---
_id: '14254'
abstract:
- lang: eng
  text: In [10] Nam proved a Lieb–Thirring Inequality for the kinetic energy of a
    fermionic quantum system, with almost optimal (semi-classical) constant and a
    gradient correction term. We present a stronger version of this inequality, with
    a much simplified proof. As a corollary we obtain a simple proof of the original
    Lieb–Thirring inequality.
acknowledgement: J.P.S. thanks the Institute of Science and Technology Austria for
  the hospitality and support during a visit where this work was done. J.P.S. was
  also partially supported by the VILLUM Centre of Excellence for the Mathematics
  of Quantum Theory (QMATH) (grant No. 10059).
article_number: '110129'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
- first_name: Jan Philip
  full_name: Solovej, Jan Philip
  last_name: Solovej
citation:
  ama: Seiringer R, Solovej JP. A simple approach to Lieb-Thirring type inequalities.
    <i>Journal of Functional Analysis</i>. 2023;285(10). doi:<a href="https://doi.org/10.1016/j.jfa.2023.110129">10.1016/j.jfa.2023.110129</a>
  apa: Seiringer, R., &#38; Solovej, J. P. (2023). A simple approach to Lieb-Thirring
    type inequalities. <i>Journal of Functional Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jfa.2023.110129">https://doi.org/10.1016/j.jfa.2023.110129</a>
  chicago: Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring
    Type Inequalities.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a
    href="https://doi.org/10.1016/j.jfa.2023.110129">https://doi.org/10.1016/j.jfa.2023.110129</a>.
  ieee: R. Seiringer and J. P. Solovej, “A simple approach to Lieb-Thirring type inequalities,”
    <i>Journal of Functional Analysis</i>, vol. 285, no. 10. Elsevier, 2023.
  ista: Seiringer R, Solovej JP. 2023. A simple approach to Lieb-Thirring type inequalities.
    Journal of Functional Analysis. 285(10), 110129.
  mla: Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring
    Type Inequalities.” <i>Journal of Functional Analysis</i>, vol. 285, no. 10, 110129,
    Elsevier, 2023, doi:<a href="https://doi.org/10.1016/j.jfa.2023.110129">10.1016/j.jfa.2023.110129</a>.
  short: R. Seiringer, J.P. Solovej, Journal of Functional Analysis 285 (2023).
date_created: 2023-09-03T22:01:14Z
date_published: 2023-11-15T00:00:00Z
date_updated: 2024-01-30T14:17:23Z
day: '15'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1016/j.jfa.2023.110129
external_id:
  arxiv:
  - '2303.04504'
  isi:
  - '001071552300001'
file:
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intvolume: '       285'
isi: 1
issue: '10'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
  eissn:
  - 1096-0783
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: A simple approach to Lieb-Thirring type inequalities
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: 285
year: '2023'
...
---
_id: '12911'
abstract:
- lang: eng
  text: 'This paper establishes new connections between many-body quantum systems,
    One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport
    (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional
    composite quantum system at positive temperature as a non-commutative entropy
    regularized Optimal Transport problem. We develop a new approach to fully characterize
    the dual-primal solutions in such non-commutative setting. The mathematical formalism
    is particularly relevant in quantum chemistry: numerical realizations of the many-electron
    ground-state energy can be computed via a non-commutative version of Sinkhorn
    algorithm. Our approach allows to prove convergence and robustness of this algorithm,
    which, to our best knowledge, were unknown even in the two marginal case. Our
    methods are based on a priori estimates in the dual problem, which we believe
    to be of independent interest. Finally, the above results are extended in 1RDMFT
    setting, where bosonic or fermionic symmetry conditions are enforced on the problem.'
acknowledgement: "This work started when A.G. was visiting the Erwin Schrödinger Institute
  and then continued when D.F. and L.P visited the Theoretical Chemistry Department
  of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places
  and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature
  suggestions in the early state of the project. The authors also thank J. Maas and
  R. Seiringer for their feedback and useful comments to a first draft of the article.
  Finally, we acknowledge the high quality review done by the anonymous referee of
  our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F
  acknowledges support by the European Research Council (ERC) under the European Union's
  Horizon 2020 research and innovation programme (grant agreements No 716117 and No
  694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council
  under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of
  his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences
  and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges
  support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the
  Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813."
article_number: '109963'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dario
  full_name: Feliciangeli, Dario
  id: 41A639AA-F248-11E8-B48F-1D18A9856A87
  last_name: Feliciangeli
  orcid: 0000-0003-0754-8530
- first_name: Augusto
  full_name: Gerolin, Augusto
  last_name: Gerolin
- first_name: Lorenzo
  full_name: Portinale, Lorenzo
  id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
  last_name: Portinale
citation:
  ama: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal
    transport approach to quantum composite systems at positive temperature. <i>Journal
    of Functional Analysis</i>. 2023;285(4). doi:<a href="https://doi.org/10.1016/j.jfa.2023.109963">10.1016/j.jfa.2023.109963</a>
  apa: Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (2023). A non-commutative
    entropic optimal transport approach to quantum composite systems at positive temperature.
    <i>Journal of Functional Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jfa.2023.109963">https://doi.org/10.1016/j.jfa.2023.109963</a>
  chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative
    Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.”
    <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href="https://doi.org/10.1016/j.jfa.2023.109963">https://doi.org/10.1016/j.jfa.2023.109963</a>.
  ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic
    optimal transport approach to quantum composite systems at positive temperature,”
    <i>Journal of Functional Analysis</i>, vol. 285, no. 4. Elsevier, 2023.
  ista: Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal
    transport approach to quantum composite systems at positive temperature. Journal
    of Functional Analysis. 285(4), 109963.
  mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach
    to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional
    Analysis</i>, vol. 285, no. 4, 109963, Elsevier, 2023, doi:<a href="https://doi.org/10.1016/j.jfa.2023.109963">10.1016/j.jfa.2023.109963</a>.
  short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis
    285 (2023).
date_created: 2023-05-07T22:01:02Z
date_published: 2023-08-15T00:00:00Z
date_updated: 2023-11-14T13:21:01Z
day: '15'
department:
- _id: RoSe
- _id: JaMa
doi: 10.1016/j.jfa.2023.109963
ec_funded: 1
external_id:
  arxiv:
  - '2106.11217'
  isi:
  - '000990804300001'
intvolume: '       285'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2106.11217
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
- _id: 260482E2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: ' F06504'
  name: Taming Complexity in Partial Di erential Systems
publication: Journal of Functional Analysis
publication_identifier:
  eissn:
  - 1096-0783
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
  record:
  - id: '9792'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: A non-commutative entropic optimal transport approach to quantum composite
  systems at positive temperature
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 285
year: '2023'
...
---
_id: '10732'
abstract:
- lang: eng
  text: We compute the deterministic approximation of products of Sobolev functions
    of large Wigner matrices W and provide an optimal error bound on their fluctuation
    with very high probability. This generalizes Voiculescu's seminal theorem from
    polynomials to general Sobolev functions, as well as from tracial quantities to
    individual matrix elements. Applying the result to eitW for large t, we obtain
    a precise decay rate for the overlaps of several deterministic matrices with temporally
    well separated Heisenberg time evolutions; thus we demonstrate the thermalisation
    effect of the unitary group generated by Wigner matrices.
acknowledgement: We compute the deterministic approximation of products of Sobolev
  functions of large Wigner matrices W and provide an optimal error bound on their
  fluctuation with very high probability. This generalizes Voiculescu's seminal theorem
  from polynomials to general Sobolev functions, as well as from tracial quantities
  to individual matrix elements. Applying the result to  for large t, we obtain a
  precise decay rate for the overlaps of several deterministic matrices with temporally
  well separated Heisenberg time evolutions; thus we demonstrate the thermalisation
  effect of the unitary group generated by Wigner matrices.
article_number: '109394'
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. Thermalisation for Wigner matrices. <i>Journal
    of Functional Analysis</i>. 2022;282(8). doi:<a href="https://doi.org/10.1016/j.jfa.2022.109394">10.1016/j.jfa.2022.109394</a>
  apa: Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Thermalisation for
    Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jfa.2022.109394">https://doi.org/10.1016/j.jfa.2022.109394</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation
    for Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a
    href="https://doi.org/10.1016/j.jfa.2022.109394">https://doi.org/10.1016/j.jfa.2022.109394</a>.
  ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,”
    <i>Journal of Functional Analysis</i>, vol. 282, no. 8. Elsevier, 2022.
  ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices.
    Journal of Functional Analysis. 282(8), 109394.
  mla: Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” <i>Journal
    of Functional Analysis</i>, vol. 282, no. 8, 109394, Elsevier, 2022, doi:<a href="https://doi.org/10.1016/j.jfa.2022.109394">10.1016/j.jfa.2022.109394</a>.
  short: G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282
    (2022).
date_created: 2022-02-06T23:01:30Z
date_published: 2022-04-15T00:00:00Z
date_updated: 2023-08-02T14:12:35Z
day: '15'
ddc:
- '500'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2022.109394
external_id:
  arxiv:
  - '2102.09975'
  isi:
  - '000781239100004'
file:
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  date_updated: 2022-07-29T07:22:08Z
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intvolume: '       282'
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language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
  eissn:
  - 1096-0783
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Thermalisation for Wigner matrices
tmp:
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  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: 282
year: '2022'
...
---
_id: '10887'
abstract:
- lang: eng
  text: "We introduce a new way of representing logarithmically concave functions
    on Rd. It allows us to extend the notion of the largest volume ellipsoid contained
    in a convex body to the setting of logarithmically concave functions as follows.
    For every s>0, we define a class of non-negative functions on Rd derived from
    ellipsoids in Rd+1. For any log-concave function f on Rd , and any fixed s>0,
    we consider functions belonging to this class, and find the one with the largest
    integral under the condition that it is pointwise less than or equal to f, and
    we call it the John s-function of f. After establishing existence and uniqueness,
    we give a characterization of this function similar to the one given by John in
    his fundamental theorem. We find that John s-functions converge to characteristic
    functions of ellipsoids as s tends to zero and to Gaussian densities as s tends
    to infinity.\r\nAs an application, we prove a quantitative Helly type result:
    the integral of the pointwise minimum of any family of log-concave functions is
    at least a constant cd multiple of the integral of the pointwise minimum of a
    properly chosen subfamily of size 3d+2, where cd depends only on d."
acknowledgement: 'G.I. was supported by the Ministry of Education and Science of the
  Russian Federation in the framework of MegaGrant no 075-15-2019-1926. M.N. was supported
  by the National Research, Development and Innovation Fund (NRDI) grants K119670
  and KKP-133864 as well as the Bolyai Scholarship of the Hungarian Academy of Sciences
  and the New National Excellence Programme and the TKP2020-NKA-06 program provided
  by the NRDI. '
article_number: '109441'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Grigory
  full_name: Ivanov, Grigory
  id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
  last_name: Ivanov
- first_name: Márton
  full_name: Naszódi, Márton
  last_name: Naszódi
citation:
  ama: Ivanov G, Naszódi M. Functional John ellipsoids. <i>Journal of Functional Analysis</i>.
    2022;282(11). doi:<a href="https://doi.org/10.1016/j.jfa.2022.109441">10.1016/j.jfa.2022.109441</a>
  apa: Ivanov, G., &#38; Naszódi, M. (2022). Functional John ellipsoids. <i>Journal
    of Functional Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jfa.2022.109441">https://doi.org/10.1016/j.jfa.2022.109441</a>
  chicago: Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” <i>Journal
    of Functional Analysis</i>. Elsevier, 2022. <a href="https://doi.org/10.1016/j.jfa.2022.109441">https://doi.org/10.1016/j.jfa.2022.109441</a>.
  ieee: G. Ivanov and M. Naszódi, “Functional John ellipsoids,” <i>Journal of Functional
    Analysis</i>, vol. 282, no. 11. Elsevier, 2022.
  ista: Ivanov G, Naszódi M. 2022. Functional John ellipsoids. Journal of Functional
    Analysis. 282(11), 109441.
  mla: Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” <i>Journal
    of Functional Analysis</i>, vol. 282, no. 11, 109441, Elsevier, 2022, doi:<a href="https://doi.org/10.1016/j.jfa.2022.109441">10.1016/j.jfa.2022.109441</a>.
  short: G. Ivanov, M. Naszódi, Journal of Functional Analysis 282 (2022).
date_created: 2022-03-20T23:01:38Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2023-08-02T14:51:11Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1016/j.jfa.2022.109441
external_id:
  arxiv:
  - '2006.09934'
  isi:
  - '000781371300008'
file:
- access_level: open_access
  checksum: 1cf185e264e04c87cb1ce67a00db88ab
  content_type: application/pdf
  creator: dernst
  date_created: 2022-08-02T10:40:48Z
  date_updated: 2022-08-02T10:40:48Z
  file_id: '11721'
  file_name: 2022_JourFunctionalAnalysis_Ivanov.pdf
  file_size: 734482
  relation: main_file
  success: 1
file_date_updated: 2022-08-02T10:40:48Z
has_accepted_license: '1'
intvolume: '       282'
isi: 1
issue: '11'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
  eissn:
  - 1096-0783
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functional John ellipsoids
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: 282
year: '2022'
...
---
_id: '9348'
abstract:
- lang: eng
  text: We consider the stochastic quantization of a quartic double-well energy functional
    in the semiclassical regime and derive optimal asymptotics for the exponentially
    small splitting of the ground state energy. Our result provides an infinite-dimensional
    version of some sharp tunneling estimates known in finite dimensions for semiclassical
    Witten Laplacians in degree zero. From a stochastic point of view it proves that
    the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite
    volume satisfies a Kramers-type formula in the limit of vanishing noise. We work
    with finite-dimensional lattice approximations and establish semiclassical estimates
    which are uniform in the dimension. Our key estimate shows that the constant separating
    the two exponentially small eigenvalues from the rest of the spectrum can be taken
    independently of the dimension.
acknowledgement: GDG gratefully acknowledges the financial support of HIM Bonn in
  the framework of the 2019 Junior Trimester Programs “Kinetic Theory” and “Randomness,
  PDEs and Nonlinear Fluctuations” and the hospitality at the University of Rome La
  Sapienza during his frequent visits.
article_number: '109029'
article_processing_charge: No
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: Giacomo
  full_name: Di Gesù, Giacomo
  last_name: Di Gesù
citation:
  ama: Brooks M, Di Gesù G. Sharp tunneling estimates for a double-well model in infinite
    dimension. <i>Journal of Functional Analysis</i>. 2021;281(3). doi:<a href="https://doi.org/10.1016/j.jfa.2021.109029">10.1016/j.jfa.2021.109029</a>
  apa: Brooks, M., &#38; Di Gesù, G. (2021). Sharp tunneling estimates for a double-well
    model in infinite dimension. <i>Journal of Functional Analysis</i>. Elsevier.
    <a href="https://doi.org/10.1016/j.jfa.2021.109029">https://doi.org/10.1016/j.jfa.2021.109029</a>
  chicago: Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well
    Model in Infinite Dimension.” <i>Journal of Functional Analysis</i>. Elsevier,
    2021. <a href="https://doi.org/10.1016/j.jfa.2021.109029">https://doi.org/10.1016/j.jfa.2021.109029</a>.
  ieee: M. Brooks and G. Di Gesù, “Sharp tunneling estimates for a double-well model
    in infinite dimension,” <i>Journal of Functional Analysis</i>, vol. 281, no. 3.
    Elsevier, 2021.
  ista: Brooks M, Di Gesù G. 2021. Sharp tunneling estimates for a double-well model
    in infinite dimension. Journal of Functional Analysis. 281(3), 109029.
  mla: Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well
    Model in Infinite Dimension.” <i>Journal of Functional Analysis</i>, vol. 281,
    no. 3, 109029, Elsevier, 2021, doi:<a href="https://doi.org/10.1016/j.jfa.2021.109029">10.1016/j.jfa.2021.109029</a>.
  short: M. Brooks, G. Di Gesù, Journal of Functional Analysis 281 (2021).
date_created: 2021-04-25T22:01:29Z
date_published: 2021-04-07T00:00:00Z
date_updated: 2023-08-08T13:15:11Z
day: '07'
department:
- _id: RoSe
doi: 10.1016/j.jfa.2021.109029
external_id:
  arxiv:
  - '1911.03187'
  isi:
  - '000644702800005'
intvolume: '       281'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1911.03187
month: '04'
oa: 1
oa_version: Preprint
publication: Journal of Functional Analysis
publication_identifier:
  eissn:
  - 1096-0783
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sharp tunneling estimates for a double-well model in infinite dimension
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 281
year: '2021'
...
---
_id: '9462'
abstract:
- lang: eng
  text: We consider a system of N trapped bosons with repulsive interactions in a
    combined semiclassical mean-field limit at positive temperature. We show that
    the free energy is well approximated by the minimum of the Hartree free energy
    functional – a natural extension of the Hartree energy functional to positive
    temperatures. The Hartree free energy functional converges in the same limit to
    a semiclassical free energy functional, and we show that the system displays Bose–Einstein
    condensation if and only if it occurs in the semiclassical free energy functional.
    This allows us to show that for weak coupling the critical temperature decreases
    due to the repulsive interactions.
acknowledgement: Funding from the European Union's Horizon 2020 research and innovation
  programme under the ERC grant agreement No 694227 (R.S.) and under the Marie Sklodowska-Curie
  grant agreement No 836146 (A.D.) is gratefully acknowledged. A.D. acknowledges support
  of the Swiss National Science Foundation through the Ambizione grant PZ00P2 185851.
article_number: '109096'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Andreas
  full_name: Deuchert, Andreas
  last_name: Deuchert
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Deuchert A, Seiringer R. Semiclassical approximation and critical temperature
    shift for weakly interacting trapped bosons. <i>Journal of Functional Analysis</i>.
    2021;281(6). doi:<a href="https://doi.org/10.1016/j.jfa.2021.109096">10.1016/j.jfa.2021.109096</a>
  apa: Deuchert, A., &#38; Seiringer, R. (2021). Semiclassical approximation and critical
    temperature shift for weakly interacting trapped bosons. <i>Journal of Functional
    Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jfa.2021.109096">https://doi.org/10.1016/j.jfa.2021.109096</a>
  chicago: Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and
    Critical Temperature Shift for Weakly Interacting Trapped Bosons.” <i>Journal
    of Functional Analysis</i>. Elsevier, 2021. <a href="https://doi.org/10.1016/j.jfa.2021.109096">https://doi.org/10.1016/j.jfa.2021.109096</a>.
  ieee: A. Deuchert and R. Seiringer, “Semiclassical approximation and critical temperature
    shift for weakly interacting trapped bosons,” <i>Journal of Functional Analysis</i>,
    vol. 281, no. 6. Elsevier, 2021.
  ista: Deuchert A, Seiringer R. 2021. Semiclassical approximation and critical temperature
    shift for weakly interacting trapped bosons. Journal of Functional Analysis. 281(6),
    109096.
  mla: Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical
    Temperature Shift for Weakly Interacting Trapped Bosons.” <i>Journal of Functional
    Analysis</i>, vol. 281, no. 6, 109096, Elsevier, 2021, doi:<a href="https://doi.org/10.1016/j.jfa.2021.109096">10.1016/j.jfa.2021.109096</a>.
  short: A. Deuchert, R. Seiringer, Journal of Functional Analysis 281 (2021).
date_created: 2021-06-06T22:01:28Z
date_published: 2021-09-15T00:00:00Z
date_updated: 2023-08-08T13:56:27Z
day: '15'
department:
- _id: RoSe
doi: 10.1016/j.jfa.2021.109096
ec_funded: 1
external_id:
  arxiv:
  - '2009.00992'
  isi:
  - '000656508600008'
intvolume: '       281'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2009.00992
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Journal of Functional Analysis
publication_identifier:
  eissn:
  - 1096-0783
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Semiclassical approximation and critical temperature shift for weakly interacting
  trapped bosons
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 281
year: '2021'
...
---
_id: '10070'
abstract:
- lang: eng
  text: We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties
    for generalized intrinsic distances on strongly local Dirichlet spaces possibly
    without square field operator. We present many non-smooth and infinite-dimensional
    examples. As an application, we prove the integral Varadhan short-time asymptotic
    with respect to a given distance function for a large class of strongly local
    Dirichlet forms.
acknowledgement: 'The authors are grateful to Professor Kazuhiro Kuwae for kindly
  providing a copy of [49]. They are also grateful to Dr. Bang-Xian Han for helpful
  discussions on the Sobolev-to-Lipschitz property on metric measure spaces. They
  wish to express their deepest gratitude to an anonymous Reviewer, whose punctual
  remarks and comments greatly improved the accessibility and overall quality of the
  initial submission. This work was completed while L.D.S. was a member of the Institut
  für Angewandte Mathematik of the University of Bonn. He acknowledges funding of
  his position at that time by the Deutsche Forschungsgemeinschaft (DFG, German Research
  Foundation) through the Sonderforschungsbereich (Sfb, Collaborative Research Center)
  1060 - project number 211504053. He also acknowledges funding of his current position
  by the Austrian Science Fund (FWF) grant F65, and by the European Research Council
  (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas). K.S. gratefully acknowledges
  funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier
  International Research Center Initiative (WPI), MEXT, Japan; and JSPS Grant-in-Aid
  for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials
  Design”, Grant Number 17H06465.'
article_number: '109234'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
  full_name: Dello Schiavo, Lorenzo
  id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
  last_name: Dello Schiavo
  orcid: 0000-0002-9881-6870
- first_name: Kohei
  full_name: Suzuki, Kohei
  last_name: Suzuki
citation:
  ama: Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz
    properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>.
    2021;281(11). doi:<a href="https://doi.org/10.1016/j.jfa.2021.109234">10.1016/j.jfa.2021.109234</a>
  apa: Dello Schiavo, L., &#38; Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz
    properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.jfa.2021.109234">https://doi.org/10.1016/j.jfa.2021.109234</a>
  chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and
    Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal
    of Functional Analysis</i>. Elsevier, 2021. <a href="https://doi.org/10.1016/j.jfa.2021.109234">https://doi.org/10.1016/j.jfa.2021.109234</a>.
  ieee: L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz
    properties for strongly local Dirichlet spaces,” <i>Journal of Functional Analysis</i>,
    vol. 281, no. 11. Elsevier, 2021.
  ista: Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz
    properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
    281(11), 109234.
  mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz
    Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>,
    vol. 281, no. 11, 109234, Elsevier, 2021, doi:<a href="https://doi.org/10.1016/j.jfa.2021.109234">10.1016/j.jfa.2021.109234</a>.
  short: L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).
date_created: 2021-10-03T22:01:21Z
date_published: 2021-09-15T00:00:00Z
date_updated: 2023-08-14T07:05:44Z
day: '15'
department:
- _id: JaMa
doi: 10.1016/j.jfa.2021.109234
ec_funded: 1
external_id:
  arxiv:
  - '2008.01492'
  isi:
  - '000703896600005'
intvolume: '       281'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2008.01492
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
publication: Journal of Functional Analysis
publication_identifier:
  eissn:
  - 1096-0783
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local
  Dirichlet spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 281
year: '2021'
...