---
_id: '9036'
abstract:
- lang: eng
text: In this short note, we prove that the square root of the quantum Jensen-Shannon
divergence is a true metric on the cone of positive matrices, and hence in particular
on the quantum state space.
acknowledgement: D. Virosztek was supported by the European Union's Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294,
and partially supported by the Hungarian National Research, Development and Innovation
Office (NKFIH) via grants no. K124152, and no. KH129601.
article_number: '107595'
article_processing_charge: No
article_type: original
author:
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Virosztek D. The metric property of the quantum Jensen-Shannon divergence.
Advances in Mathematics. 2021;380(3). doi:10.1016/j.aim.2021.107595
apa: Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence.
Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107595
chicago: Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.”
Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595.
ieee: D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,”
Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021.
ista: Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence.
Advances in Mathematics. 380(3), 107595.
mla: Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.”
Advances in Mathematics, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595.
short: D. Virosztek, Advances in Mathematics 380 (2021).
date_created: 2021-01-22T17:55:17Z
date_published: 2021-03-26T00:00:00Z
date_updated: 2023-08-07T13:34:48Z
day: '26'
department:
- _id: LaEr
doi: 10.1016/j.aim.2021.107595
ec_funded: 1
external_id:
arxiv:
- '1910.10447'
isi:
- '000619676100035'
intvolume: ' 380'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
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url: https://arxiv.org/abs/1910.10447
month: '03'
oa: 1
oa_version: Preprint
project:
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call_identifier: H2020
grant_number: '846294'
name: Geometric study of Wasserstein spaces and free probability
publication: Advances in Mathematics
publication_identifier:
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: The metric property of the quantum Jensen-Shannon divergence
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 380
year: '2021'
...
---
_id: '9412'
abstract:
- lang: eng
text: We extend our recent result [22] on the central limit theorem for the linear
eigenvalue statistics of non-Hermitian matrices X with independent, identically
distributed complex entries to the real symmetry class. We find that the expectation
and variance substantially differ from their complex counterparts, reflecting
(i) the special spectral symmetry of real matrices onto the real axis; and (ii)
the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes
the previously known special cases where either the test function is analytic
[49] or the first four moments of the matrix elements match the real Gaussian
[59, 44]. The key element of the proof is the analysis of several weakly dependent
Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared
with [22] is that the correlation structure of the stochastic differentials in
each individual DBM is non-trivial, potentially even jeopardising its well-posedness.
article_number: '24'
article_processing_charge: No
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. Fluctuation around the circular law for
random matrices with real entries. Electronic Journal of Probability. 2021;26.
doi:10.1214/21-EJP591
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Fluctuation around
the circular law for random matrices with real entries. Electronic Journal
of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP591
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation
around the Circular Law for Random Matrices with Real Entries.” Electronic
Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP591.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular
law for random matrices with real entries,” Electronic Journal of Probability,
vol. 26. Institute of Mathematical Statistics, 2021.
ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Fluctuation around the circular law
for random matrices with real entries. Electronic Journal of Probability. 26,
24.
mla: Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random
Matrices with Real Entries.” Electronic Journal of Probability, vol. 26,
24, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP591.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability
26 (2021).
date_created: 2021-05-23T22:01:44Z
date_published: 2021-03-23T00:00:00Z
date_updated: 2023-08-08T13:39:19Z
day: '23'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/21-EJP591
ec_funded: 1
external_id:
arxiv:
- '2002.02438'
isi:
- '000641855600001'
file:
- access_level: open_access
checksum: 864ab003ad4cffea783f65aa8c2ba69f
content_type: application/pdf
creator: kschuh
date_created: 2021-05-25T13:24:19Z
date_updated: 2021-05-25T13:24:19Z
file_id: '9423'
file_name: 2021_EJP_Cipolloni.pdf
file_size: 865148
relation: main_file
success: 1
file_date_updated: 2021-05-25T13:24:19Z
has_accepted_license: '1'
intvolume: ' 26'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Electronic Journal of Probability
publication_identifier:
eissn:
- '10836489'
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fluctuation around the circular law for random matrices with real entries
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: 26
year: '2021'
...
---
_id: '9550'
abstract:
- lang: eng
text: 'We prove that the energy of any eigenvector of a sum of several independent
large Wigner matrices is equally distributed among these matrices with very high
precision. This shows a particularly strong microcanonical form of the equipartition
principle for quantum systems whose components are modelled by Wigner matrices. '
acknowledgement: The first author is supported in part by Hong Kong RGC Grant GRF
16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced
Grant RANMAT 338804. The third author is supported in part by Swedish Research Council
Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation
article_number: e44
article_processing_charge: No
article_type: original
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum
of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38
apa: Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for
Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press.
https://doi.org/10.1017/fms.2021.38
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle
for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University
Press, 2021. https://doi.org/10.1017/fms.2021.38.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,”
Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021.
ista: Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices.
Forum of Mathematics, Sigma. 9, e44.
mla: Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” Forum
of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38.
short: Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).
date_created: 2021-06-13T22:01:33Z
date_published: 2021-05-27T00:00:00Z
date_updated: 2023-08-08T14:03:40Z
day: '27'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2021.38
ec_funded: 1
external_id:
arxiv:
- '2008.07061'
isi:
- '000654960800001'
file:
- access_level: open_access
checksum: 47c986578de132200d41e6d391905519
content_type: application/pdf
creator: cziletti
date_created: 2021-06-15T14:40:45Z
date_updated: 2021-06-15T14:40:45Z
file_id: '9555'
file_name: 2021_ForumMath_Bao.pdf
file_size: 483458
relation: main_file
success: 1
file_date_updated: 2021-06-15T14:40:45Z
has_accepted_license: '1'
intvolume: ' 9'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- '20505094'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equipartition principle for Wigner matrices
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: 9
year: '2021'
...
---
_id: '9912'
abstract:
- lang: eng
text: "In the customary random matrix model for transport in quantum dots with M
internal degrees of freedom coupled to a chaotic environment via \U0001D441≪\U0001D440
channels, the density \U0001D70C of transmission eigenvalues is computed from
a specific invariant ensemble for which explicit formula for the joint probability
density of all eigenvalues is available. We revisit this problem in the large
N regime allowing for (i) arbitrary ratio \U0001D719:=\U0001D441/\U0001D440≤1;
and (ii) general distributions for the matrix elements of the Hamiltonian of the
quantum dot. In the limit \U0001D719→0, we recover the formula for the density
\U0001D70C that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special
matrix ensemble. We also prove that the inverse square root singularity of the
density at zero and full transmission in Beenakker’s formula persists for any
\U0001D719<1 but in the borderline case \U0001D719=1 an anomalous \U0001D706−2/3
singularity arises at zero. To access this level of generality, we develop the
theory of global and local laws on the spectral density of a large class of noncommutative
rational expressions in large random matrices with i.i.d. entries."
acknowledgement: The authors are very grateful to Yan Fyodorov for discussions on
the physical background and for providing references, and to the anonymous referee
for numerous valuable remarks.
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative
rational functions. Annales Henri Poincaré . 2021;22:4205–4269. doi:10.1007/s00023-021-01085-6
apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2021). Scattering in quantum dots
via noncommutative rational functions. Annales Henri Poincaré . Springer
Nature. https://doi.org/10.1007/s00023-021-01085-6
chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum
Dots via Noncommutative Rational Functions.” Annales Henri Poincaré . Springer
Nature, 2021. https://doi.org/10.1007/s00023-021-01085-6.
ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative
rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature,
pp. 4205–4269, 2021.
ista: Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative
rational functions. Annales Henri Poincaré . 22, 4205–4269.
mla: Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational
Functions.” Annales Henri Poincaré , vol. 22, Springer Nature, 2021, pp.
4205–4269, doi:10.1007/s00023-021-01085-6.
short: L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.
date_created: 2021-08-15T22:01:29Z
date_published: 2021-12-01T00:00:00Z
date_updated: 2023-08-11T10:31:48Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-021-01085-6
ec_funded: 1
external_id:
arxiv:
- '1911.05112'
isi:
- '000681531500001'
file:
- access_level: open_access
checksum: 8d6bac0e2b0a28539608b0538a8e3b38
content_type: application/pdf
creator: dernst
date_created: 2022-05-12T12:50:27Z
date_updated: 2022-05-12T12:50:27Z
file_id: '11365'
file_name: 2021_AnnHenriPoincare_Erdoes.pdf
file_size: 1162454
relation: main_file
success: 1
file_date_updated: 2022-05-12T12:50:27Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 4205–4269
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: 'Annales Henri Poincaré '
publication_identifier:
eissn:
- 1424-0661
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scattering in quantum dots via noncommutative rational functions
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: 22
year: '2021'
...
---
_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
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'
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file_size: 841426
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file_date_updated: 2022-02-02T10:19:55Z
has_accepted_license: '1'
intvolume: ' 388'
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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'
...