---
_id: '14427'
abstract:
- lang: eng
text: In the paper, we establish Squash Rigidity Theorem—the dynamical spectral
rigidity for piecewise analytic Bunimovich squash-type stadia whose convex arcs
are homothetic. We also establish Stadium Rigidity Theorem—the dynamical spectral
rigidity for piecewise analytic Bunimovich stadia whose flat boundaries are a
priori fixed. In addition, for smooth Bunimovich squash-type stadia we compute
the Lyapunov exponents along the maximal period two orbit, as well as the value
of the Peierls’ Barrier function from the maximal marked length spectrum associated
to the rotation number 2n/4n+1.
acknowledgement: 'VK acknowledges a partial support by the NSF grant DMS-1402164 and
ERC Grant #885707. Discussions with Martin Leguil and Jacopo De Simoi were very
useful. JC visited the University of Maryland and thanks for the hospitality. Also,
JC was partially supported by the National Key Research and Development Program
of China (No.2022YFA1005802), the NSFC Grant 12001392 and NSF of Jiangsu BK20200850.
H.-K. Zhang is partially supported by the National Science Foundation (DMS-2220211),
as well as Simons Foundation Collaboration Grants for Mathematicians (706383).'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jianyu
full_name: Chen, Jianyu
last_name: Chen
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Hong Kun
full_name: Zhang, Hong Kun
last_name: Zhang
citation:
ama: Chen J, Kaloshin V, Zhang HK. Length spectrum rigidity for piecewise analytic
Bunimovich billiards. Communications in Mathematical Physics. 2023. doi:10.1007/s00220-023-04837-z
apa: Chen, J., Kaloshin, V., & Zhang, H. K. (2023). Length spectrum rigidity
for piecewise analytic Bunimovich billiards. Communications in Mathematical
Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04837-z
chicago: Chen, Jianyu, Vadim Kaloshin, and Hong Kun Zhang. “Length Spectrum Rigidity
for Piecewise Analytic Bunimovich Billiards.” Communications in Mathematical
Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04837-z.
ieee: J. Chen, V. Kaloshin, and H. K. Zhang, “Length spectrum rigidity for piecewise
analytic Bunimovich billiards,” Communications in Mathematical Physics.
Springer Nature, 2023.
ista: Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise
analytic Bunimovich billiards. Communications in Mathematical Physics.
mla: Chen, Jianyu, et al. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich
Billiards.” Communications in Mathematical Physics, Springer Nature, 2023,
doi:10.1007/s00220-023-04837-z.
short: J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics
(2023).
date_created: 2023-10-15T22:01:11Z
date_published: 2023-09-29T00:00:00Z
date_updated: 2023-12-13T13:02:44Z
day: '29'
department:
- _id: VaKa
doi: 10.1007/s00220-023-04837-z
ec_funded: 1
external_id:
arxiv:
- '1902.07330'
isi:
- '001073177200001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.07330
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Length spectrum rigidity for piecewise analytic Bunimovich billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14441'
abstract:
- lang: eng
text: We study the Fröhlich polaron model in R3, and establish the subleading term
in the strong coupling asymptotics of its ground state energy, corresponding to
the quantum corrections to the classical energy determined by the Pekar approximation.
acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation
programme under the ERC grant agreement No 694227 is acknowledged. Open access funding
provided by Institute of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Morris
full_name: Brooks, Morris
id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
last_name: Brooks
orcid: 0000-0002-6249-0928
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Brooks M, Seiringer R. The Fröhlich Polaron at strong coupling: Part I - The
quantum correction to the classical energy. Communications in Mathematical
Physics. 2023;404:287-337. doi:10.1007/s00220-023-04841-3'
apa: 'Brooks, M., & Seiringer, R. (2023). The Fröhlich Polaron at strong coupling:
Part I - The quantum correction to the classical energy. Communications in
Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04841-3'
chicago: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong
Coupling: Part I - The Quantum Correction to the Classical Energy.” Communications
in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04841-3.'
ieee: 'M. Brooks and R. Seiringer, “The Fröhlich Polaron at strong coupling: Part
I - The quantum correction to the classical energy,” Communications in Mathematical
Physics, vol. 404. Springer Nature, pp. 287–337, 2023.'
ista: 'Brooks M, Seiringer R. 2023. The Fröhlich Polaron at strong coupling: Part
I - The quantum correction to the classical energy. Communications in Mathematical
Physics. 404, 287–337.'
mla: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling:
Part I - The Quantum Correction to the Classical Energy.” Communications in
Mathematical Physics, vol. 404, Springer Nature, 2023, pp. 287–337, doi:10.1007/s00220-023-04841-3.'
short: M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023)
287–337.
date_created: 2023-10-22T22:01:13Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2023-10-31T12:22:51Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00220-023-04841-3
ec_funded: 1
external_id:
arxiv:
- '2207.03156'
file:
- access_level: open_access
checksum: 1ae49b39247cb6b40ff75997381581b8
content_type: application/pdf
creator: dernst
date_created: 2023-10-31T12:21:39Z
date_updated: 2023-10-31T12:21:39Z
file_id: '14477'
file_name: 2023_CommMathPhysics_Brooks.pdf
file_size: 832375
relation: main_file
success: 1
file_date_updated: 2023-10-31T12:21:39Z
has_accepted_license: '1'
intvolume: ' 404'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 287-337
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The Fröhlich Polaron at strong coupling: Part I - The quantum correction to
the classical energy'
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: 404
year: '2023'
...
---
_id: '13319'
abstract:
- lang: eng
text: We prove that the generator of the L2 implementation of a KMS-symmetric quantum
Markov semigroup can be expressed as the square of a derivation with values in
a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially
symmetric semigroups and the second-named author for GNS-symmetric semigroups.
This result hinges on the introduction of a new completely positive map on the
algebra of bounded operators on the GNS Hilbert space. This transformation maps
symmetric Markov operators to symmetric Markov operators and is essential to obtain
the required inner product on the Hilbert bimodule.
acknowledgement: The authors are grateful to Martijn Caspers for helpful comments
on a preliminary version of this manuscript. M. V. was supported by the NWO Vidi
grant VI.Vidi.192.018 ‘Non-commutative harmonic analysis and rigidity of operator
algebras’. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit
Programme [ESP 156]. For the purpose of Open Access, the authors have applied a
CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising
from this submission. Open access funding provided by Austrian Science Fund (FWF).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Matthijs
full_name: Vernooij, Matthijs
last_name: Vernooij
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups.
Communications in Mathematical Physics. 2023;403:381-416. doi:10.1007/s00220-023-04795-6
apa: Vernooij, M., & Wirth, M. (2023). Derivations and KMS-symmetric quantum
Markov semigroups. Communications in Mathematical Physics. Springer Nature.
https://doi.org/10.1007/s00220-023-04795-6
chicago: Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric
Quantum Markov Semigroups.” Communications in Mathematical Physics. Springer
Nature, 2023. https://doi.org/10.1007/s00220-023-04795-6.
ieee: M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,”
Communications in Mathematical Physics, vol. 403. Springer Nature, pp.
381–416, 2023.
ista: Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups.
Communications in Mathematical Physics. 403, 381–416.
mla: Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum
Markov Semigroups.” Communications in Mathematical Physics, vol. 403, Springer
Nature, 2023, pp. 381–416, doi:10.1007/s00220-023-04795-6.
short: M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023)
381–416.
date_created: 2023-07-30T22:01:03Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2024-01-30T12:16:32Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00220-023-04795-6
external_id:
arxiv:
- '2303.15949'
isi:
- '001033655400002'
file:
- access_level: open_access
checksum: cca204e81891270216a0c84eb8bcd398
content_type: application/pdf
creator: dernst
date_created: 2024-01-30T12:15:11Z
date_updated: 2024-01-30T12:15:11Z
file_id: '14905'
file_name: 2023_CommMathPhysics_Vernooij.pdf
file_size: 481209
relation: main_file
success: 1
file_date_updated: 2024-01-30T12:15:11Z
has_accepted_license: '1'
intvolume: ' 403'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 381-416
project:
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivations and KMS-symmetric quantum Markov semigroups
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: 403
year: '2023'
...
---
_id: '12792'
abstract:
- lang: eng
text: In the physics literature the spectral form factor (SFF), the squared Fourier
transform of the empirical eigenvalue density, is the most common tool to test
universality for disordered quantum systems, yet previous mathematical results
have been restricted only to two exactly solvable models (Forrester in J Stat
Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys
387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously
prove the physics prediction on SFF up to an intermediate time scale for a large
class of random matrices using a robust method, the multi-resolvent local laws.
Beyond Wigner matrices we also consider the monoparametric ensemble and prove
that universality of SFF can already be triggered by a single random parameter,
supplementing the recently proven Wigner–Dyson universality (Cipolloni et al.
in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7)
to larger spectral scales. Remarkably, extensive numerics indicates that our formulas
correctly predict the SFF in the entire slope-dip-ramp regime, as customarily
called in physics.
acknowledgement: "We are grateful to the authors of [25] for sharing with us their
insights and preliminary numerical results. We are especially thankful to Stephen
Shenker for very valuable advice over several email communications. Helpful comments
on the manuscript from Peter Forrester and from the anonymous referees are also
acknowledged.\r\nOpen access funding provided by Institute of Science and Technology
(IST Austria).\r\nLászló Erdős: Partially supported by ERC Advanced Grant \"RMTBeyond\"
No. 101020331. Dominik Schröder: Supported by Dr. Max Rössler, the Walter Haefner
Foundation and the ETH Zürich Foundation."
article_processing_charge: Yes (via OA deal)
article_type: original
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: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. On the spectral form factor for random matrices.
Communications in Mathematical Physics. 2023;401:1665-1700. doi:10.1007/s00220-023-04692-y
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). On the spectral form
factor for random matrices. Communications in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s00220-023-04692-y
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral
Form Factor for Random Matrices.” Communications in Mathematical Physics.
Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04692-y.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for
random matrices,” Communications in Mathematical Physics, vol. 401. Springer
Nature, pp. 1665–1700, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random
matrices. Communications in Mathematical Physics. 401, 1665–1700.
mla: Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.”
Communications in Mathematical Physics, vol. 401, Springer Nature, 2023,
pp. 1665–700, doi:10.1007/s00220-023-04692-y.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics
401 (2023) 1665–1700.
date_created: 2023-04-02T22:01:11Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-10-04T12:10:31Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-023-04692-y
ec_funded: 1
external_id:
isi:
- '000957343500001'
file:
- access_level: open_access
checksum: 72057940f76654050ca84a221f21786c
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T12:09:18Z
date_updated: 2023-10-04T12:09:18Z
file_id: '14397'
file_name: 2023_CommMathPhysics_Cipolloni.pdf
file_size: 859967
relation: main_file
success: 1
file_date_updated: 2023-10-04T12:09:18Z
has_accepted_license: '1'
intvolume: ' 401'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 1665-1700
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the spectral form factor for random 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: 401
year: '2023'
...
---
_id: '11332'
abstract:
- lang: eng
text: We show that the fluctuations of the largest eigenvalue of a real symmetric
or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws
at a rate O(N^{-1/3+\omega }), as N tends to infinity. For Wigner matrices this
improves the previous rate O(N^{-2/9+\omega }) obtained by Bourgade (J Eur Math
Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function
comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515,
2012) to prove edge universality, on a finer spectral parameter scale with improved
error estimates. The proof relies on the continuous Green function flow induced
by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions
from the third and fourth order moments of the matrix entries are obtained using
iterative cumulant expansions and recursive comparisons for correlation functions,
along with uniform convergence estimates for correlation kernels of the Gaussian
invariant ensembles.
acknowledgement: Kevin Schnelli is supported in parts by the Swedish Research Council
Grant VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Yuanyuan Xu is
supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced
Grant “RMTBeyond” No. 101020331.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
- first_name: Yuanyuan
full_name: Xu, Yuanyuan
id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3
last_name: Xu
citation:
ama: Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest
Eigenvalue of Wigner matrices. Communications in Mathematical Physics.
2022;393:839-907. doi:10.1007/s00220-022-04377-y
apa: Schnelli, K., & Xu, Y. (2022). Convergence rate to the Tracy–Widom laws
for the largest Eigenvalue of Wigner matrices. Communications in Mathematical
Physics. Springer Nature. https://doi.org/10.1007/s00220-022-04377-y
chicago: Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom
Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical
Physics. Springer Nature, 2022. https://doi.org/10.1007/s00220-022-04377-y.
ieee: K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest
Eigenvalue of Wigner matrices,” Communications in Mathematical Physics,
vol. 393. Springer Nature, pp. 839–907, 2022.
ista: Schnelli K, Xu Y. 2022. Convergence rate to the Tracy–Widom laws for the largest
Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 393, 839–907.
mla: Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws
for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical
Physics, vol. 393, Springer Nature, 2022, pp. 839–907, doi:10.1007/s00220-022-04377-y.
short: K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.
date_created: 2022-04-24T22:01:44Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-08-03T06:34:24Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-022-04377-y
ec_funded: 1
external_id:
arxiv:
- '2102.04330'
isi:
- '000782737200001'
file:
- access_level: open_access
checksum: bee0278c5efa9a33d9a2dc8d354a6c51
content_type: application/pdf
creator: dernst
date_created: 2022-08-05T06:01:13Z
date_updated: 2022-08-05T06:01:13Z
file_id: '11726'
file_name: 2022_CommunMathPhys_Schnelli.pdf
file_size: 1141462
relation: main_file
success: 1
file_date_updated: 2022-08-05T06:01:13Z
has_accepted_license: '1'
intvolume: ' 393'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 839-907
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 393
year: '2022'
...
---
_id: '10221'
abstract:
- lang: eng
text: We prove that any deterministic matrix is approximately the identity in the
eigenbasis of a large random Wigner matrix with very high probability and with
an optimal error inversely proportional to the square root of the dimension. Our
theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch
(Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner
ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity
(QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing
previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278,
2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).
article_processing_charge: Yes (via OA deal)
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: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for
Wigner matrices. Communications in Mathematical Physics. 2021;388(2):1005–1048.
doi:10.1007/s00220-021-04239-z
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Eigenstate thermalization
hypothesis for Wigner matrices. Communications in Mathematical Physics.
Springer Nature. https://doi.org/10.1007/s00220-021-04239-z
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization
Hypothesis for Wigner Matrices.” Communications in Mathematical Physics.
Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04239-z.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis
for Wigner matrices,” Communications in Mathematical Physics, vol. 388,
no. 2. Springer Nature, pp. 1005–1048, 2021.
ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis
for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.
mla: Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner
Matrices.” Communications in Mathematical Physics, vol. 388, no. 2, Springer
Nature, 2021, pp. 1005–1048, doi:10.1007/s00220-021-04239-z.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics
388 (2021) 1005–1048.
date_created: 2021-11-07T23:01:25Z
date_published: 2021-10-29T00:00:00Z
date_updated: 2023-08-14T10:29:49Z
day: '29'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-021-04239-z
external_id:
arxiv:
- '2012.13215'
isi:
- '000712232700001'
file:
- access_level: open_access
checksum: a2c7b6f5d23b5453cd70d1261272283b
content_type: application/pdf
creator: cchlebak
date_created: 2022-02-02T10:19:55Z
date_updated: 2022-02-02T10:19:55Z
file_id: '10715'
file_name: 2021_CommunMathPhys_Cipolloni.pdf
file_size: 841426
relation: main_file
success: 1
file_date_updated: 2022-02-02T10:19:55Z
has_accepted_license: '1'
intvolume: ' 388'
isi: 1
issue: '2'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1005–1048
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Eigenstate thermalization hypothesis 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 388
year: '2021'
...
---
_id: '9973'
abstract:
- lang: eng
text: In this article we introduce a complete gradient estimate for symmetric quantum
Markov semigroups on von Neumann algebras equipped with a normal faithful tracial
state, which implies semi-convexity of the entropy with respect to the recently
introduced noncommutative 2-Wasserstein distance. We show that this complete gradient
estimate is stable under tensor products and free products and establish its validity
for a number of examples. As an application we prove a complete modified logarithmic
Sobolev inequality with optimal constant for Poisson-type semigroups on free group
factors.
acknowledgement: Both authors would like to thank Jan Maas for fruitful discussions
and helpful comments.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 2021;387:761–791. doi:10.1007/s00220-021-04199-4
apa: Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov
semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4
chicago: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” Communications in Mathematical Physics. Springer Nature,
2021. https://doi.org/10.1007/s00220-021-04199-4.
ieee: M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,”
Communications in Mathematical Physics, vol. 387. Springer Nature, pp.
761–791, 2021.
ista: Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 387, 761–791.
mla: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” Communications in Mathematical Physics, vol. 387, Springer
Nature, 2021, pp. 761–791, doi:10.1007/s00220-021-04199-4.
short: M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.
date_created: 2021-08-30T10:07:44Z
date_published: 2021-08-30T00:00:00Z
date_updated: 2023-08-11T11:09:07Z
day: '30'
ddc:
- '621'
department:
- _id: JaMa
doi: 10.1007/s00220-021-04199-4
ec_funded: 1
external_id:
arxiv:
- '2007.13506'
isi:
- '000691214200001'
file:
- access_level: open_access
checksum: 8a602f916b1c2b0dc1159708b7cb204b
content_type: application/pdf
creator: cchlebak
date_created: 2021-09-08T07:34:24Z
date_updated: 2021-09-08T09:46:34Z
file_id: '9990'
file_name: 2021_CommunMathPhys_Wirth.pdf
file_size: 505971
relation: main_file
file_date_updated: 2021-09-08T09:46:34Z
has_accepted_license: '1'
intvolume: ' 387'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 761–791
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Complete gradient estimates of quantum Markov semigroups
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: 387
year: '2021'
...
---
_id: '6649'
abstract:
- lang: eng
text: "While Hartree–Fock theory is well established as a fundamental approximation
for interacting fermions, it has been unclear how to describe corrections to it
due to many-body correlations. In this paper we start from the Hartree–Fock state
given by plane waves and introduce collective particle–hole pair excitations.
These pairs can be approximately described by a bosonic quadratic Hamiltonian.
We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type
upper bound to the ground state energy. Our result justifies the random-phase
approximation in the mean-field scaling regime, for repulsive, regular interaction
potentials.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Niels P
full_name: Benedikter, Niels P
id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
last_name: Benedikter
orcid: 0000-0002-1071-6091
- first_name: Phan Thành
full_name: Nam, Phan Thành
last_name: Nam
- first_name: Marcello
full_name: Porta, Marcello
last_name: Porta
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Optimal upper bound
for the correlation energy of a Fermi gas in the mean-field regime. Communications
in Mathematical Physics. 2020;374:2097–2150. doi:10.1007/s00220-019-03505-5
apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R.
(2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field
regime. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03505-5
chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi
Gas in the Mean-Field Regime.” Communications in Mathematical Physics.
Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03505-5.
ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal
upper bound for the correlation energy of a Fermi gas in the mean-field regime,”
Communications in Mathematical Physics, vol. 374. Springer Nature, pp.
2097–2150, 2020.
ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper
bound for the correlation energy of a Fermi gas in the mean-field regime. Communications
in Mathematical Physics. 374, 2097–2150.
mla: Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy
of a Fermi Gas in the Mean-Field Regime.” Communications in Mathematical Physics,
vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:10.1007/s00220-019-03505-5.
short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications
in Mathematical Physics 374 (2020) 2097–2150.
date_created: 2019-07-18T13:30:04Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2023-08-17T13:51:50Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00220-019-03505-5
ec_funded: 1
external_id:
arxiv:
- '1809.01902'
isi:
- '000527910700019'
file:
- access_level: open_access
checksum: f9dd6dd615a698f1d3636c4a092fed23
content_type: application/pdf
creator: dernst
date_created: 2019-07-24T07:19:10Z
date_updated: 2020-07-14T12:47:35Z
file_id: '6668'
file_name: 2019_CommMathPhysics_Benedikter.pdf
file_size: 853289
relation: main_file
file_date_updated: 2020-07-14T12:47:35Z
has_accepted_license: '1'
intvolume: ' 374'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 2097–2150
project:
- _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1
call_identifier: FWF
name: FWF Open Access Fund
- _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: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal upper bound for the correlation energy of a Fermi gas in the mean-field
regime
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: 374
year: '2020'
...
---
_id: '6906'
abstract:
- lang: eng
text: We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime.
We show that low-energy states exhibit complete Bose–Einstein condensation with
an optimal bound on the number of orthogonal excitations. This extends recent
results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing
the assumption of small interaction potential.
acknowledgement: "We would like to thank P. T. Nam and R. Seiringer for several useful
discussions and\r\nfor suggesting us to use the localization techniques from [9].
C. Boccato has received funding from the\r\nEuropean Research Council (ERC) under
the programme Horizon 2020 (Grant Agreement 694227). B. Schlein gratefully acknowledges
support from the NCCR SwissMAP and from the Swiss National Foundation of Science
(Grant No. 200020_1726230) through the SNF Grant “Dynamical and energetic properties
of Bose–Einstein condensates”."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
full_name: Boccato, Chiara
id: 342E7E22-F248-11E8-B48F-1D18A9856A87
last_name: Boccato
- first_name: Christian
full_name: Brennecke, Christian
last_name: Brennecke
- first_name: Serena
full_name: Cenatiempo, Serena
last_name: Cenatiempo
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
citation:
ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. Optimal rate for Bose-Einstein
condensation in the Gross-Pitaevskii regime. Communications in Mathematical
Physics. 2020;376:1311-1395. doi:10.1007/s00220-019-03555-9
apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2020). Optimal
rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. Communications
in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-019-03555-9
chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
“Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.”
Communications in Mathematical Physics. Springer, 2020. https://doi.org/10.1007/s00220-019-03555-9.
ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Optimal rate for
Bose-Einstein condensation in the Gross-Pitaevskii regime,” Communications
in Mathematical Physics, vol. 376. Springer, pp. 1311–1395, 2020.
ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. Optimal rate for Bose-Einstein
condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics.
376, 1311–1395.
mla: Boccato, Chiara, et al. “Optimal Rate for Bose-Einstein Condensation in the
Gross-Pitaevskii Regime.” Communications in Mathematical Physics, vol.
376, Springer, 2020, pp. 1311–95, doi:10.1007/s00220-019-03555-9.
short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical
Physics 376 (2020) 1311–1395.
date_created: 2019-09-24T17:30:59Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2024-02-22T13:33:02Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00220-019-03555-9
ec_funded: 1
external_id:
arxiv:
- '1812.03086'
isi:
- '000536053300012'
intvolume: ' 376'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1812.03086
month: '06'
oa: 1
oa_version: Preprint
page: 1311-1395
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 376
year: '2020'
...
---
_id: '7004'
abstract:
- lang: eng
text: We define an action of the (double of) Cohomological Hall algebra of Kontsevich
and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov.
We identify this action with the one of the affine Yangian of gl(1). Based on
that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák.
We conjecture that our approach works for a big class of Calabi–Yau categories,
including those associated with toric Calabi–Yau 3-folds.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Miroslav
full_name: Rapcak, Miroslav
last_name: Rapcak
- first_name: Yan
full_name: Soibelman, Yan
last_name: Soibelman
- first_name: Yaping
full_name: Yang, Yaping
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: Rapcak M, Soibelman Y, Yang Y, Zhao G. Cohomological Hall algebras, vertex
algebras and instantons. Communications in Mathematical Physics. 2020;376:1803-1873.
doi:10.1007/s00220-019-03575-5
apa: Rapcak, M., Soibelman, Y., Yang, Y., & Zhao, G. (2020). Cohomological Hall
algebras, vertex algebras and instantons. Communications in Mathematical Physics.
Springer Nature. https://doi.org/10.1007/s00220-019-03575-5
chicago: Rapcak, Miroslav, Yan Soibelman, Yaping Yang, and Gufang Zhao. “Cohomological
Hall Algebras, Vertex Algebras and Instantons.” Communications in Mathematical
Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03575-5.
ieee: M. Rapcak, Y. Soibelman, Y. Yang, and G. Zhao, “Cohomological Hall algebras,
vertex algebras and instantons,” Communications in Mathematical Physics,
vol. 376. Springer Nature, pp. 1803–1873, 2020.
ista: Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras,
vertex algebras and instantons. Communications in Mathematical Physics. 376, 1803–1873.
mla: Rapcak, Miroslav, et al. “Cohomological Hall Algebras, Vertex Algebras and
Instantons.” Communications in Mathematical Physics, vol. 376, Springer
Nature, 2020, pp. 1803–73, doi:10.1007/s00220-019-03575-5.
short: M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical
Physics 376 (2020) 1803–1873.
date_created: 2019-11-12T14:01:27Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-08-17T14:02:59Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00220-019-03575-5
ec_funded: 1
external_id:
arxiv:
- '1810.10402'
isi:
- '000536255500004'
intvolume: ' 376'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1810.10402
month: '06'
oa: 1
oa_version: Preprint
page: 1803-1873
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Cohomological Hall algebras, vertex algebras and instantons
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 376
year: '2020'
...
---
_id: '6185'
abstract:
- lang: eng
text: For complex Wigner-type matrices, i.e. Hermitian random matrices with independent,
not necessarily identically distributed entries above the diagonal, we show that
at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue
statistics are universal and form a Pearcey process. Since the density of states
typically exhibits only square root or cubic root cusp singularities, our work
complements previous results on the bulk and edge universality and it thus completes
the resolution of the Wigner–Dyson–Mehta universality conjecture for the last
remaining universality type in the complex Hermitian class. Our analysis holds
not only for exact cusps, but approximate cusps as well, where an extended Pearcey
process emerges. As a main technical ingredient we prove an optimal local law
at the cusp for both symmetry classes. This result is also the key input in the
companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where
the cusp universality for real symmetric Wigner-type matrices is proven. The novel
cusp fluctuation mechanism is also essential for the recent results on the spectral
radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random
matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian
edge universality (Cipolloni et al. in Edge universality for non-Hermitian random
matrices, 2019. arXiv:1908.00969).
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). The authors are very grateful to Johannes Alt for numerous discussions
on the Dyson equation and for his invaluable help in adjusting [10] to the needs
of the present work.
article_processing_charge: Yes (via OA deal)
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. Cusp universality for random matrices I:
Local law and the complex Hermitian case. Communications in Mathematical Physics.
2020;378:1203-1278. doi:10.1007/s00220-019-03657-4'
apa: 'Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Cusp universality
for random matrices I: Local law and the complex Hermitian case. Communications
in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03657-4'
chicago: 'Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality
for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications
in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03657-4.'
ieee: 'L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random
matrices I: Local law and the complex Hermitian case,” Communications in Mathematical
Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.'
ista: 'Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices
I: Local law and the complex Hermitian case. Communications in Mathematical Physics.
378, 1203–1278.'
mla: 'Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law
and the Complex Hermitian Case.” Communications in Mathematical Physics,
vol. 378, Springer Nature, 2020, pp. 1203–78, doi:10.1007/s00220-019-03657-4.'
short: L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics
378 (2020) 1203–1278.
date_created: 2019-03-28T10:21:15Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2023-09-07T12:54:12Z
day: '01'
ddc:
- '530'
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-019-03657-4
ec_funded: 1
external_id:
arxiv:
- '1809.03971'
isi:
- '000529483000001'
file:
- access_level: open_access
checksum: c3a683e2afdcea27afa6880b01e53dc2
content_type: application/pdf
creator: dernst
date_created: 2020-11-18T11:14:37Z
date_updated: 2020-11-18T11:14:37Z
file_id: '8771'
file_name: 2020_CommMathPhysics_Erdoes.pdf
file_size: 2904574
relation: main_file
success: 1
file_date_updated: 2020-11-18T11:14:37Z
has_accepted_license: '1'
intvolume: ' 378'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1203-1278
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: 'Cusp universality for random matrices I: Local law and the complex Hermitian
case'
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: 378
year: '2020'
...
---
_id: '8415'
abstract:
- lang: eng
text: 'We consider billiards obtained by removing three strictly convex obstacles
satisfying the non-eclipse condition on the plane. The restriction of the dynamics
to the set of non-escaping orbits is conjugated to a subshift on three symbols
that provides a natural labeling of all periodic orbits. We study the following
inverse problem: does the Marked Length Spectrum (i.e., the set of lengths of
periodic orbits together with their labeling), determine the geometry of the billiard
table? We show that from the Marked Length Spectrum it is possible to recover
the curvature at periodic points of period two, as well as the Lyapunov exponent
of each periodic orbit.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Péter
full_name: Bálint, Péter
last_name: Bálint
- first_name: Jacopo
full_name: De Simoi, Jacopo
last_name: De Simoi
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Martin
full_name: Leguil, Martin
last_name: Leguil
citation:
ama: Bálint P, De Simoi J, Kaloshin V, Leguil M. Marked length spectrum, homoclinic
orbits and the geometry of open dispersing billiards. Communications in Mathematical
Physics. 2019;374(3):1531-1575. doi:10.1007/s00220-019-03448-x
apa: Bálint, P., De Simoi, J., Kaloshin, V., & Leguil, M. (2019). Marked length
spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications
in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03448-x
chicago: Bálint, Péter, Jacopo De Simoi, Vadim Kaloshin, and Martin Leguil. “Marked
Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.”
Communications in Mathematical Physics. Springer Nature, 2019. https://doi.org/10.1007/s00220-019-03448-x.
ieee: P. Bálint, J. De Simoi, V. Kaloshin, and M. Leguil, “Marked length spectrum,
homoclinic orbits and the geometry of open dispersing billiards,” Communications
in Mathematical Physics, vol. 374, no. 3. Springer Nature, pp. 1531–1575,
2019.
ista: Bálint P, De Simoi J, Kaloshin V, Leguil M. 2019. Marked length spectrum,
homoclinic orbits and the geometry of open dispersing billiards. Communications
in Mathematical Physics. 374(3), 1531–1575.
mla: Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry
of Open Dispersing Billiards.” Communications in Mathematical Physics,
vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:10.1007/s00220-019-03448-x.
short: P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical
Physics 374 (2019) 1531–1575.
date_created: 2020-09-17T10:41:27Z
date_published: 2019-05-09T00:00:00Z
date_updated: 2021-01-12T08:19:08Z
day: '09'
doi: 10.1007/s00220-019-03448-x
extern: '1'
external_id:
arxiv:
- '1809.08947'
intvolume: ' 374'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1809.08947
month: '05'
oa: 1
oa_version: Preprint
page: 1531-1575
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Marked length spectrum, homoclinic orbits and the geometry of open dispersing
billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 374
year: '2019'
...
---
_id: '7100'
abstract:
- lang: eng
text: We present microscopic derivations of the defocusing two-dimensional cubic
nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman
interacting N-particle system of bosons. We consider the interaction potential
to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx),
for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R).
In both cases we prove the convergence of the reduced density corresponding to
the exact time evolution to the projector onto the solution of the corresponding
nonlinear Schrödinger equation in trace norm. For the latter potential VN we show
that it is crucial to take the microscopic structure of the condensate into account
in order to obtain the correct dynamics.
acknowledgement: OA fund by IST Austria
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Maximilian
full_name: Jeblick, Maximilian
last_name: Jeblick
- first_name: Nikolai K
full_name: Leopold, Nikolai K
id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
last_name: Leopold
orcid: 0000-0002-0495-6822
- first_name: Peter
full_name: Pickl, Peter
last_name: Pickl
citation:
ama: Jeblick M, Leopold NK, Pickl P. Derivation of the time dependent Gross–Pitaevskii
equation in two dimensions. Communications in Mathematical Physics. 2019;372(1):1-69.
doi:10.1007/s00220-019-03599-x
apa: Jeblick, M., Leopold, N. K., & Pickl, P. (2019). Derivation of the time
dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical
Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03599-x
chicago: Jeblick, Maximilian, Nikolai K Leopold, and Peter Pickl. “Derivation of
the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” Communications
in Mathematical Physics. Springer Nature, 2019. https://doi.org/10.1007/s00220-019-03599-x.
ieee: M. Jeblick, N. K. Leopold, and P. Pickl, “Derivation of the time dependent
Gross–Pitaevskii equation in two dimensions,” Communications in Mathematical
Physics, vol. 372, no. 1. Springer Nature, pp. 1–69, 2019.
ista: Jeblick M, Leopold NK, Pickl P. 2019. Derivation of the time dependent Gross–Pitaevskii
equation in two dimensions. Communications in Mathematical Physics. 372(1), 1–69.
mla: Jeblick, Maximilian, et al. “Derivation of the Time Dependent Gross–Pitaevskii
Equation in Two Dimensions.” Communications in Mathematical Physics, vol.
372, no. 1, Springer Nature, 2019, pp. 1–69, doi:10.1007/s00220-019-03599-x.
short: M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics
372 (2019) 1–69.
date_created: 2019-11-25T08:08:02Z
date_published: 2019-11-08T00:00:00Z
date_updated: 2023-09-06T10:47:43Z
day: '08'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00220-019-03599-x
ec_funded: 1
external_id:
isi:
- '000495193700002'
file:
- access_level: open_access
checksum: cd283b475dd739e04655315abd46f528
content_type: application/pdf
creator: dernst
date_created: 2019-11-25T08:11:11Z
date_updated: 2020-07-14T12:47:49Z
file_id: '7101'
file_name: 2019_CommMathPhys_Jeblick.pdf
file_size: 884469
relation: main_file
file_date_updated: 2020-07-14T12:47:49Z
has_accepted_license: '1'
intvolume: ' 372'
isi: 1
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 1-69
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivation of the time dependent Gross–Pitaevskii equation in two dimensions
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 372
year: '2019'
...
---
_id: '8417'
abstract:
- lang: eng
text: The restricted planar elliptic three body problem (RPETBP) describes the motion
of a massless particle (a comet or an asteroid) under the gravitational field
of two massive bodies (the primaries, say the Sun and Jupiter) revolving around
their center of mass on elliptic orbits with some positive eccentricity. The aim
of this paper is to show the existence of orbits whose angular momentum performs
arbitrary excursions in a large region. In particular, there exist diffusive orbits,
that is, with a large variation of angular momentum. The leading idea of the proof
consists in analyzing parabolic motions of the comet. By a well-known result of
McGehee, the union of future (resp. past) parabolic orbits is an analytic manifold
P+ (resp. P−). In a properly chosen coordinate system these manifolds are stable
(resp. unstable) manifolds of a manifold at infinity P∞, which we call the manifold
at parabolic infinity. On P∞ it is possible to define two scattering maps, which
contain the map structure of the homoclinic trajectories to it, i.e. orbits parabolic
both in the future and the past. Since the inner dynamics inside P∞ is trivial,
two different scattering maps are used. The combination of these two scattering
maps permits the design of the desired diffusive pseudo-orbits. Using shadowing
techniques and these pseudo orbits we show the existence of true trajectories
of the RPETBP whose angular momentum varies in any predetermined fashion.
article_processing_charge: No
article_type: original
author:
- first_name: Amadeu
full_name: Delshams, Amadeu
last_name: Delshams
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Abraham
full_name: de la Rosa, Abraham
last_name: de la Rosa
- first_name: Tere M.
full_name: Seara, Tere M.
last_name: Seara
citation:
ama: Delshams A, Kaloshin V, de la Rosa A, Seara TM. Global instability in the restricted
planar elliptic three body problem. Communications in Mathematical Physics.
2018;366(3):1173-1228. doi:10.1007/s00220-018-3248-z
apa: Delshams, A., Kaloshin, V., de la Rosa, A., & Seara, T. M. (2018). Global
instability in the restricted planar elliptic three body problem. Communications
in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-018-3248-z
chicago: Delshams, Amadeu, Vadim Kaloshin, Abraham de la Rosa, and Tere M. Seara.
“Global Instability in the Restricted Planar Elliptic Three Body Problem.” Communications
in Mathematical Physics. Springer Nature, 2018. https://doi.org/10.1007/s00220-018-3248-z.
ieee: A. Delshams, V. Kaloshin, A. de la Rosa, and T. M. Seara, “Global instability
in the restricted planar elliptic three body problem,” Communications in Mathematical
Physics, vol. 366, no. 3. Springer Nature, pp. 1173–1228, 2018.
ista: Delshams A, Kaloshin V, de la Rosa A, Seara TM. 2018. Global instability in
the restricted planar elliptic three body problem. Communications in Mathematical
Physics. 366(3), 1173–1228.
mla: Delshams, Amadeu, et al. “Global Instability in the Restricted Planar Elliptic
Three Body Problem.” Communications in Mathematical Physics, vol. 366,
no. 3, Springer Nature, 2018, pp. 1173–228, doi:10.1007/s00220-018-3248-z.
short: A. Delshams, V. Kaloshin, A. de la Rosa, T.M. Seara, Communications in Mathematical
Physics 366 (2018) 1173–1228.
date_created: 2020-09-17T10:41:43Z
date_published: 2018-09-05T00:00:00Z
date_updated: 2021-01-12T08:19:08Z
day: '05'
doi: 10.1007/s00220-018-3248-z
extern: '1'
intvolume: ' 366'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '09'
oa_version: None
page: 1173-1228
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Global instability in the restricted planar elliptic three body problem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 366
year: '2018'
...
---
_id: '8493'
abstract:
- lang: eng
text: In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko
(Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43,
1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644,
2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive
a second order expansion of this map for trigonometric perturbations. In Castejon
et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint
available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive
behavior through big gaps in a priori unstable systems (in preparation), 2015),
and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior
for the generalized Arnold example away from resonances. Preprint available at
http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present
paper, we describe a class of nearly integrable deterministic systems with stochastic
diffusive behavior.
article_processing_charge: No
article_type: original
author:
- first_name: M.
full_name: Guardia, M.
last_name: Guardia
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: J.
full_name: Zhang, J.
last_name: Zhang
citation:
ama: Guardia M, Kaloshin V, Zhang J. A second order expansion of the separatrix
map for trigonometric perturbations of a priori unstable systems. Communications
in Mathematical Physics. 2016;348:321-361. doi:10.1007/s00220-016-2705-9
apa: Guardia, M., Kaloshin, V., & Zhang, J. (2016). A second order expansion
of the separatrix map for trigonometric perturbations of a priori unstable systems.
Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-016-2705-9
chicago: Guardia, M., Vadim Kaloshin, and J. Zhang. “A Second Order Expansion of
the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.”
Communications in Mathematical Physics. Springer Nature, 2016. https://doi.org/10.1007/s00220-016-2705-9.
ieee: M. Guardia, V. Kaloshin, and J. Zhang, “A second order expansion of the separatrix
map for trigonometric perturbations of a priori unstable systems,” Communications
in Mathematical Physics, vol. 348. Springer Nature, pp. 321–361, 2016.
ista: Guardia M, Kaloshin V, Zhang J. 2016. A second order expansion of the separatrix
map for trigonometric perturbations of a priori unstable systems. Communications
in Mathematical Physics. 348, 321–361.
mla: Guardia, M., et al. “A Second Order Expansion of the Separatrix Map for Trigonometric
Perturbations of a Priori Unstable Systems.” Communications in Mathematical
Physics, vol. 348, Springer Nature, 2016, pp. 321–61, doi:10.1007/s00220-016-2705-9.
short: M. Guardia, V. Kaloshin, J. Zhang, Communications in Mathematical Physics
348 (2016) 321–361.
date_created: 2020-09-18T10:45:50Z
date_published: 2016-11-01T00:00:00Z
date_updated: 2021-01-12T08:19:39Z
day: '01'
doi: 10.1007/s00220-016-2705-9
extern: '1'
intvolume: ' 348'
language:
- iso: eng
month: '11'
oa_version: None
page: 321-361
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: A second order expansion of the separatrix map for trigonometric perturbations
of a priori unstable systems
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 348
year: '2016'
...
---
_id: '1935'
abstract:
- lang: eng
text: 'We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor
ferromagnetic and long-range antiferromagnetic interactions, the latter decaying
as (distance)-p, p > 2d, at large distances. If the strength J of the ferromagnetic
interaction is larger than a critical value J c, then the ground state is homogeneous.
It has been conjectured that when J is smaller than but close to J c, the ground
state is periodic and striped, with stripes of constant width h = h(J), and h
→ ∞ as J → Jc -. (In d = 3 stripes mean slabs, not columns.) Here we rigorously
prove that, if we normalize the energy in such a way that the energy of the homogeneous
state is zero, then the ratio e 0(J)/e S(J) tends to 1 as J → Jc -, with e S(J)
being the energy per site of the optimal periodic striped/slabbed state and e
0(J) the actual ground state energy per site of the system. Our proof comes with
explicit bounds on the difference e 0(J)-e S(J) at small but positive J c-J, and
also shows that in this parameter range the ground state is striped/slabbed in
a certain sense: namely, if one looks at a randomly chosen window, of suitable
size ℓ (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed
state with high probability.'
acknowledgement: "2014 by the authors. This paper may be reproduced, in its entirety,
for non-commercial purposes.\r\n\r\nThe research leading to these results has received
funding from the European Research\r\nCouncil under the European Union’s Seventh
Framework Programme ERC Starting Grant CoMBoS (Grant Agreement No. 239694; A.G.
and R.S.), the U.S. National Science Foundation (Grant PHY 0965859; E.H.L.), the
Simons Foundation (Grant # 230207; E.H.L) and the NSERC (R.S.). The work is part
of a project started in collaboration with Joel Lebowitz, whom we thank for many
useful discussions and for his constant encouragement."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Alessandro
full_name: Giuliani, Alessandro
last_name: Giuliani
- first_name: Élliott
full_name: Lieb, Élliott
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Giuliani A, Lieb É, Seiringer R. Formation of stripes and slabs near the ferromagnetic
transition. Communications in Mathematical Physics. 2014;331:333-350. doi:10.1007/s00220-014-1923-2
apa: Giuliani, A., Lieb, É., & Seiringer, R. (2014). Formation of stripes and
slabs near the ferromagnetic transition. Communications in Mathematical Physics.
Springer. https://doi.org/10.1007/s00220-014-1923-2
chicago: Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Formation of
Stripes and Slabs near the Ferromagnetic Transition.” Communications in Mathematical
Physics. Springer, 2014. https://doi.org/10.1007/s00220-014-1923-2.
ieee: A. Giuliani, É. Lieb, and R. Seiringer, “Formation of stripes and slabs near
the ferromagnetic transition,” Communications in Mathematical Physics,
vol. 331. Springer, pp. 333–350, 2014.
ista: Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near
the ferromagnetic transition. Communications in Mathematical Physics. 331, 333–350.
mla: Giuliani, Alessandro, et al. “Formation of Stripes and Slabs near the Ferromagnetic
Transition.” Communications in Mathematical Physics, vol. 331, Springer,
2014, pp. 333–50, doi:10.1007/s00220-014-1923-2.
short: A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics
331 (2014) 333–350.
date_created: 2018-12-11T11:54:48Z
date_published: 2014-10-01T00:00:00Z
date_updated: 2022-05-24T08:32:50Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00220-014-1923-2
external_id:
arxiv:
- '1304.6344'
file:
- access_level: open_access
checksum: c8423271cd1e1ba9e44c47af75efe7b6
content_type: application/pdf
creator: dernst
date_created: 2022-05-24T08:30:40Z
date_updated: 2022-05-24T08:30:40Z
file_id: '11409'
file_name: 2014_CommMathPhysics_Giuliani.pdf
file_size: 334064
relation: main_file
success: 1
file_date_updated: 2022-05-24T08:30:40Z
has_accepted_license: '1'
intvolume: ' 331'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 333 - 350
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer
publist_id: '5159'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Formation of stripes and slabs near the ferromagnetic transition
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 331
year: '2014'
...
---
_id: '8502'
abstract:
- lang: eng
text: 'The famous ergodic hypothesis suggests that for a typical Hamiltonian on
a typical energy surface nearly all trajectories are dense. KAM theory disproves
it. Ehrenfest (The Conceptual Foundations of the Statistical Approach in Mechanics.
Ithaca, NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers.
Vol 2, New York: Dover, pp 462–465, 1968) stated the quasi-ergodic hypothesis
claiming that a typical Hamiltonian on a typical energy surface has a dense orbit.
This question is wide open. Herman (Proceedings of the International Congress
of Mathematicians, Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin:
Int Math Union, pp 797–808, 1998) proposed to look for an example of a Hamiltonian
near H0(I)=⟨I,I⟩2 with a dense orbit on the unit energy surface. In this paper
we construct a Hamiltonian H0(I)+εH1(θ,I,ε) which has an orbit dense in a set
of maximal Hausdorff dimension equal to 5 on the unit energy surface.'
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Maria
full_name: Saprykina, Maria
last_name: Saprykina
citation:
ama: Kaloshin V, Saprykina M. An example of a nearly integrable Hamiltonian system
with a trajectory dense in a set of maximal Hausdorff dimension. Communications
in Mathematical Physics. 2012;315(3):643-697. doi:10.1007/s00220-012-1532-x
apa: Kaloshin, V., & Saprykina, M. (2012). An example of a nearly integrable
Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension.
Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-012-1532-x
chicago: Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable
Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.”
Communications in Mathematical Physics. Springer Nature, 2012. https://doi.org/10.1007/s00220-012-1532-x.
ieee: V. Kaloshin and M. Saprykina, “An example of a nearly integrable Hamiltonian
system with a trajectory dense in a set of maximal Hausdorff dimension,” Communications
in Mathematical Physics, vol. 315, no. 3. Springer Nature, pp. 643–697, 2012.
ista: Kaloshin V, Saprykina M. 2012. An example of a nearly integrable Hamiltonian
system with a trajectory dense in a set of maximal Hausdorff dimension. Communications
in Mathematical Physics. 315(3), 643–697.
mla: Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian
System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” Communications
in Mathematical Physics, vol. 315, no. 3, Springer Nature, 2012, pp. 643–97,
doi:10.1007/s00220-012-1532-x.
short: V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012)
643–697.
date_created: 2020-09-18T10:47:16Z
date_published: 2012-11-01T00:00:00Z
date_updated: 2021-01-12T08:19:44Z
day: '01'
doi: 10.1007/s00220-012-1532-x
extern: '1'
intvolume: ' 315'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '11'
oa_version: None
page: 643-697
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: An example of a nearly integrable Hamiltonian system with a trajectory dense
in a set of maximal Hausdorff dimension
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 315
year: '2012'
...
---
_id: '2739'
abstract:
- lang: eng
text: We define the two dimensional Pauli operator and identify its core for magnetic
fields that are regular Borel measures. The magnetic field is generated by a scalar
potential hence we bypass the usual A L 2loc condition on the vector potential,
which does not allow to consider such singular fields. We extend the Aharonov-Casher
theorem for magnetic fields that are measures with finite total variation and
we present a counterexample in case of infinite total variation. One of the key
technical tools is a weighted L 2 estimate on a singular integral operator.
acknowledgement: "This work started during the first author’s visit at the Erwin Schrödinger
Institute, Vienna.\r\nValuable discussions with T. Hoffmann-Ostenhof and M. Loss
are gratefully acknowledged. The authors thank\r\nthe referee for careful reading
and comments"
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: Vitali
full_name: Vougalter, Vitali
last_name: Vougalter
citation:
ama: Erdös L, Vougalter V. Pauli operator and Aharonov–Casher theorem¶ for measure
valued magnetic fields. Communications in Mathematical Physics. 2002;225(2):399-421.
doi:10.1007/s002200100585
apa: Erdös, L., & Vougalter, V. (2002). Pauli operator and Aharonov–Casher theorem¶
for measure valued magnetic fields. Communications in Mathematical Physics.
Springer. https://doi.org/10.1007/s002200100585
chicago: Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov–Casher
Theorem¶ for Measure Valued Magnetic Fields.” Communications in Mathematical
Physics. Springer, 2002. https://doi.org/10.1007/s002200100585.
ieee: L. Erdös and V. Vougalter, “Pauli operator and Aharonov–Casher theorem¶ for
measure valued magnetic fields,” Communications in Mathematical Physics,
vol. 225, no. 2. Springer, pp. 399–421, 2002.
ista: Erdös L, Vougalter V. 2002. Pauli operator and Aharonov–Casher theorem¶ for
measure valued magnetic fields. Communications in Mathematical Physics. 225(2),
399–421.
mla: Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov–Casher Theorem¶
for Measure Valued Magnetic Fields.” Communications in Mathematical Physics,
vol. 225, no. 2, Springer, 2002, pp. 399–421, doi:10.1007/s002200100585.
short: L. Erdös, V. Vougalter, Communications in Mathematical Physics 225 (2002)
399–421.
date_created: 2018-12-11T11:59:21Z
date_published: 2002-02-01T00:00:00Z
date_updated: 2023-07-18T08:57:54Z
day: '01'
doi: 10.1007/s002200100585
extern: '1'
external_id:
arxiv:
- math-ph/0109015v1
intvolume: ' 225'
issue: '2'
language:
- iso: eng
month: '02'
oa_version: None
page: 399 - 421
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
publication_status: published
publisher: Springer
publist_id: '4153'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 225
year: '2002'
...
---
_id: '2347'
abstract:
- lang: eng
text: We consider the ground state properties of an inhomogeneous two-dimensional
Bose gas with a repulsive, short range pair interaction and an external confining
potential. In the limit when the particle number N is large but ρ̅a 2 is small,
where ρ̅ is the average particle density and a the scattering length, the ground
state energy and density are rigorously shown to be given to leading order by
a Gross–Pitaevskii (GP) energy functional with a coupling constant g~1/|1n(ρ̅a
2)|. In contrast to the 3D case the coupling constant depends on N through the
mean density. The GP energy per particle depends only on Ng. In 2D this parameter
is typically so large that the gradient term in the GP energy functional is negligible
and the simpler description by a Thomas–Fermi type functional is adequate.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Élliott
full_name: Lieb, Élliott
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: Lieb É, Seiringer R, Yngvason J. A rigorous derivation of the Gross-Pitaevskii
energy functional for a two-dimensional Bose gas. Communications in Mathematical
Physics. 2001;224(1):17-31. doi:10.1007/s002200100533
apa: Lieb, É., Seiringer, R., & Yngvason, J. (2001). A rigorous derivation of
the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Communications
in Mathematical Physics. Springer. https://doi.org/10.1007/s002200100533
chicago: Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “A Rigorous Derivation
of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas.” Communications
in Mathematical Physics. Springer, 2001. https://doi.org/10.1007/s002200100533.
ieee: É. Lieb, R. Seiringer, and J. Yngvason, “A rigorous derivation of the Gross-Pitaevskii
energy functional for a two-dimensional Bose gas,” Communications in Mathematical
Physics, vol. 224, no. 1. Springer, pp. 17–31, 2001.
ista: Lieb É, Seiringer R, Yngvason J. 2001. A rigorous derivation of the Gross-Pitaevskii
energy functional for a two-dimensional Bose gas. Communications in Mathematical
Physics. 224(1), 17–31.
mla: Lieb, Élliott, et al. “A Rigorous Derivation of the Gross-Pitaevskii Energy
Functional for a Two-Dimensional Bose Gas.” Communications in Mathematical
Physics, vol. 224, no. 1, Springer, 2001, pp. 17–31, doi:10.1007/s002200100533.
short: É. Lieb, R. Seiringer, J. Yngvason, Communications in Mathematical Physics
224 (2001) 17–31.
date_created: 2018-12-11T11:57:08Z
date_published: 2001-11-01T00:00:00Z
date_updated: 2023-05-30T12:28:46Z
day: '01'
doi: 10.1007/s002200100533
extern: '1'
external_id:
arxiv:
- cond-mat/0005026
intvolume: ' 224'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/cond-mat/0005026
month: '11'
oa: 1
oa_version: Published Version
page: 17 - 31
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
publication_status: published
publisher: Springer
publist_id: '4579'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional
Bose gas
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 224
year: '2001'
...
---
_id: '2348'
abstract:
- lang: eng
text: This paper concerns the asymptotic ground state properties of heavy atoms
in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z
tends to ∞ with the magnetic field B satisfying B ≫ Z4/3 all the electrons are
confined to the lowest Landau band. We consider here an energy functional, whose
variable is a sequence of one-dimensional density matrices corresponding to different
angular momentum functions in the lowest Landau band. We study this functional
in detail and derive various interesting properties, which are compared with the
density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast
to the DM theory the variable perpendicular to the field is replaced by the discrete
angular momentum quantum numbers. Hence we call the new functional a discrete
density matrix (DDM) functional. We relate this DDM theory to the lowest Landau
band quantum mechanics and show that it reproduces correctly the ground state
energy apart from errors due to the indirect part of the Coulomb interaction energy.
acknowledgement: The authors would like to thank Bernhard Baumgartner and Jakob Yngvason
for proofreading and valuable comments.
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. A discrete density matrix theory for atoms in strong
magnetic fields. Communications in Mathematical Physics. 2001;217(1):229-248.
doi:10.1007/s002200100373
apa: Hainzl, C., & Seiringer, R. (2001). A discrete density matrix theory for
atoms in strong magnetic fields. Communications in Mathematical Physics.
Springer. https://doi.org/10.1007/s002200100373
chicago: Hainzl, Christian, and Robert Seiringer. “A Discrete Density Matrix Theory
for Atoms in Strong Magnetic Fields.” Communications in Mathematical Physics.
Springer, 2001. https://doi.org/10.1007/s002200100373.
ieee: C. Hainzl and R. Seiringer, “A discrete density matrix theory for atoms in
strong magnetic fields,” Communications in Mathematical Physics, vol. 217,
no. 1. Springer, pp. 229–248, 2001.
ista: Hainzl C, Seiringer R. 2001. A discrete density matrix theory for atoms in
strong magnetic fields. Communications in Mathematical Physics. 217(1), 229–248.
mla: Hainzl, Christian, and Robert Seiringer. “A Discrete Density Matrix Theory
for Atoms in Strong Magnetic Fields.” Communications in Mathematical Physics,
vol. 217, no. 1, Springer, 2001, pp. 229–48, doi:10.1007/s002200100373.
short: C. Hainzl, R. Seiringer, Communications in Mathematical Physics 217 (2001)
229–248.
date_created: 2018-12-11T11:57:08Z
date_published: 2001-02-01T00:00:00Z
date_updated: 2023-05-30T06:54:54Z
day: '01'
doi: 10.1007/s002200100373
extern: '1'
external_id:
arxiv:
- math-ph/0010005
intvolume: ' 217'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0010005
month: '02'
oa: 1
oa_version: Preprint
page: 229 - 248
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
publication_status: published
publisher: Springer
publist_id: '4578'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A discrete density matrix theory for atoms in strong magnetic fields
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 217
year: '2001'
...