---
_id: '12232'
abstract:
- lang: eng
  text: We derive a precise asymptotic formula for the density of the small singular
    values of the real Ginibre matrix ensemble shifted by a complex parameter z as
    the dimension tends to infinity. For z away from the real axis the formula coincides
    with that for the complex Ginibre ensemble we derived earlier in Cipolloni et
    al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of
    the low lying singular values we thus confirm the transition from real to complex
    Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous
    phenomenon has been well known for eigenvalues. We use the superbosonization formula
    (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the
    main contribution comes from a three dimensional saddle manifold.
acknowledgement: Open access funding provided by Swiss Federal Institute of Technology
  Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH
  Zürich Foundation.
article_processing_charge: No
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. Density of small singular values of the
    shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. 2022;23(11):3981-4002.
    doi:<a href="https://doi.org/10.1007/s00023-022-01188-8">10.1007/s00023-022-01188-8</a>
  apa: Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Density of small singular
    values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00023-022-01188-8">https://doi.org/10.1007/s00023-022-01188-8</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small
    Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>.
    Springer Nature, 2022. <a href="https://doi.org/10.1007/s00023-022-01188-8">https://doi.org/10.1007/s00023-022-01188-8</a>.
  ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values
    of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, vol. 23,
    no. 11. Springer Nature, pp. 3981–4002, 2022.
  ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values
    of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.
  mla: Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted
    Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>, vol. 23, no. 11, Springer
    Nature, 2022, pp. 3981–4002, doi:<a href="https://doi.org/10.1007/s00023-022-01188-8">10.1007/s00023-022-01188-8</a>.
  short: G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.
date_created: 2023-01-16T09:50:26Z
date_published: 2022-11-01T00:00:00Z
date_updated: 2023-08-04T09:33:52Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-022-01188-8
external_id:
  isi:
  - '000796323500001'
file:
- access_level: open_access
  checksum: 5582f059feeb2f63e2eb68197a34d7dc
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  creator: dernst
  date_created: 2023-01-27T11:06:47Z
  date_updated: 2023-01-27T11:06:47Z
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  file_size: 1333638
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has_accepted_license: '1'
intvolume: '        23'
isi: 1
issue: '11'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 3981-4002
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: Density of small singular values of the shifted real Ginibre ensemble
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: 23
year: '2022'
...
---
_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
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: 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. <i>Annales Henri Poincaré </i>. 2021;22:4205–4269. doi:<a
    href="https://doi.org/10.1007/s00023-021-01085-6">10.1007/s00023-021-01085-6</a>
  apa: Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2021). Scattering in quantum dots
    via noncommutative rational functions. <i>Annales Henri Poincaré </i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00023-021-01085-6">https://doi.org/10.1007/s00023-021-01085-6</a>
  chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum
    Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>. Springer
    Nature, 2021. <a href="https://doi.org/10.1007/s00023-021-01085-6">https://doi.org/10.1007/s00023-021-01085-6</a>.
  ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative
    rational functions,” <i>Annales Henri Poincaré </i>, 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.” <i>Annales Henri Poincaré </i>, vol. 22, Springer Nature, 2021, pp.
    4205–4269, doi:<a href="https://doi.org/10.1007/s00023-021-01085-6">10.1007/s00023-021-01085-6</a>.
  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
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  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: '6788'
abstract:
- lang: eng
  text: We consider the Nelson model with ultraviolet cutoff, which describes the
    interaction between non-relativistic particles and a positive or zero mass quantized
    scalar field. We take the non-relativistic particles to obey Fermi statistics
    and discuss the time evolution in a mean-field limit of many fermions. In this
    case, the limit is known to be also a semiclassical limit. We prove convergence
    in terms of reduced density matrices of the many-body state to a tensor product
    of a Slater determinant with semiclassical structure and a coherent state, which
    evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- 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: Sören P
  full_name: Petrat, Sören P
  id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
  last_name: Petrat
  orcid: 0000-0002-9166-5889
citation:
  ama: Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions.
    <i>Annales Henri Poincare</i>. 2019;20(10):3471–3508. doi:<a href="https://doi.org/10.1007/s00023-019-00828-w">10.1007/s00023-019-00828-w</a>
  apa: Leopold, N. K., &#38; Petrat, S. P. (2019). Mean-field dynamics for the Nelson
    model with fermions. <i>Annales Henri Poincare</i>. Springer Nature. <a href="https://doi.org/10.1007/s00023-019-00828-w">https://doi.org/10.1007/s00023-019-00828-w</a>
  chicago: Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson
    Model with Fermions.” <i>Annales Henri Poincare</i>. Springer Nature, 2019. <a
    href="https://doi.org/10.1007/s00023-019-00828-w">https://doi.org/10.1007/s00023-019-00828-w</a>.
  ieee: N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model
    with fermions,” <i>Annales Henri Poincare</i>, vol. 20, no. 10. Springer Nature,
    pp. 3471–3508, 2019.
  ista: Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with
    fermions. Annales Henri Poincare. 20(10), 3471–3508.
  mla: Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson
    Model with Fermions.” <i>Annales Henri Poincare</i>, vol. 20, no. 10, Springer
    Nature, 2019, pp. 3471–3508, doi:<a href="https://doi.org/10.1007/s00023-019-00828-w">10.1007/s00023-019-00828-w</a>.
  short: N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 3471–3508.
date_created: 2019-08-11T21:59:21Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2023-08-29T07:09:06Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00023-019-00828-w
ec_funded: 1
external_id:
  arxiv:
  - '1807.06781'
  isi:
  - '000487036900008'
file:
- access_level: open_access
  checksum: b6dbf0d837d809293d449adf77138904
  content_type: application/pdf
  creator: dernst
  date_created: 2019-08-12T12:05:58Z
  date_updated: 2020-07-14T12:47:40Z
  file_id: '6801'
  file_name: 2019_AnnalesHenriPoincare_Leopold.pdf
  file_size: 681139
  relation: main_file
file_date_updated: 2020-07-14T12:47:40Z
has_accepted_license: '1'
intvolume: '        20'
isi: 1
issue: '10'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 3471–3508
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: Annales Henri Poincare
publication_identifier:
  eissn:
  - 1424-0661
  issn:
  - 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mean-field dynamics for the Nelson model with fermions
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: 20
year: '2019'
...