---
_id: '9318'
abstract:
- lang: eng
  text: We consider a system of N bosons in the mean-field scaling regime for a class
    of interactions including the repulsive Coulomb potential. We derive an asymptotic
    expansion of the low-energy eigenstates and the corresponding energies, which
    provides corrections to Bogoliubov theory to any order in 1/N.
acknowledgement: The first author gratefully acknowledges funding from the European
  Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie
  Grant Agreement No. 754411. The third author was supported by the European Research
  Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
  (Grant Agreement No. 694227).
article_number: e28
article_processing_charge: Yes (via OA deal)
article_type: original
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
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Bossmann L, Petrat SP, Seiringer R. Asymptotic expansion of low-energy excitations
    for weakly interacting bosons. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a
    href="https://doi.org/10.1017/fms.2021.22">10.1017/fms.2021.22</a>
  apa: Bossmann, L., Petrat, S. P., &#38; Seiringer, R. (2021). Asymptotic expansion
    of low-energy excitations for weakly interacting bosons. <i>Forum of Mathematics,
    Sigma</i>. Cambridge University Press. <a href="https://doi.org/10.1017/fms.2021.22">https://doi.org/10.1017/fms.2021.22</a>
  chicago: Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion
    of Low-Energy Excitations for Weakly Interacting Bosons.” <i>Forum of Mathematics,
    Sigma</i>. Cambridge University Press, 2021. <a href="https://doi.org/10.1017/fms.2021.22">https://doi.org/10.1017/fms.2021.22</a>.
  ieee: L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy
    excitations for weakly interacting bosons,” <i>Forum of Mathematics, Sigma</i>,
    vol. 9. Cambridge University Press, 2021.
  ista: Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy
    excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28.
  mla: Bossmann, Lea, et al. “Asymptotic Expansion of Low-Energy Excitations for Weakly
    Interacting Bosons.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e28, Cambridge
    University Press, 2021, doi:<a href="https://doi.org/10.1017/fms.2021.22">10.1017/fms.2021.22</a>.
  short: L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).
date_created: 2021-04-11T22:01:15Z
date_published: 2021-03-26T00:00:00Z
date_updated: 2023-08-07T14:35:06Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1017/fms.2021.22
ec_funded: 1
external_id:
  isi:
  - '000634006900001'
file:
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language:
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month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Forum of Mathematics, Sigma
publication_identifier:
  eissn:
  - '20505094'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Asymptotic expansion of low-energy excitations for weakly interacting bosons
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 9
year: '2021'
...
---
_id: '9550'
abstract:
- lang: eng
  text: 'We prove that the energy of any eigenvector of a sum of several independent
    large Wigner matrices is equally distributed among these matrices with very high
    precision. This shows a particularly strong microcanonical form of the equipartition
    principle for quantum systems whose components are modelled by Wigner matrices. '
acknowledgement: The first author is supported in part by Hong Kong RGC Grant GRF
  16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced
  Grant RANMAT 338804. The third author is supported in part by Swedish Research Council
  Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation
article_number: e44
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Kevin
  full_name: Schnelli, Kevin
  id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
  last_name: Schnelli
  orcid: 0000-0003-0954-3231
citation:
  ama: Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. <i>Forum
    of Mathematics, Sigma</i>. 2021;9. doi:<a href="https://doi.org/10.1017/fms.2021.38">10.1017/fms.2021.38</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2021). Equipartition principle for
    Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press.
    <a href="https://doi.org/10.1017/fms.2021.38">https://doi.org/10.1017/fms.2021.38</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle
    for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University
    Press, 2021. <a href="https://doi.org/10.1017/fms.2021.38">https://doi.org/10.1017/fms.2021.38</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,”
    <i>Forum of Mathematics, Sigma</i>, vol. 9. Cambridge University Press, 2021.
  ista: Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices.
    Forum of Mathematics, Sigma. 9, e44.
  mla: Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” <i>Forum
    of Mathematics, Sigma</i>, vol. 9, e44, Cambridge University Press, 2021, doi:<a
    href="https://doi.org/10.1017/fms.2021.38">10.1017/fms.2021.38</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).
date_created: 2021-06-13T22:01:33Z
date_published: 2021-05-27T00:00:00Z
date_updated: 2023-08-08T14:03:40Z
day: '27'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2021.38
ec_funded: 1
external_id:
  arxiv:
  - '2008.07061'
  isi:
  - '000654960800001'
file:
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  checksum: 47c986578de132200d41e6d391905519
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  file_size: 483458
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file_date_updated: 2021-06-15T14:40:45Z
has_accepted_license: '1'
intvolume: '         9'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Forum of Mathematics, Sigma
publication_identifier:
  eissn:
  - '20505094'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equipartition principle for Wigner matrices
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type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 9
year: '2021'
...
---
_id: '7790'
abstract:
- lang: eng
  text: "We prove a lower bound for the free energy (per unit volume) of the two-dimensional
    Bose gas in the thermodynamic limit. We show that the free energy at density \U0001D70C
    and inverse temperature \U0001D6FD differs from the one of the noninteracting
    system by the correction term \U0001D70B\U0001D70C\U0001D70C\U0001D6FD\U0001D6FD
    . Here, is the scattering length of the interaction potential, and \U0001D6FD
    is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity.
    The result is valid in the dilute limit \U0001D70C and if \U0001D6FD\U0001D70C
    ."
article_number: e20
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Andreas
  full_name: Deuchert, Andreas
  id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
  last_name: Deuchert
  orcid: 0000-0003-3146-6746
- first_name: Simon
  full_name: Mayer, Simon
  id: 30C4630A-F248-11E8-B48F-1D18A9856A87
  last_name: Mayer
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute
    Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. 2020;8. doi:<a href="https://doi.org/10.1017/fms.2020.17">10.1017/fms.2020.17</a>
  apa: Deuchert, A., Mayer, S., &#38; Seiringer, R. (2020). The free energy of the
    two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>.
    Cambridge University Press. <a href="https://doi.org/10.1017/fms.2020.17">https://doi.org/10.1017/fms.2020.17</a>
  chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy
    of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics,
    Sigma</i>. Cambridge University Press, 2020. <a href="https://doi.org/10.1017/fms.2020.17">https://doi.org/10.1017/fms.2020.17</a>.
  ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional
    dilute Bose gas. I. Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 8.
    Cambridge University Press, 2020.
  ista: Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional
    dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20.
  mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose
    Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 8, e20, Cambridge
    University Press, 2020, doi:<a href="https://doi.org/10.1017/fms.2020.17">10.1017/fms.2020.17</a>.
  short: A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020).
date_created: 2020-05-03T22:00:48Z
date_published: 2020-03-14T00:00:00Z
date_updated: 2023-08-21T06:18:49Z
day: '14'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1017/fms.2020.17
ec_funded: 1
external_id:
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  - '1910.03372'
  isi:
  - '000527342000001'
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  date_updated: 2020-07-14T12:48:03Z
  file_id: '7797'
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  file_size: 692530
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file_date_updated: 2020-07-14T12:48:03Z
has_accepted_license: '1'
intvolume: '         8'
isi: 1
language:
- iso: eng
month: '03'
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
publication: Forum of Mathematics, Sigma
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  eissn:
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publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
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scopus_import: '1'
status: public
title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound
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  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 8
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...
---
_id: '6182'
abstract:
- lang: eng
  text: "We consider large random matrices with a general slowly decaying correlation
    among its entries. We prove universality of the local eigenvalue statistics and
    optimal local laws for the resolvent away from the spectral edges, generalizing
    the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and
    random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019),
    293–373] to allow slow correlation decay and arbitrary expectation. The main novel
    tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion."
article_number: e8
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: Torben H
  full_name: Krüger, Torben H
  id: 3020C786-F248-11E8-B48F-1D18A9856A87
  last_name: Krüger
  orcid: 0000-0002-4821-3297
- 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: Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay.
    <i>Forum of Mathematics, Sigma</i>. 2019;7. doi:<a href="https://doi.org/10.1017/fms.2019.2">10.1017/fms.2019.2</a>
  apa: Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Random matrices with
    slow correlation decay. <i>Forum of Mathematics, Sigma</i>. Cambridge University
    Press. <a href="https://doi.org/10.1017/fms.2019.2">https://doi.org/10.1017/fms.2019.2</a>
  chicago: Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices
    with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>. Cambridge University
    Press, 2019. <a href="https://doi.org/10.1017/fms.2019.2">https://doi.org/10.1017/fms.2019.2</a>.
  ieee: L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation
    decay,” <i>Forum of Mathematics, Sigma</i>, vol. 7. Cambridge University Press,
    2019.
  ista: Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation
    decay. Forum of Mathematics, Sigma. 7, e8.
  mla: Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” <i>Forum
    of Mathematics, Sigma</i>, vol. 7, e8, Cambridge University Press, 2019, doi:<a
    href="https://doi.org/10.1017/fms.2019.2">10.1017/fms.2019.2</a>.
  short: L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).
date_created: 2019-03-28T09:05:23Z
date_published: 2019-03-26T00:00:00Z
date_updated: 2023-09-07T12:54:12Z
day: '26'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2019.2
ec_funded: 1
external_id:
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  - '1705.10661'
  isi:
  - '000488847100001'
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  date_created: 2019-09-17T14:24:13Z
  date_updated: 2020-07-14T12:47:22Z
  file_id: '6883'
  file_name: 2019_Forum_Erdoes.pdf
  file_size: 1520344
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file_date_updated: 2020-07-14T12:47:22Z
has_accepted_license: '1'
intvolume: '         7'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Forum of Mathematics, Sigma
publication_identifier:
  eissn:
  - '20505094'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
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scopus_import: '1'
status: public
title: Random matrices with slow correlation decay
tmp:
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  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 7
year: '2019'
...