---
_id: '17154'
abstract:
- lang: eng
  text: We compute the deterministic approximation for mixed fluctuation moments of
    products of deterministic matrices and general Sobolev functions of Wigner matrices.
    Restricting to polynomials, our formulas reproduce recent results of Male et al.
    (Random Matrices Theory Appl. 11(2):2250015, 2022), showing that the underlying
    combinatorics of non-crossing partitions and annular non-crossing permutations
    continue to stay valid beyond the setting of second-order free probability theory.
    The formulas obtained further characterize the variance in the functional central
    limit theorem given in the recent companion paper (Reker in Preprint, arXiv:2204.03419,
    2023). and thus allow identifying the fluctuation around the thermal value in
    certain thermalization problems.
article_number: '10'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jana
  full_name: Reker, Jana
  id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
  last_name: Reker
citation:
  ama: Reker J. Fluctuation moments for regular functions of Wigner Matrices. <i>Mathematical
    Physics, Analysis and Geometry</i>. 2024;27(3). doi:<a href="https://doi.org/10.1007/s11040-024-09483-y">10.1007/s11040-024-09483-y</a>
  apa: Reker, J. (2024). Fluctuation moments for regular functions of Wigner Matrices.
    <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature. <a href="https://doi.org/10.1007/s11040-024-09483-y">https://doi.org/10.1007/s11040-024-09483-y</a>
  chicago: Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.”
    <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature, 2024. <a
    href="https://doi.org/10.1007/s11040-024-09483-y">https://doi.org/10.1007/s11040-024-09483-y</a>.
  ieee: J. Reker, “Fluctuation moments for regular functions of Wigner Matrices,”
    <i>Mathematical Physics, Analysis and Geometry</i>, vol. 27, no. 3. Springer Nature,
    2024.
  ista: Reker J. 2024. Fluctuation moments for regular functions of Wigner Matrices.
    Mathematical Physics, Analysis and Geometry. 27(3), 10.
  mla: Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.”
    <i>Mathematical Physics, Analysis and Geometry</i>, vol. 27, no. 3, 10, Springer
    Nature, 2024, doi:<a href="https://doi.org/10.1007/s11040-024-09483-y">10.1007/s11040-024-09483-y</a>.
  short: J. Reker, Mathematical Physics, Analysis and Geometry 27 (2024).
das_tickbox: '1'
dataavailabilitystatement: Data sharing not applicable to this article as no datasets
  were generated or analysed during the current study.
date_created: 2024-06-21T09:31:17Z
date_published: 2024-06-20T00:00:00Z
date_updated: 2026-10-16T08:35:04Z
day: '20'
ddc:
- '519'
department:
- _id: LaEr
doi: 10.1007/s11040-024-09483-y
ec_funded: 1
external_id:
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  - '2307.11029'
  isi:
  - '001251464300001'
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isi: 1
issue: '3'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
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  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
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  issn:
  - 1385-0172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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supplementarymaterial: yes
title: Fluctuation moments for regular functions of Wigner Matrices
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type: journal_article
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...
---
_id: '14192'
abstract:
- lang: eng
  text: For the Fröhlich model of the large polaron, we prove that the ground state
    energy as a function of the total momentum has a unique global minimum at momentum
    zero. This implies the non-existence of a ground state of the translation invariant
    Fröhlich Hamiltonian and thus excludes the possibility of a localization transition
    at finite coupling.
acknowledgement: D.M. and K.M. thank Robert Seiringer for helpful discussions. Open
  access funding provided by Institute of Science and Technology (IST Austria). Financial
  support from the Agence Nationale de la Recherche (ANR) through the projects ANR-17-CE40-0016,
  ANR-17-CE40-0007-01, ANR-17-EURE-0002 (J.L.) and from the European Union’s Horizon
  2020 research and innovation programme under the Maria Skłodowska-Curie grant agreement
  No. 665386 (K.M.) is gratefully acknowledged.
article_number: '17'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jonas
  full_name: Lampart, Jonas
  last_name: Lampart
- first_name: David Johannes
  full_name: Mitrouskas, David Johannes
  id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
  last_name: Mitrouskas
- first_name: Krzysztof
  full_name: Mysliwy, Krzysztof
  id: 316457FC-F248-11E8-B48F-1D18A9856A87
  last_name: Mysliwy
citation:
  ama: Lampart J, Mitrouskas DJ, Mysliwy K. On the global minimum of the energy–momentum
    relation for the polaron. <i>Mathematical Physics, Analysis and Geometry</i>.
    2023;26(3). doi:<a href="https://doi.org/10.1007/s11040-023-09460-x">10.1007/s11040-023-09460-x</a>
  apa: Lampart, J., Mitrouskas, D. J., &#38; Mysliwy, K. (2023). On the global minimum
    of the energy–momentum relation for the polaron. <i>Mathematical Physics, Analysis
    and Geometry</i>. Springer Nature. <a href="https://doi.org/10.1007/s11040-023-09460-x">https://doi.org/10.1007/s11040-023-09460-x</a>
  chicago: Lampart, Jonas, David Johannes Mitrouskas, and Krzysztof Mysliwy. “On the
    Global Minimum of the Energy–Momentum Relation for the Polaron.” <i>Mathematical
    Physics, Analysis and Geometry</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s11040-023-09460-x">https://doi.org/10.1007/s11040-023-09460-x</a>.
  ieee: J. Lampart, D. J. Mitrouskas, and K. Mysliwy, “On the global minimum of the
    energy–momentum relation for the polaron,” <i>Mathematical Physics, Analysis and
    Geometry</i>, vol. 26, no. 3. Springer Nature, 2023.
  ista: Lampart J, Mitrouskas DJ, Mysliwy K. 2023. On the global minimum of the energy–momentum
    relation for the polaron. Mathematical Physics, Analysis and Geometry. 26(3),
    17.
  mla: Lampart, Jonas, et al. “On the Global Minimum of the Energy–Momentum Relation
    for the Polaron.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 26,
    no. 3, 17, Springer Nature, 2023, doi:<a href="https://doi.org/10.1007/s11040-023-09460-x">10.1007/s11040-023-09460-x</a>.
  short: J. Lampart, D.J. Mitrouskas, K. Mysliwy, Mathematical Physics, Analysis and
    Geometry 26 (2023).
corr_author: '1'
date_created: 2023-08-22T14:09:47Z
date_published: 2023-07-26T00:00:00Z
date_updated: 2024-10-09T21:06:41Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11040-023-09460-x
external_id:
  arxiv:
  - '2206.14708'
  isi:
  - '001032992600001'
file:
- access_level: open_access
  checksum: f0941cc66cb3ed06a12ca4b7e356cfd6
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  creator: dernst
  date_created: 2023-08-23T10:59:15Z
  date_updated: 2023-08-23T10:59:15Z
  file_id: '14225'
  file_name: 2023_MathPhysics_Lampart.pdf
  file_size: 317026
  relation: main_file
  success: 1
file_date_updated: 2023-08-23T10:59:15Z
fulldoi: https://doi.org/10.1007/s11040-023-09460-x
has_accepted_license: '1'
intvolume: '        26'
isi: 1
issue: '3'
keyword:
- Geometry and Topology
- Mathematical Physics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
  eissn:
  - 1572-9656
  issn:
  - 1385-0172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the global minimum of the energy–momentum relation for the polaron
tmp:
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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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 26
year: '2023'
...
---
_id: '10623'
abstract:
- lang: eng
  text: We investigate the BCS critical temperature Tc in the high-density limit and
    derive an asymptotic formula, which strongly depends on the behavior of the interaction
    potential V on the Fermi-surface. Our results include a rigorous confirmation
    for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev
    Lett 122:157001, 2019) and identify precise conditions under which superconducting
    domes arise in BCS theory.
acknowledgement: I am very grateful to Robert Seiringer for his guidance during this
  project and for many valuable comments on an earlier version of the manuscript.
  Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions
  and comments, pointing out the reference [22] and for his involvement in a closely
  related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable
  comments on an earlier version of the manuscript and Andreas Deuchert for interesting
  discussions.
article_number: '3'
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
citation:
  ama: Henheik SJ. The BCS critical temperature at high density. <i>Mathematical Physics,
    Analysis and Geometry</i>. 2022;25(1). doi:<a href="https://doi.org/10.1007/s11040-021-09415-0">10.1007/s11040-021-09415-0</a>
  apa: Henheik, S. J. (2022). The BCS critical temperature at high density. <i>Mathematical
    Physics, Analysis and Geometry</i>. Springer Nature. <a href="https://doi.org/10.1007/s11040-021-09415-0">https://doi.org/10.1007/s11040-021-09415-0</a>
  chicago: Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” <i>Mathematical
    Physics, Analysis and Geometry</i>. Springer Nature, 2022. <a href="https://doi.org/10.1007/s11040-021-09415-0">https://doi.org/10.1007/s11040-021-09415-0</a>.
  ieee: S. J. Henheik, “The BCS critical temperature at high density,” <i>Mathematical
    Physics, Analysis and Geometry</i>, vol. 25, no. 1. Springer Nature, 2022.
  ista: Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical
    Physics, Analysis and Geometry. 25(1), 3.
  mla: Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” <i>Mathematical
    Physics, Analysis and Geometry</i>, vol. 25, no. 1, 3, Springer Nature, 2022,
    doi:<a href="https://doi.org/10.1007/s11040-021-09415-0">10.1007/s11040-021-09415-0</a>.
  short: S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).
corr_author: '1'
date_created: 2022-01-13T15:40:53Z
date_published: 2022-01-11T00:00:00Z
date_updated: 2026-07-29T13:18:16Z
day: '11'
ddc:
- '514'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11040-021-09415-0
ec_funded: 1
external_id:
  arxiv:
  - '2106.02015'
  isi:
  - '000741387600001'
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fulldoi: https://doi.org/10.1007/s11040-021-09415-0
has_accepted_license: '1'
intvolume: '        25'
isi: 1
issue: '1'
keyword:
- geometry and topology
- mathematical physics
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
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  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
  eissn:
  - 1572-9656
  issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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scopus_import: '1'
status: public
title: The BCS critical temperature at high density
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...
---
_id: '154'
abstract:
- lang: eng
  text: We give a lower bound on the ground state energy of a system of two fermions
    of one species interacting with two fermions of another species via point interactions.
    We show that there is a critical mass ratio m2 ≈ 0.58 such that the system is
    stable, i.e., the energy is bounded from below, for m∈[m2,m2−1]. So far it was
    not known whether this 2 + 2 system exhibits a stable region at all or whether
    the formation of four-body bound states causes an unbounded spectrum for all mass
    ratios, similar to the Thomas effect. Our result gives further evidence for the
    stability of the more general N + M system.
acknowledgement: Open access funding provided by Austrian Science Fund (FWF).
article_number: '19'
article_processing_charge: No
article_type: original
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. Stability of the 2+2 fermionic system with point interactions.
    <i>Mathematical Physics, Analysis and Geometry</i>. 2018;21(3). doi:<a href="https://doi.org/10.1007/s11040-018-9275-3">10.1007/s11040-018-9275-3</a>
  apa: Moser, T., &#38; Seiringer, R. (2018). Stability of the 2+2 fermionic system
    with point interactions. <i>Mathematical Physics, Analysis and Geometry</i>. Springer.
    <a href="https://doi.org/10.1007/s11040-018-9275-3">https://doi.org/10.1007/s11040-018-9275-3</a>
  chicago: Moser, Thomas, and Robert Seiringer. “Stability of the 2+2 Fermionic System
    with Point Interactions.” <i>Mathematical Physics, Analysis and Geometry</i>.
    Springer, 2018. <a href="https://doi.org/10.1007/s11040-018-9275-3">https://doi.org/10.1007/s11040-018-9275-3</a>.
  ieee: T. Moser and R. Seiringer, “Stability of the 2+2 fermionic system with point
    interactions,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 21, no.
    3. Springer, 2018.
  ista: Moser T, Seiringer R. 2018. Stability of the 2+2 fermionic system with point
    interactions. Mathematical Physics, Analysis and Geometry. 21(3), 19.
  mla: Moser, Thomas, and Robert Seiringer. “Stability of the 2+2 Fermionic System
    with Point Interactions.” <i>Mathematical Physics, Analysis and Geometry</i>,
    vol. 21, no. 3, 19, Springer, 2018, doi:<a href="https://doi.org/10.1007/s11040-018-9275-3">10.1007/s11040-018-9275-3</a>.
  short: T. Moser, R. Seiringer, Mathematical Physics, Analysis and Geometry 21 (2018).
date_created: 2018-12-11T11:44:55Z
date_published: 2018-09-01T00:00:00Z
date_updated: 2026-08-12T14:12:56Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s11040-018-9275-3
ec_funded: 1
external_id:
  isi:
  - '000439639700001'
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  file_size: 496973
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file_date_updated: 2020-07-14T12:45:01Z
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isi: 1
issue: '3'
language:
- iso: eng
month: '09'
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: 25C878CE-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P27533_N27
  name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
- _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1
  call_identifier: FWF
  name: FWF Open Access Fund
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
  eissn:
  - 1572-9656
  issn:
  - 1385-0172
publication_status: published
publisher: Springer
publist_id: '7767'
quality_controlled: '1'
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scopus_import: '1'
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title: Stability of the 2+2 fermionic system with point interactions
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type: journal_article
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...