---
_id: '14343'
abstract:
- lang: eng
text: The total energy of an eigenstate in a composite quantum system tends to be
distributed equally among its constituents. We identify the quantum fluctuation
around this equipartition principle in the simplest disordered quantum system
consisting of linear combinations of Wigner matrices. As our main ingredient,
we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for
general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary
deformation.
acknowledgement: "G.C. and L.E. gratefully acknowledge many discussions with Dominik
Schröder at the preliminary stage of this project, especially his essential contribution
to identify the correct generalisation of traceless observables to the deformed
Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’
No. 101020331."
article_number: e74
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Oleksii
full_name: Kolupaiev, Oleksii
id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61
last_name: Kolupaiev
citation:
ama: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the
equipartition principle for Wigner matrices. Forum of Mathematics, Sigma.
2023;11. doi:10.1017/fms.2023.70
apa: Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (2023). Gaussian
fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics,
Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2023.70
chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev.
“Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” Forum
of Mathematics, Sigma. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.70.
ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations
in the equipartition principle for Wigner matrices,” Forum of Mathematics,
Sigma, vol. 11. Cambridge University Press, 2023.
ista: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations
in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma.
11, e74.
mla: Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle
for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 11, e74, Cambridge
University Press, 2023, doi:10.1017/fms.2023.70.
short: G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics,
Sigma 11 (2023).
date_created: 2023-09-17T22:01:09Z
date_published: 2023-08-23T00:00:00Z
date_updated: 2023-12-13T12:24:23Z
day: '23'
ddc:
- '510'
department:
- _id: LaEr
- _id: GradSch
doi: 10.1017/fms.2023.70
ec_funded: 1
external_id:
arxiv:
- '2301.05181'
isi:
- '001051980200001'
file:
- access_level: open_access
checksum: eb747420e6a88a7796fa934151957676
content_type: application/pdf
creator: dernst
date_created: 2023-09-20T11:09:35Z
date_updated: 2023-09-20T11:09:35Z
file_id: '14352'
file_name: 2023_ForumMathematics_Cipolloni.pdf
file_size: 852652
relation: main_file
success: 1
file_date_updated: 2023-09-20T11:09:35Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gaussian fluctuations in the 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)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2023'
...
---
_id: '13178'
abstract:
- lang: eng
text: We consider the large polaron described by the Fröhlich Hamiltonian and study
its energy-momentum relation defined as the lowest possible energy as a function
of the total momentum. Using a suitable family of trial states, we derive an optimal
parabolic upper bound for the energy-momentum relation in the limit of strong
coupling. The upper bound consists of a momentum independent term that agrees
with the predicted two-term expansion for the ground state energy of the strongly
coupled polaron at rest and a term that is quadratic in the momentum with coefficient
given by the inverse of twice the classical effective mass introduced by Landau
and Pekar.
acknowledgement: This research was supported by the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme grant
agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie grant agreement No. 665386
(K.M.).
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- 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
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Mitrouskas DJ, Mysliwy K, Seiringer R. Optimal parabolic upper bound for the
energy-momentum relation of a strongly coupled polaron. Forum of Mathematics.
2023;11:1-52. doi:10.1017/fms.2023.45
apa: Mitrouskas, D. J., Mysliwy, K., & Seiringer, R. (2023). Optimal parabolic
upper bound for the energy-momentum relation of a strongly coupled polaron. Forum
of Mathematics. Cambridge University Press. https://doi.org/10.1017/fms.2023.45
chicago: Mitrouskas, David Johannes, Krzysztof Mysliwy, and Robert Seiringer. “Optimal
Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.”
Forum of Mathematics. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.45.
ieee: D. J. Mitrouskas, K. Mysliwy, and R. Seiringer, “Optimal parabolic upper bound
for the energy-momentum relation of a strongly coupled polaron,” Forum of Mathematics,
vol. 11. Cambridge University Press, pp. 1–52, 2023.
ista: Mitrouskas DJ, Mysliwy K, Seiringer R. 2023. Optimal parabolic upper bound
for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics.
11, 1–52.
mla: Mitrouskas, David Johannes, et al. “Optimal Parabolic Upper Bound for the Energy-Momentum
Relation of a Strongly Coupled Polaron.” Forum of Mathematics, vol. 11,
Cambridge University Press, 2023, pp. 1–52, doi:10.1017/fms.2023.45.
short: D.J. Mitrouskas, K. Mysliwy, R. Seiringer, Forum of Mathematics 11 (2023)
1–52.
date_created: 2023-07-02T22:00:43Z
date_published: 2023-06-13T00:00:00Z
date_updated: 2023-11-02T12:30:50Z
day: '13'
ddc:
- '500'
department:
- _id: RoSe
doi: 10.1017/fms.2023.45
ec_funded: 1
external_id:
arxiv:
- '2203.02454'
isi:
- '001005008800001'
file:
- access_level: open_access
checksum: f672eb7dd015c472c9a04f1b9bf9df7d
content_type: application/pdf
creator: alisjak
date_created: 2023-07-03T10:36:25Z
date_updated: 2023-07-03T10:36:25Z
file_id: '13186'
file_name: 2023_ForumofMathematics.Sigma_Mitrouskas.pdf
file_size: 943192
relation: main_file
success: 1
file_date_updated: 2023-07-03T10:36:25Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 1-52
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Forum of Mathematics
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal parabolic upper bound for the energy-momentum relation of a strongly
coupled polaron
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2023'
...
---
_id: '14239'
abstract:
- lang: eng
text: "Given a resolution of rational singularities π:X~→X over a field of characteristic
zero, we use a Hodge-theoretic argument to prove that the image of the functor
\ Rπ∗:Db(X~)→Db(X)\r\n between bounded derived categories of coherent sheaves
generates Db(X)\r\n as a triangulated category. This gives a weak version of
the Bondal–Orlov localization conjecture [BO02], answering a question from [PS21].
The same result is established more generally for proper (not necessarily birational)
morphisms π:X~→X , with X~\r\n smooth, satisfying Rπ∗(OX~)=OX ."
acknowledgement: "We thank Agnieszka Bodzenta-Skibińska, Paolo Cascini, Wahei Hara,
Sándor Kovács, Alexander Kuznetsov, Mircea Musta ă, Nebojsa Pavic, Pavel Sechin,
and Michael Wemyss for discussions and e-mail correspondence. We also thank the
anonymous referee for the helpful comments. M.M. was supported by the Institute
of Science and Technology Austria. This project has received funding from the European
Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
grant agreement no. 101034413. E.S. was partially supported by the EPSRC grant EP/T019379/1
“Derived categories and algebraic K-theory of singularities”, and by the ERC Synergy
grant “Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler
Varieties.”\r\n\r\n"
article_number: e66
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Mirko
full_name: Mauri, Mirko
id: 2cf70c34-09c1-11ed-bd8d-c34fac206130
last_name: Mauri
- first_name: Evgeny
full_name: Shinder, Evgeny
last_name: Shinder
citation:
ama: Mauri M, Shinder E. Homological Bondal-Orlov localization conjecture for rational
singularities. Forum of Mathematics, Sigma. 2023;11. doi:10.1017/fms.2023.65
apa: Mauri, M., & Shinder, E. (2023). Homological Bondal-Orlov localization
conjecture for rational singularities. Forum of Mathematics, Sigma. Cambridge
University Press. https://doi.org/10.1017/fms.2023.65
chicago: Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization
Conjecture for Rational Singularities.” Forum of Mathematics, Sigma. Cambridge
University Press, 2023. https://doi.org/10.1017/fms.2023.65.
ieee: M. Mauri and E. Shinder, “Homological Bondal-Orlov localization conjecture
for rational singularities,” Forum of Mathematics, Sigma, vol. 11. Cambridge
University Press, 2023.
ista: Mauri M, Shinder E. 2023. Homological Bondal-Orlov localization conjecture
for rational singularities. Forum of Mathematics, Sigma. 11, e66.
mla: Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture
for Rational Singularities.” Forum of Mathematics, Sigma, vol. 11, e66,
Cambridge University Press, 2023, doi:10.1017/fms.2023.65.
short: M. Mauri, E. Shinder, Forum of Mathematics, Sigma 11 (2023).
date_created: 2023-08-27T22:01:16Z
date_published: 2023-08-03T00:00:00Z
date_updated: 2023-12-13T12:18:18Z
day: '03'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1017/fms.2023.65
ec_funded: 1
external_id:
arxiv:
- '2212.06786'
isi:
- '001041926700001'
file:
- access_level: open_access
checksum: c36241750cc5cb06890aec0ecdfee626
content_type: application/pdf
creator: dernst
date_created: 2023-09-05T06:43:11Z
date_updated: 2023-09-05T06:43:11Z
file_id: '14266'
file_name: 2023_ForumMathematics_Mauri.pdf
file_size: 280865
relation: main_file
success: 1
file_date_updated: 2023-09-05T06:43:11Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Homological Bondal-Orlov localization conjecture for rational singularities
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: 11
year: '2023'
...
---
_id: '10643'
abstract:
- lang: eng
text: "We prove a generalised super-adiabatic theorem for extended fermionic systems
assuming a spectral gap only in the bulk. More precisely, we assume that the infinite
system has a unique ground state and that the corresponding Gelfand–Naimark–Segal
Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that
a similar adiabatic theorem also holds in the bulk of finite systems up to errors
that vanish faster than any inverse power of the system size, although the corresponding
finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"
acknowledgement: J.H. acknowledges partial financial support by the ERC Advanced Grant
‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft
and the Open Access Publishing Fund of the University of Tübingen is gratefully
acknowledged.
article_number: e4
article_processing_charge: Yes
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
citation:
ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems
with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80'
apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic
limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge
University Press. https://doi.org/10.1017/fms.2021.80'
chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge
University Press, 2022. https://doi.org/10.1017/fms.2021.80.'
ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit:
Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10.
Cambridge University Press, 2022.'
ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit:
Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.'
mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol.
10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.'
short: S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).
date_created: 2022-01-18T16:18:51Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2023-08-02T13:53:11Z
day: '18'
ddc:
- '510'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1017/fms.2021.80
ec_funded: 1
external_id:
arxiv:
- '2012.15239'
isi:
- '000743615000001'
file:
- access_level: open_access
checksum: 87592a755adcef22ea590a99dc728dd3
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-19T09:27:43Z
date_updated: 2022-01-19T09:27:43Z
file_id: '10646'
file_name: 2022_ForumMathSigma_Henheik.pdf
file_size: 705323
relation: main_file
success: 1
file_date_updated: 2022-01-19T09:27:43Z
has_accepted_license: '1'
intvolume: ' 10'
isi: 1
keyword:
- computational mathematics
- discrete mathematics and combinatorics
- geometry and topology
- mathematical physics
- statistics and probability
- algebra and number theory
- theoretical computer science
- analysis
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
status: public
title: 'Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 10
year: '2022'
...
---
_id: '9583'
abstract:
- lang: eng
text: We show that for any n divisible by 3, almost all order-n Steiner triple systems
admit a decomposition of almost all their triples into disjoint perfect matchings
(that is, almost all Steiner triple systems are almost resolvable).
article_number: e39
article_processing_charge: No
article_type: original
author:
- first_name: Asaf
full_name: Ferber, Asaf
last_name: Ferber
- first_name: Matthew Alan
full_name: Kwan, Matthew Alan
id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
last_name: Kwan
orcid: 0000-0002-4003-7567
citation:
ama: Ferber A, Kwan MA. Almost all Steiner triple systems are almost resolvable.
Forum of Mathematics. 2020;8. doi:10.1017/fms.2020.29
apa: Ferber, A., & Kwan, M. A. (2020). Almost all Steiner triple systems are
almost resolvable. Forum of Mathematics. Cambridge University Press. https://doi.org/10.1017/fms.2020.29
chicago: Ferber, Asaf, and Matthew Alan Kwan. “Almost All Steiner Triple Systems
Are Almost Resolvable.” Forum of Mathematics. Cambridge University Press,
2020. https://doi.org/10.1017/fms.2020.29.
ieee: A. Ferber and M. A. Kwan, “Almost all Steiner triple systems are almost resolvable,”
Forum of Mathematics, vol. 8. Cambridge University Press, 2020.
ista: Ferber A, Kwan MA. 2020. Almost all Steiner triple systems are almost resolvable.
Forum of Mathematics. 8, e39.
mla: Ferber, Asaf, and Matthew Alan Kwan. “Almost All Steiner Triple Systems Are
Almost Resolvable.” Forum of Mathematics, vol. 8, e39, Cambridge University
Press, 2020, doi:10.1017/fms.2020.29.
short: A. Ferber, M.A. Kwan, Forum of Mathematics 8 (2020).
date_created: 2021-06-22T09:12:23Z
date_published: 2020-11-03T00:00:00Z
date_updated: 2023-02-23T14:01:48Z
day: '03'
ddc:
- '510'
doi: 10.1017/fms.2020.29
extern: '1'
external_id:
pmid:
- '1907.06744'
file:
- access_level: open_access
checksum: 5553c596bb4db0f38226a56bee9c87a1
content_type: application/pdf
creator: asandaue
date_created: 2021-06-22T09:23:59Z
date_updated: 2021-06-22T09:23:59Z
file_id: '9584'
file_name: 2020_CambridgeUniversityPress_Ferber.pdf
file_size: 601516
relation: main_file
success: 1
file_date_updated: 2021-06-22T09:23:59Z
has_accepted_license: '1'
intvolume: ' 8'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
pmid: 1
publication: Forum of Mathematics
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Almost all Steiner triple systems are almost resolvable
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: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 8
year: '2020'
...