---
OA_place: repository
OA_type: green
_id: '18656'
abstract:
- lang: eng
text: "We consider the time evolution of the out-of-time-ordered correlator (OTOC)
of two general observables \r\n and \r\n in a mean field chaotic quantum system
described by a random Wigner matrix as its Hamiltonian. We rigorously identify
three time regimes separated by the physically relevant scrambling and relaxation
times. The main feature of our analysis is that we express the error terms in
the optimal Schatten (tracial) norms of the observables, allowing us to track
the exact dependence of the errors on their rank. In particular, for significantly
overlapping observables with low rank the OTOC is shown to exhibit a significant
local maximum at the scrambling time, a feature that may not have been noticed
in the physics literature before. Our main tool is a novel multi-resolvent local
law with Schatten norms that unifies and improves previous local laws involving
either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf.
[11])."
acknowledgement: LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No.
101020331
article_processing_charge: No
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
citation:
ama: Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner
matrices. Advances in Theoretical and Mathematical Physics. 2024;28(6):2025-2083.
doi:10.4310/ATMP.241031013250
apa: Cipolloni, G., Erdös, L., & Henheik, S. J. (2024). Out-of-time-ordered
correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics.
International Press of Boston. https://doi.org/10.4310/ATMP.241031013250
chicago: Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered
Correlators for Wigner Matrices.” Advances in Theoretical and Mathematical
Physics. International Press of Boston, 2024. https://doi.org/10.4310/ATMP.241031013250.
ieee: G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators
for Wigner matrices,” Advances in Theoretical and Mathematical Physics,
vol. 28, no. 6. International Press of Boston, pp. 2025–2083, 2024.
ista: Cipolloni G, Erdös L, Henheik SJ. 2024. Out-of-time-ordered correlators for
Wigner matrices. Advances in Theoretical and Mathematical Physics. 28(6), 2025–2083.
mla: Cipolloni, Giorgio, et al. “Out-of-Time-Ordered Correlators for Wigner Matrices.”
Advances in Theoretical and Mathematical Physics, vol. 28, no. 6, International
Press of Boston, 2024, pp. 2025–83, doi:10.4310/ATMP.241031013250.
short: G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical
Physics 28 (2024) 2025–2083.
corr_author: '1'
das_tickbox: '1'
date_created: 2024-12-15T23:01:51Z
date_published: 2024-10-30T00:00:00Z
date_updated: 2026-07-29T13:18:17Z
day: '30'
department:
- _id: LaEr
doi: 10.4310/ATMP.241031013250
ec_funded: 1
external_id:
arxiv:
- '2402.17609'
fulldoi: https://doi.org/10.4310/ATMP.241031013250
intvolume: ' 28'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2402.17609
month: '10'
oa: 1
oa_version: Preprint
page: 2025-2083
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
eissn:
- 1095-0753
issn:
- 1095-0761
publication_status: published
publisher: International Press of Boston
quality_controlled: '1'
related_material:
record:
- id: '19540'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Out-of-time-ordered correlators for Wigner matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2024'
...
---
_id: '484'
abstract:
- lang: eng
text: We consider the dynamics of a large quantum system of N identical bosons in
3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed
0 = β < 1/3 and large N, we obtain a norm approximation to the many-body evolution
in the Nparticle Hilbert space. The leading order behaviour of the dynamics is
determined by Hartree theory while the second order is given by Bogoliubov theory.
article_processing_charge: No
arxiv: 1
author:
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
citation:
ama: Nam P, Napiórkowski MM. Bogoliubov correction to the mean-field dynamics of
interacting bosons. Advances in Theoretical and Mathematical Physics. 2017;21(3):683-738.
doi:10.4310/ATMP.2017.v21.n3.a4
apa: Nam, P., & Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field
dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics.
International Press of Boston. https://doi.org/10.4310/ATMP.2017.v21.n3.a4
chicago: Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field
Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics.
International Press of Boston, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a4.
ieee: P. Nam and M. M. Napiórkowski, “Bogoliubov correction to the mean-field dynamics
of interacting bosons,” Advances in Theoretical and Mathematical Physics,
vol. 21, no. 3. International Press of Boston, pp. 683–738, 2017.
ista: Nam P, Napiórkowski MM. 2017. Bogoliubov correction to the mean-field dynamics
of interacting bosons. Advances in Theoretical and Mathematical Physics. 21(3),
683–738.
mla: Nam, Phan, and Marcin M. Napiórkowski. “Bogoliubov Correction to the Mean-Field
Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics,
vol. 21, no. 3, International Press of Boston, 2017, pp. 683–738, doi:10.4310/ATMP.2017.v21.n3.a4.
short: P. Nam, M.M. Napiórkowski, Advances in Theoretical and Mathematical Physics
21 (2017) 683–738.
das_tickbox: '1'
date_created: 2018-12-11T11:46:43Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2026-07-06T13:34:16Z
day: '01'
department:
- _id: RoSe
doi: 10.4310/ATMP.2017.v21.n3.a4
ec_funded: 1
external_id:
arxiv:
- '1509.04631'
isi:
- '000409382300004'
fulldoi: https://doi.org/10.4310/ATMP.2017.v21.n3.a4
intvolume: ' 21'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1509.04631
month: '01'
oa: 1
oa_version: Submitted Version
page: 683 - 738
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- 1095-0761
publication_status: published
publisher: International Press of Boston
publist_id: '7336'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bogoliubov correction to the mean-field dynamics of interacting bosons
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2017'
...
---
_id: '483'
abstract:
- lang: eng
text: We prove the universality for the eigenvalue gap statistics in the bulk of
the spectrum for band matrices, in the regime where the band width is comparable
with the dimension of the matrix, W ~ N. All previous results concerning universality
of non-Gaussian random matrices are for mean-field models. By relying on a new
mean-field reduction technique, we deduce universality from quantum unique ergodicity
for band matrices.
article_processing_charge: No
arxiv: 1
author:
- first_name: Paul
full_name: Bourgade, Paul
last_name: Bourgade
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng
last_name: Yau
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band
matrices. Advances in Theoretical and Mathematical Physics. 2017;21(3):739-800.
doi:10.4310/ATMP.2017.v21.n3.a5
apa: Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a
class of random band matrices. Advances in Theoretical and Mathematical Physics.
International Press of Boston. https://doi.org/10.4310/ATMP.2017.v21.n3.a5
chicago: Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for
a Class of Random Band Matrices.” Advances in Theoretical and Mathematical
Physics. International Press of Boston, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a5.
ieee: P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random
band matrices,” Advances in Theoretical and Mathematical Physics, vol.
21, no. 3. International Press of Boston, pp. 739–800, 2017.
ista: Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random
band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.
mla: Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.”
Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International
Press of Boston, 2017, pp. 739–800, doi:10.4310/ATMP.2017.v21.n3.a5.
short: P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical
Physics 21 (2017) 739–800.
das_tickbox: '1'
date_created: 2018-12-11T11:46:43Z
date_published: 2017-08-25T00:00:00Z
date_updated: 2026-07-06T13:35:08Z
day: '25'
department:
- _id: LaEr
doi: 10.4310/ATMP.2017.v21.n3.a5
ec_funded: 1
external_id:
arxiv:
- '1602.02312'
isi:
- '000409382300005'
fulldoi: https://doi.org/10.4310/ATMP.2017.v21.n3.a5
intvolume: ' 21'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1602.02312
month: '08'
oa: 1
oa_version: Submitted Version
page: 739 - 800
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- 1095-0761
publication_status: published
publisher: International Press of Boston
publist_id: '7337'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Universality for a class of random band matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2017'
...
---
_id: '2350'
abstract:
- lang: eng
text: Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we
calculate the binding energy of an electron in the field of a nucleus of charge
Z and in presence of the quantized radiation field. We consider the case of small
coupling constant α, but fixed Zα and ultraviolet cut-off Λ. We prove that after
renormalizing the mass the binding energy has, to leading order in α, a finite
limit as Λ goes to infinity; i.e., the cut-off can be removed. The expression
for the ground state energy shift thus obtained agrees with Bethe's formula for
small values of Zα, but shows a different behavior for bigger values.
acknowledgement: "We are grateful to Elliott Lieb for helpful discussions. C.H. was
supported by a Marie Curie Fellowship of the European Community programme “Improving
Human Research Potential and the Socioeconomic Knowledge Base” under contract number
HPMFCT-2000-00660 and by the Deutsche Forschungsgemeinschaft, and acknowledges kind
hospitality at Princeton University, where part of this work was done. R.S. was
supported by the Austrian Science Fund in the form of an Erwin Schrödinger Fellowship.\r\n"
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. Mass renormalization and energy level shift in non-relativistic
QED. Advances in Theoretical and Mathematical Physics. 2002;6(5):847-871.
doi:10.4310/ATMP.2002.v6.n5.a3
apa: Hainzl, C., & Seiringer, R. (2002). Mass renormalization and energy level
shift in non-relativistic QED. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.2002.v6.n5.a3
chicago: Hainzl, Christian, and Robert Seiringer. “Mass Renormalization and Energy
Level Shift in Non-Relativistic QED.” Advances in Theoretical and Mathematical
Physics. International Press, 2002. https://doi.org/10.4310/ATMP.2002.v6.n5.a3.
ieee: C. Hainzl and R. Seiringer, “Mass renormalization and energy level shift in
non-relativistic QED,” Advances in Theoretical and Mathematical Physics,
vol. 6, no. 5. International Press, pp. 847–871, 2002.
ista: Hainzl C, Seiringer R. 2002. Mass renormalization and energy level shift in
non-relativistic QED. Advances in Theoretical and Mathematical Physics. 6(5),
847–871.
mla: Hainzl, Christian, and Robert Seiringer. “Mass Renormalization and Energy Level
Shift in Non-Relativistic QED.” Advances in Theoretical and Mathematical Physics,
vol. 6, no. 5, International Press, 2002, pp. 847–71, doi:10.4310/ATMP.2002.v6.n5.a3.
short: C. Hainzl, R. Seiringer, Advances in Theoretical and Mathematical Physics
6 (2002) 847–871.
date_created: 2018-12-11T11:57:09Z
date_published: 2002-09-01T00:00:00Z
date_updated: 2023-07-26T08:29:28Z
day: '01'
doi: 10.4310/ATMP.2002.v6.n5.a3
extern: '1'
external_id:
arxiv:
- math-ph/0205044v3
fulldoi: https://doi.org/10.4310/ATMP.2002.v6.n5.a3
intvolume: ' 6'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0205044
month: '09'
oa: 1
oa_version: Published Version
page: 847 - 871
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- 1095-0761
publication_status: published
publisher: International Press
publist_id: '4574'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mass renormalization and energy level shift in non-relativistic QED
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 6
year: '2002'
...
---
_id: '2736'
abstract:
- lang: eng
text: We consider the time evolution of N bosonic particles interacting via a mean
field Coulomb potential. Suppose the initial state is a product wavefunction.
We show that at any finite time the correlation functions factorize in the limit
N → ∞. Furthermore, the limiting one particle density matrix satisfies the nonlinear
Hartree equation. The key ingredients are the uniqueness of the BBGKY hierarchy
for the correlation functions and a new apriori estimate for the many-body Schrödinger
equations.
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: Horng
full_name: Yau, Horng
last_name: Yau
citation:
ama: Erdös L, Yau H. Derivation of the nonlinear Schrödinger equation from a many
body Coulomb system. Advances in Theoretical and Mathematical Physics.
2001;5(6):1169-1205. doi:10.48550/arXiv.math-ph/0111042
apa: Erdös, L., & Yau, H. (2001). Derivation of the nonlinear Schrödinger equation
from a many body Coulomb system. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.48550/arXiv.math-ph/0111042
chicago: Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger
Equation from a Many Body Coulomb System.” Advances in Theoretical and Mathematical
Physics. International Press, 2001. https://doi.org/10.48550/arXiv.math-ph/0111042.
ieee: L. Erdös and H. Yau, “Derivation of the nonlinear Schrödinger equation from
a many body Coulomb system,” Advances in Theoretical and Mathematical Physics,
vol. 5, no. 6. International Press, pp. 1169–1205, 2001.
ista: Erdös L, Yau H. 2001. Derivation of the nonlinear Schrödinger equation from
a many body Coulomb system. Advances in Theoretical and Mathematical Physics.
5(6), 1169–1205.
mla: Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger Equation
from a Many Body Coulomb System.” Advances in Theoretical and Mathematical
Physics, vol. 5, no. 6, International Press, 2001, pp. 1169–205, doi:10.48550/arXiv.math-ph/0111042.
short: L. Erdös, H. Yau, Advances in Theoretical and Mathematical Physics 5 (2001)
1169–1205.
date_created: 2018-12-11T11:59:20Z
date_published: 2001-11-01T00:00:00Z
date_updated: 2023-05-16T12:12:41Z
day: '01'
doi: 10.48550/arXiv.math-ph/0111042
extern: '1'
external_id:
arxiv:
- math-ph/0111042
fulldoi: https://doi.org/10.48550/arXiv.math-ph/0111042
intvolume: ' 5'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0111042
month: '11'
oa: 1
oa_version: Published Version
page: 1169 - 1205
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- 1095-0761
publication_status: published
publisher: International Press
publist_id: '4156'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 5
year: '2001'
...
---
_id: '1450'
abstract:
- lang: eng
text: In this paper we consider the topological side of a problem which is the analogue
of Sen's S-duality testing conjecture for Hitchin's moduli space M of rank 2 stable
Higgs bundles of fixed determinant of odd degree over a Riemann surface ∑. We
prove that all intersection numbers in the compactly supported cohomology of M
vanish, i.e. "there are no topological L2 harmonic forms on M". This
result generalizes the well known vanishing of the Euler characteristic of the
moduli space of rank 2 stable bundles N of fixed determinant of odd degree over
∑. Our proof shows that the vanishing of all intersection numbers of H* cpt(M)
is given by relations analogous to the Mumford relations in the cohomology ring
of N.
acknowledgement: "First of all I would like to thank my supervisor Nigel Hitchin for
suggesting Problem 1, and for his help and \r\n encouragement. I am grateful to
Michael Thaddeus for his inspiring paper [Thai], enlightening communications and
his constant interest in my work. I am also indebted to Manfred Lehn for the idea
of the proof of Theorem 6.2. I have found\r\nconversations with Michael Atiyah,
Frances Kirwan and Graeme Segal very stimulating. I thank the Mathematical Institute
and St. Catherine's College, Oxford for their hospitality during the preparation
of this work. Finally I thank Trinity College, Cambridge for financial support."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tamas
full_name: Hausel, Tamas
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
citation:
ama: Hausel T. Vanishing of intersection numbers on the moduli space of Higgs bundles.
Advances in Theoretical and Mathematical Physics. 1998;2(5):1011-1040.
doi:10.4310/ATMP.1998.v2.n5.a3
apa: Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of
Higgs bundles. Advances in Theoretical and Mathematical Physics. International
Press. https://doi.org/10.4310/ATMP.1998.v2.n5.a3
chicago: Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of
Higgs Bundles.” Advances in Theoretical and Mathematical Physics. International
Press, 1998. https://doi.org/10.4310/ATMP.1998.v2.n5.a3.
ieee: T. Hausel, “Vanishing of intersection numbers on the moduli space of Higgs
bundles,” Advances in Theoretical and Mathematical Physics, vol. 2, no.
5. International Press, pp. 1011–1040, 1998.
ista: Hausel T. 1998. Vanishing of intersection numbers on the moduli space of Higgs
bundles. Advances in Theoretical and Mathematical Physics. 2(5), 1011–1040.
mla: Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs
Bundles.” Advances in Theoretical and Mathematical Physics, vol. 2, no.
5, International Press, 1998, pp. 1011–40, doi:10.4310/ATMP.1998.v2.n5.a3.
short: T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 1011–1040.
date_created: 2018-12-11T11:52:06Z
date_published: 1998-09-01T00:00:00Z
date_updated: 2022-09-01T14:09:49Z
day: '01'
doi: 10.4310/ATMP.1998.v2.n5.a3
extern: '1'
external_id:
arxiv:
- math/9805071
fulldoi: https://doi.org/10.4310/ATMP.1998.v2.n5.a3
intvolume: ' 2'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math/9805071
month: '09'
oa: 1
oa_version: Preprint
page: 1011 - 1040
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- 1095-0761
publication_status: published
publisher: International Press
publist_id: '5747'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Vanishing of intersection numbers on the moduli space of Higgs bundles
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 2
year: '1998'
...