the paramagnetic inequality. '
article_processing_charge: No
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: Erdös L. Ground-state density of the Pauli operator in the large field limit.
    <i>Letters in Mathematical Physics</i>. 1993;29(3):219-240. doi:<a href="https://doi.org/10.1007/BF00761110">10.1007/BF00761110</a>
  apa: Erdös, L. (1993). Ground-state density of the Pauli operator in the large field
    limit. <i>Letters in Mathematical Physics</i>. Springer. <a href="https://doi.org/10.1007/BF00761110">https://doi.org/10.1007/BF00761110</a>
  chicago: Erdös, László. “Ground-State Density of the Pauli Operator in the Large
    Field Limit.” <i>Letters in Mathematical Physics</i>. Springer, 1993. <a href="https://doi.org/10.1007/BF00761110">https://doi.org/10.1007/BF00761110</a>.
  ieee: L. Erdös, “Ground-state density of the Pauli operator in the large field limit,”
    <i>Letters in Mathematical Physics</i>, vol. 29, no. 3. Springer, pp. 219–240,
    1993.
  ista: Erdös L. 1993. Ground-state density of the Pauli operator in the large field
    limit. Letters in Mathematical Physics. 29(3), 219–240.
  mla: Erdös, László. “Ground-State Density of the Pauli Operator in the Large Field
    Limit.” <i>Letters in Mathematical Physics</i>, vol. 29, no. 3, Springer, 1993,
    pp. 219–40, doi:<a href="https://doi.org/10.1007/BF00761110">10.1007/BF00761110</a>.
  short: L. Erdös, Letters in Mathematical Physics 29 (1993) 219–240.
date_created: 2018-12-11T11:59:16Z
date_published: 1993-11-01T00:00:00Z
date_updated: 2022-03-30T15:02:00Z
day: '01'
doi: 10.1007/BF00761110
extern: '1'
intvolume: '        29'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF00761110
month: '11'
oa_version: None
page: 219 - 240
publication: Letters in Mathematical Physics
publication_identifier:
  issn:
  - 0377-9017
publication_status: published
publisher: Springer
publist_id: '4169'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ground-state density of the Pauli operator in the large field limit
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 29
year: '1993'
...