---
_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. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.22
apa: Bossmann, L., Petrat, S. P., & Seiringer, R. (2021). Asymptotic expansion
of low-energy excitations for weakly interacting bosons. Forum of Mathematics,
Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.22
chicago: Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion
of Low-Energy Excitations for Weakly Interacting Bosons.” Forum of Mathematics,
Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.22.
ieee: L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy
excitations for weakly interacting bosons,” Forum of Mathematics, Sigma,
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.” Forum of Mathematics, Sigma, vol. 9, e28, Cambridge
University Press, 2021, doi:10.1017/fms.2021.22.
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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checksum: 17a3e6786d1e930cf0c14a880a6d7e92
content_type: application/pdf
creator: dernst
date_created: 2021-04-12T07:15:58Z
date_updated: 2021-04-12T07:15:58Z
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month: '03'
oa: 1
oa_version: Published Version
project:
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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
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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
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. Forum
of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38
apa: Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for
Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press.
https://doi.org/10.1017/fms.2021.38
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle
for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University
Press, 2021. https://doi.org/10.1017/fms.2021.38.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,”
Forum of Mathematics, Sigma, 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.” Forum
of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38.
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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date_updated: 2021-06-15T14:40:45Z
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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
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)
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type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
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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
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. Forum of Mathematics, Sigma. 2020;8. doi:10.1017/fms.2020.17
apa: Deuchert, A., Mayer, S., & Seiringer, R. (2020). The free energy of the
two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma.
Cambridge University Press. https://doi.org/10.1017/fms.2020.17
chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy
of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” Forum of Mathematics,
Sigma. Cambridge University Press, 2020. https://doi.org/10.1017/fms.2020.17.
ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional
dilute Bose gas. I. Lower bound,” Forum of Mathematics, Sigma, 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.” Forum of Mathematics, Sigma, vol. 8, e20, Cambridge
University Press, 2020, doi:10.1017/fms.2020.17.
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:
arxiv:
- '1910.03372'
isi:
- '000527342000001'
file:
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checksum: 8a64da99d107686997876d7cad8cfe1e
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creator: dernst
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intvolume: ' 8'
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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
publication_identifier:
eissn:
- '20505094'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
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relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound
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)
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type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 8
year: '2020'
...
---
_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
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.
Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2
apa: Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with
slow correlation decay. Forum of Mathematics, Sigma. Cambridge University
Press. https://doi.org/10.1017/fms.2019.2
chicago: Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices
with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University
Press, 2019. https://doi.org/10.1017/fms.2019.2.
ieee: L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation
decay,” Forum of Mathematics, Sigma, 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.” Forum
of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2.
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:
arxiv:
- '1705.10661'
isi:
- '000488847100001'
file:
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checksum: 933a472568221c73b2c3ce8c87bf6d15
content_type: application/pdf
creator: dernst
date_created: 2019-09-17T14:24:13Z
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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'
related_material:
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title: Random matrices with slow correlation decay
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...