---
_id: '13225'
abstract:
- lang: eng
  text: Recently the leading order of the correlation energy of a Fermi gas in a coupled
    mean-field and semiclassical scaling regime has been derived, under the assumption
    of an interaction potential with a small norm and with compact support in Fourier
    space. We generalize this result to large interaction potentials, requiring only
    |⋅|V^∈ℓ1(Z3). Our proof is based on approximate, collective bosonization in three
    dimensions. Significant improvements compared to recent work include stronger
    bounds on non-bosonizable terms and more efficient control on the bosonization
    of the kinetic energy.
acknowledgement: "RS was supported by the European Research Council under the European
  Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227).
  MP acknowledges financial support from the European Research Council under the European
  Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, Grant Agreement
  No. 802901). BS acknowledges financial support from the NCCR SwissMAP, from the
  Swiss National Science Foundation through the Grant “Dynamical and energetic properties
  of Bose-Einstein condensates” and from the European Research Council through the
  ERC AdG CLaQS (Grant Agreement No. 834782). NB and MP were supported by Gruppo Nazionale
  per la Fisica Matematica (GNFM) of Italy. NB was supported by the European Research
  Council’s Starting Grant FERMIMATH (Grant Agreement No. 101040991).\r\nOpen access
  funding provided by Università degli Studi di Milano within the CRUI-CARE Agreement."
article_number: '65'
article_processing_charge: Yes (via OA deal)
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: 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, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly
    interacting Fermi gas with large interaction potential. <i>Archive for Rational
    Mechanics and Analysis</i>. 2023;247(4). doi:<a href="https://doi.org/10.1007/s00205-023-01893-6">10.1007/s00205-023-01893-6</a>
  apa: Benedikter, N. P., Porta, M., Schlein, B., &#38; Seiringer, R. (2023). Correlation
    energy of a weakly interacting Fermi gas with large interaction potential. <i>Archive
    for Rational Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-023-01893-6">https://doi.org/10.1007/s00205-023-01893-6</a>
  chicago: Benedikter, Niels P, Marcello Porta, Benjamin Schlein, and Robert Seiringer.
    “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.”
    <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2023. <a
    href="https://doi.org/10.1007/s00205-023-01893-6">https://doi.org/10.1007/s00205-023-01893-6</a>.
  ieee: N. P. Benedikter, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy
    of a weakly interacting Fermi gas with large interaction potential,” <i>Archive
    for Rational Mechanics and Analysis</i>, vol. 247, no. 4. Springer Nature, 2023.
  ista: Benedikter NP, Porta M, Schlein B, Seiringer R. 2023. Correlation energy of
    a weakly interacting Fermi gas with large interaction potential. Archive for Rational
    Mechanics and Analysis. 247(4), 65.
  mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi
    Gas with Large Interaction Potential.” <i>Archive for Rational Mechanics and Analysis</i>,
    vol. 247, no. 4, 65, Springer Nature, 2023, doi:<a href="https://doi.org/10.1007/s00205-023-01893-6">10.1007/s00205-023-01893-6</a>.
  short: N.P. Benedikter, M. Porta, B. Schlein, R. Seiringer, Archive for Rational
    Mechanics and Analysis 247 (2023).
date_created: 2023-07-16T22:01:08Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2023-12-13T11:31:14Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-023-01893-6
ec_funded: 1
external_id:
  arxiv:
  - '2106.13185'
  isi:
  - '001024369000001'
file:
- access_level: open_access
  checksum: 2b45828d854a253b14bf7aa196ec55e9
  content_type: application/pdf
  creator: dernst
  date_created: 2023-11-14T13:12:12Z
  date_updated: 2023-11-14T13:12:12Z
  file_id: '14535'
  file_name: 2023_ArchiveRationalMechAnalysis_Benedikter.pdf
  file_size: 851626
  relation: main_file
  success: 1
file_date_updated: 2023-11-14T13:12:12Z
has_accepted_license: '1'
intvolume: '       247'
isi: 1
issue: '4'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Correlation energy of a weakly interacting Fermi gas with large interaction
  potential
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: 247
year: '2023'
...
---
_id: '10551'
abstract:
- lang: eng
  text: 'The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of
    fluctuating hydrodynamics; it has been proposed in the physics literature to describe
    the fluctuations of the density of N independent diffusing particles in the regime
    of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation
    presents a substantial challenge for both its analysis and its rigorous mathematical
    justification. Besides being non-renormalisable by the theory of regularity structures
    by Hairer et al., it has recently been shown to not even admit nontrivial martingale
    solutions. In the present work, we give a rigorous and fully quantitative justification
    of the Dean–Kawasaki equation by considering the natural regularisation provided
    by standard numerical discretisations: We show that structure-preserving discretisations
    of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting
    diffusing particles to arbitrary order in N−1  (in suitable weak metrics). In
    other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate
    and efficient numerical simulations of the density fluctuations of independent
    diffusing particles.'
acknowledgement: "We thank the anonymous referee for his/her careful reading of the
  manuscript and valuable suggestions. FC gratefully acknowledges funding from the
  Austrian Science Fund (FWF) through the project F65, and from the European Union’s
  Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  Grant Agreement No. 754411.\r\nOpen access funding provided by Austrian Science
  Fund (FWF)."
article_number: '76'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Federico
  full_name: Cornalba, Federico
  id: 2CEB641C-A400-11E9-A717-D712E6697425
  last_name: Cornalba
  orcid: 0000-0002-6269-5149
- first_name: Julian L
  full_name: Fischer, Julian L
  id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
  last_name: Fischer
  orcid: 0000-0002-0479-558X
citation:
  ama: Cornalba F, Fischer JL. The Dean-Kawasaki equation and the structure of density
    fluctuations in systems of diffusing particles. <i>Archive for Rational Mechanics
    and Analysis</i>. 2023;247(5). doi:<a href="https://doi.org/10.1007/s00205-023-01903-7">10.1007/s00205-023-01903-7</a>
  apa: Cornalba, F., &#38; Fischer, J. L. (2023). The Dean-Kawasaki equation and the
    structure of density fluctuations in systems of diffusing particles. <i>Archive
    for Rational Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-023-01903-7">https://doi.org/10.1007/s00205-023-01903-7</a>
  chicago: Cornalba, Federico, and Julian L Fischer. “The Dean-Kawasaki Equation and
    the Structure of Density Fluctuations in Systems of Diffusing Particles.” <i>Archive
    for Rational Mechanics and Analysis</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00205-023-01903-7">https://doi.org/10.1007/s00205-023-01903-7</a>.
  ieee: F. Cornalba and J. L. Fischer, “The Dean-Kawasaki equation and the structure
    of density fluctuations in systems of diffusing particles,” <i>Archive for Rational
    Mechanics and Analysis</i>, vol. 247, no. 5. Springer Nature, 2023.
  ista: Cornalba F, Fischer JL. 2023. The Dean-Kawasaki equation and the structure
    of density fluctuations in systems of diffusing particles. Archive for Rational
    Mechanics and Analysis. 247(5), 76.
  mla: Cornalba, Federico, and Julian L. Fischer. “The Dean-Kawasaki Equation and
    the Structure of Density Fluctuations in Systems of Diffusing Particles.” <i>Archive
    for Rational Mechanics and Analysis</i>, vol. 247, no. 5, 76, Springer Nature,
    2023, doi:<a href="https://doi.org/10.1007/s00205-023-01903-7">10.1007/s00205-023-01903-7</a>.
  short: F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247
    (2023).
date_created: 2021-12-16T12:16:03Z
date_published: 2023-08-04T00:00:00Z
date_updated: 2024-01-30T12:10:10Z
day: '04'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00205-023-01903-7
ec_funded: 1
external_id:
  arxiv:
  - '2109.06500'
  isi:
  - '001043086800001'
file:
- access_level: open_access
  checksum: 4529eeff170b6745a461d397ee611b5a
  content_type: application/pdf
  creator: dernst
  date_created: 2024-01-30T12:09:34Z
  date_updated: 2024-01-30T12:09:34Z
  file_id: '14904'
  file_name: 2023_ArchiveRationalMech_Cornalba.pdf
  file_size: 1851185
  relation: main_file
  success: 1
file_date_updated: 2024-01-30T12:09:34Z
has_accepted_license: '1'
intvolume: '       247'
isi: 1
issue: '5'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _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: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Dean-Kawasaki equation and the structure of density fluctuations in systems
  of diffusing particles
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: 247
year: '2023'
...
---
_id: '10224'
abstract:
- lang: eng
  text: We investigate the Fröhlich polaron model on a three-dimensional torus, and
    give a proof of the second-order quantum corrections to its ground-state energy
    in the strong-coupling limit. Compared to previous work in the confined case,
    the translational symmetry (and its breaking in the Pekar approximation) makes
    the analysis substantially more challenging.
acknowledgement: "Funding from the European Union’s Horizon 2020 research and innovation
  programme under the ERC grant agreement No 694227 is gratefully acknowledged. We
  would also like to thank Rupert Frank for many helpful discussions, especially related
  to the Gross coordinate transformation defined in Def. 4.7.\r\nOpen 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: Dario
  full_name: Feliciangeli, Dario
  id: 41A639AA-F248-11E8-B48F-1D18A9856A87
  last_name: Feliciangeli
  orcid: 0000-0003-0754-8530
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: 'Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum
    corrections to the Pekar asymptotics. <i>Archive for Rational Mechanics and Analysis</i>.
    2021;242(3):1835–1906. doi:<a href="https://doi.org/10.1007/s00205-021-01715-7">10.1007/s00205-021-01715-7</a>'
  apa: 'Feliciangeli, D., &#38; Seiringer, R. (2021). The strongly coupled polaron
    on the torus: Quantum corrections to the Pekar asymptotics. <i>Archive for Rational
    Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-021-01715-7">https://doi.org/10.1007/s00205-021-01715-7</a>'
  chicago: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron
    on the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>Archive for Rational
    Mechanics and Analysis</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s00205-021-01715-7">https://doi.org/10.1007/s00205-021-01715-7</a>.'
  ieee: 'D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus:
    Quantum corrections to the Pekar asymptotics,” <i>Archive for Rational Mechanics
    and Analysis</i>, vol. 242, no. 3. Springer Nature, pp. 1835–1906, 2021.'
  ista: 'Feliciangeli D, Seiringer R. 2021. The strongly coupled polaron on the torus:
    Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and
    Analysis. 242(3), 1835–1906.'
  mla: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on
    the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>Archive for Rational
    Mechanics and Analysis</i>, vol. 242, no. 3, Springer Nature, 2021, pp. 1835–1906,
    doi:<a href="https://doi.org/10.1007/s00205-021-01715-7">10.1007/s00205-021-01715-7</a>.'
  short: D. Feliciangeli, R. Seiringer, Archive for Rational Mechanics and Analysis
    242 (2021) 1835–1906.
date_created: 2021-11-07T23:01:26Z
date_published: 2021-10-25T00:00:00Z
date_updated: 2023-08-14T10:32:19Z
day: '25'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00205-021-01715-7
ec_funded: 1
external_id:
  arxiv:
  - '2101.12566'
  isi:
  - '000710850600001'
file:
- access_level: open_access
  checksum: 672e9c21b20f1a50854b7c821edbb92f
  content_type: application/pdf
  creator: alisjak
  date_created: 2021-12-14T08:35:42Z
  date_updated: 2021-12-14T08:35:42Z
  file_id: '10544'
  file_name: 2021_Springer_Feliciangeli.pdf
  file_size: 990529
  relation: main_file
  success: 1
file_date_updated: 2021-12-14T08:35:42Z
has_accepted_license: '1'
intvolume: '       242'
isi: 1
issue: '3'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1835–1906
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  record:
  - id: '9787'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: 'The strongly coupled polaron on the torus: Quantum corrections to the Pekar
  asymptotics'
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: 242
year: '2021'
...
---
_id: '10549'
abstract:
- lang: eng
  text: We derive optimal-order homogenization rates for random nonlinear elliptic
    PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely,
    for a random monotone operator on \mathbb {R}^d with stationary law (that is spatially
    homogeneous statistics) and fast decay of correlations on scales larger than the
    microscale \varepsilon >0, we establish homogenization error estimates of the
    order \varepsilon in case d\geqq 3, and of the order \varepsilon |\log \varepsilon
    |^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have
    been limited to a small algebraic rate of convergence \varepsilon ^\delta . We
    also establish error estimates for the approximation of the homogenized operator
    by the method of representative volumes of the order (L/\varepsilon )^{-d/2} for
    a representative volume of size L. Our results also hold in the case of systems
    for which a (small-scale) C^{1,\alpha } regularity theory is available.
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft
  (DFG, German Research Foundation) – project number 405009441.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
  full_name: Fischer, Julian L
  id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
  last_name: Fischer
  orcid: 0000-0002-0479-558X
- first_name: Stefan
  full_name: Neukamm, Stefan
  last_name: Neukamm
citation:
  ama: Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization
    of nonlinear uniformly elliptic equations and systems. <i>Archive for Rational
    Mechanics and Analysis</i>. 2021;242(1):343-452. doi:<a href="https://doi.org/10.1007/s00205-021-01686-9">10.1007/s00205-021-01686-9</a>
  apa: Fischer, J. L., &#38; Neukamm, S. (2021). Optimal homogenization rates in stochastic
    homogenization of nonlinear uniformly elliptic equations and systems. <i>Archive
    for Rational Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-021-01686-9">https://doi.org/10.1007/s00205-021-01686-9</a>
  chicago: Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in
    Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.”
    <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a
    href="https://doi.org/10.1007/s00205-021-01686-9">https://doi.org/10.1007/s00205-021-01686-9</a>.
  ieee: J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic
    homogenization of nonlinear uniformly elliptic equations and systems,” <i>Archive
    for Rational Mechanics and Analysis</i>, vol. 242, no. 1. Springer Nature, pp.
    343–452, 2021.
  ista: Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization
    of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics
    and Analysis. 242(1), 343–452.
  mla: Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic
    Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” <i>Archive
    for Rational Mechanics and Analysis</i>, vol. 242, no. 1, Springer Nature, 2021,
    pp. 343–452, doi:<a href="https://doi.org/10.1007/s00205-021-01686-9">10.1007/s00205-021-01686-9</a>.
  short: J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242
    (2021) 343–452.
date_created: 2021-12-16T12:12:33Z
date_published: 2021-06-30T00:00:00Z
date_updated: 2023-08-17T06:23:21Z
day: '30'
ddc:
- '530'
department:
- _id: JuFi
doi: 10.1007/s00205-021-01686-9
external_id:
  arxiv:
  - '1908.02273'
  isi:
  - '000668431200001'
file:
- access_level: open_access
  checksum: cc830b739aed83ca2e32c4e0ce266a4c
  content_type: application/pdf
  creator: cchlebak
  date_created: 2021-12-16T14:58:08Z
  date_updated: 2021-12-16T14:58:08Z
  file_id: '10558'
  file_name: 2021_ArchRatMechAnalysis_Fischer.pdf
  file_size: 1640121
  relation: main_file
  success: 1
file_date_updated: 2021-12-16T14:58:08Z
has_accepted_license: '1'
intvolume: '       242'
isi: 1
issue: '1'
keyword:
- Mechanical Engineering
- Mathematics (miscellaneous)
- Analysis
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 343-452
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal homogenization rates in stochastic homogenization of nonlinear uniformly
  elliptic equations and systems
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: 242
year: '2021'
...
---
_id: '8130'
abstract:
- lang: eng
  text: We study the dynamics of a system of N interacting bosons in a disc-shaped
    trap, which is realised by an external potential that confines the bosons in one
    spatial dimension to an interval of length of order ε. The interaction is non-negative
    and scaled in such a way that its scattering length is of order ε/N, while its
    range is proportional to (ε/N)β with scaling parameter β∈(0,1]. We consider the
    simultaneous limit (N,ε)→(∞,0) and assume that the system initially exhibits Bose–Einstein
    condensation. We prove that condensation is preserved by the N-body dynamics,
    where the time-evolved condensate wave function is the solution of a two-dimensional
    non-linear equation. The strength of the non-linearity depends on the scaling
    parameter β. For β∈(0,1), we obtain a cubic defocusing non-linear Schrödinger
    equation, while the choice β=1 yields a Gross–Pitaevskii equation featuring the
    scattering length of the interaction. In both cases, the coupling parameter depends
    on the confining potential.
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria). I thank Stefan Teufel for helpful remarks and for his involvement
  in the closely related joint project [10]. Helpful discussions with Serena Cenatiempo
  and Nikolai Leopold are gratefully acknowledged. This work was supported by the
  German Research Foundation within the Research Training Group 1838 “Spectral Theory
  and Dynamics of Quantum Systems” and has received funding from the European Union’s
  Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  Grant Agreement No. 754411.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
  full_name: Bossmann, Lea
  id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
  last_name: Bossmann
  orcid: 0000-0002-6854-1343
citation:
  ama: Bossmann L. Derivation of the 2d Gross–Pitaevskii equation for strongly confined
    3d Bosons. <i>Archive for Rational Mechanics and Analysis</i>. 2020;238(11):541-606.
    doi:<a href="https://doi.org/10.1007/s00205-020-01548-w">10.1007/s00205-020-01548-w</a>
  apa: Bossmann, L. (2020). Derivation of the 2d Gross–Pitaevskii equation for strongly
    confined 3d Bosons. <i>Archive for Rational Mechanics and Analysis</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00205-020-01548-w">https://doi.org/10.1007/s00205-020-01548-w</a>
  chicago: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly
    Confined 3d Bosons.” <i>Archive for Rational Mechanics and Analysis</i>. Springer
    Nature, 2020. <a href="https://doi.org/10.1007/s00205-020-01548-w">https://doi.org/10.1007/s00205-020-01548-w</a>.
  ieee: L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly
    confined 3d Bosons,” <i>Archive for Rational Mechanics and Analysis</i>, vol.
    238, no. 11. Springer Nature, pp. 541–606, 2020.
  ista: Bossmann L. 2020. Derivation of the 2d Gross–Pitaevskii equation for strongly
    confined 3d Bosons. Archive for Rational Mechanics and Analysis. 238(11), 541–606.
  mla: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly
    Confined 3d Bosons.” <i>Archive for Rational Mechanics and Analysis</i>, vol.
    238, no. 11, Springer Nature, 2020, pp. 541–606, doi:<a href="https://doi.org/10.1007/s00205-020-01548-w">10.1007/s00205-020-01548-w</a>.
  short: L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.
date_created: 2020-07-18T15:06:35Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2023-09-05T14:19:06Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-020-01548-w
ec_funded: 1
external_id:
  arxiv:
  - '1907.04547'
  isi:
  - '000550164400001'
file:
- access_level: open_access
  checksum: cc67a79a67bef441625fcb1cd031db3d
  content_type: application/pdf
  creator: dernst
  date_created: 2020-12-02T08:50:38Z
  date_updated: 2020-12-02T08:50:38Z
  file_id: '8826'
  file_name: 2020_ArchiveRatMech_Bossmann.pdf
  file_size: 942343
  relation: main_file
  success: 1
file_date_updated: 2020-12-02T08:50:38Z
has_accepted_license: '1'
intvolume: '       238'
isi: 1
issue: '11'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 541-606
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons
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: 238
year: '2020'
...
---
_id: '7650'
abstract:
- lang: eng
  text: We consider a dilute, homogeneous Bose gas at positive temperature. The system
    is investigated in the Gross–Pitaevskii limit, where the scattering length a is
    so small that the interaction energy is of the same order of magnitude as the
    spectral gap of the Laplacian, and for temperatures that are comparable to the
    critical temperature of the ideal gas. We show that the difference between the
    specific free energy of the interacting system and the one of the ideal gas is
    to leading order given by 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system
    and ϱ0 is the expected condensate density of the ideal gas. Additionally, we show
    that the one-particle density matrix of any approximate minimizer of the Gibbs
    free energy functional is to leading order given by the one of the ideal gas.
    This in particular proves Bose–Einstein condensation with critical temperature
    given by the one of the ideal gas to leading order. One key ingredient of our
    proof is a novel use of the Gibbs variational principle that goes hand in hand
    with the c-number substitution.
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria). It is a pleasure to thank Jakob Yngvason for helpful discussions.
  Financial support by the European Research Council (ERC) under the European Union’sHorizon
  2020 research and innovation programme (Grant Agreement No. 694227) is gratefully
  acknowledged. A. D. acknowledges funding from the European Union’s Horizon 2020
  research and innovation programme under the Marie Sklodowska-Curie Grant Agreement
  No. 836146.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Andreas
  full_name: Deuchert, Andreas
  id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
  last_name: Deuchert
  orcid: 0000-0003-3146-6746
- 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. Gross-Pitaevskii limit of a homogeneous Bose gas at
    positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. 2020;236(6):1217-1271.
    doi:<a href="https://doi.org/10.1007/s00205-020-01489-4">10.1007/s00205-020-01489-4</a>
  apa: Deuchert, A., &#38; Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous
    Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s00205-020-01489-4">https://doi.org/10.1007/s00205-020-01489-4</a>
  chicago: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous
    Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>.
    Springer Nature, 2020. <a href="https://doi.org/10.1007/s00205-020-01489-4">https://doi.org/10.1007/s00205-020-01489-4</a>.
  ieee: A. Deuchert and R. Seiringer, “Gross-Pitaevskii limit of a homogeneous Bose
    gas at positive temperature,” <i>Archive for Rational Mechanics and Analysis</i>,
    vol. 236, no. 6. Springer Nature, pp. 1217–1271, 2020.
  ista: Deuchert A, Seiringer R. 2020. Gross-Pitaevskii limit of a homogeneous Bose
    gas at positive temperature. Archive for Rational Mechanics and Analysis. 236(6),
    1217–1271.
  mla: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous
    Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>,
    vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:<a href="https://doi.org/10.1007/s00205-020-01489-4">10.1007/s00205-020-01489-4</a>.
  short: A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236
    (2020) 1217–1271.
date_created: 2020-04-08T15:18:03Z
date_published: 2020-03-09T00:00:00Z
date_updated: 2023-09-05T14:18:49Z
day: '09'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-020-01489-4
ec_funded: 1
external_id:
  arxiv:
  - '1901.11363'
  isi:
  - '000519415000001'
file:
- access_level: open_access
  checksum: b645fb64bfe95bbc05b3eea374109a9c
  content_type: application/pdf
  creator: dernst
  date_created: 2020-11-20T13:17:42Z
  date_updated: 2020-11-20T13:17:42Z
  file_id: '8785'
  file_name: 2020_ArchRatMechanicsAnalysis_Deuchert.pdf
  file_size: 704633
  relation: main_file
  success: 1
file_date_updated: 2020-11-20T13:17:42Z
has_accepted_license: '1'
intvolume: '       236'
isi: 1
issue: '6'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 1217-1271
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: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature
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: 236
year: '2020'
...
---
_id: '6617'
abstract:
- lang: eng
  text: 'The effective large-scale properties of materials with random heterogeneities
    on a small scale are typically determined by the method of representative volumes:
    a sample of the random material is chosen—the representative volume—and its effective
    properties are computed by the cell formula. Intuitively, for a fixed sample size
    it should be possible to increase the accuracy of the method by choosing a material
    sample which captures the statistical properties of the material particularly
    well; for example, for a composite material consisting of two constituents, one
    would select a representative volume in which the volume fraction of the constituents
    matches closely with their volume fraction in the overall material. Inspired by
    similar attempts in materials science, Le Bris, Legoll and Minvielle have designed
    a selection approach for representative volumes which performs remarkably well
    in numerical examples of linear materials with moderate contrast. In the present
    work, we provide a rigorous analysis of this selection approach for representative
    volumes in the context of stochastic homogenization of linear elliptic equations.
    In particular, we prove that the method essentially never performs worse than
    a random selection of the material sample and may perform much better if the selection
    criterion for the material samples is chosen suitably.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
  full_name: Fischer, Julian L
  id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
  last_name: Fischer
  orcid: 0000-0002-0479-558X
citation:
  ama: Fischer JL. The choice of representative volumes in the approximation of effective
    properties of random materials. <i>Archive for Rational Mechanics and Analysis</i>.
    2019;234(2):635–726. doi:<a href="https://doi.org/10.1007/s00205-019-01400-w">10.1007/s00205-019-01400-w</a>
  apa: Fischer, J. L. (2019). The choice of representative volumes in the approximation
    of effective properties of random materials. <i>Archive for Rational Mechanics
    and Analysis</i>. Springer. <a href="https://doi.org/10.1007/s00205-019-01400-w">https://doi.org/10.1007/s00205-019-01400-w</a>
  chicago: Fischer, Julian L. “The Choice of Representative Volumes in the Approximation
    of Effective Properties of Random Materials.” <i>Archive for Rational Mechanics
    and Analysis</i>. Springer, 2019. <a href="https://doi.org/10.1007/s00205-019-01400-w">https://doi.org/10.1007/s00205-019-01400-w</a>.
  ieee: J. L. Fischer, “The choice of representative volumes in the approximation
    of effective properties of random materials,” <i>Archive for Rational Mechanics
    and Analysis</i>, vol. 234, no. 2. Springer, pp. 635–726, 2019.
  ista: Fischer JL. 2019. The choice of representative volumes in the approximation
    of effective properties of random materials. Archive for Rational Mechanics and
    Analysis. 234(2), 635–726.
  mla: Fischer, Julian L. “The Choice of Representative Volumes in the Approximation
    of Effective Properties of Random Materials.” <i>Archive for Rational Mechanics
    and Analysis</i>, vol. 234, no. 2, Springer, 2019, pp. 635–726, doi:<a href="https://doi.org/10.1007/s00205-019-01400-w">10.1007/s00205-019-01400-w</a>.
  short: J.L. Fischer, Archive for Rational Mechanics and Analysis 234 (2019) 635–726.
date_created: 2019-07-07T21:59:23Z
date_published: 2019-11-01T00:00:00Z
date_updated: 2023-08-28T12:31:21Z
day: '01'
ddc:
- '500'
department:
- _id: JuFi
doi: 10.1007/s00205-019-01400-w
external_id:
  arxiv:
  - '1807.00834'
  isi:
  - '000482386000006'
file:
- access_level: open_access
  checksum: 4cff75fa6addb0770991ad9c474ab404
  content_type: application/pdf
  creator: kschuh
  date_created: 2019-07-08T15:56:47Z
  date_updated: 2020-07-14T12:47:34Z
  file_id: '6626'
  file_name: Springer_2019_Fischer.pdf
  file_size: 1377659
  relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
intvolume: '       234'
isi: 1
issue: '2'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 635–726
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: The choice of representative volumes in the approximation of effective properties
  of random materials
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: 234
year: '2019'
...
---
_id: '6002'
abstract:
- lang: eng
  text: The Bogoliubov free energy functional is analysed. The functional serves as
    a model of a translation-invariant Bose gas at positive temperature. We prove
    the existence of minimizers in the case of repulsive interactions given by a sufficiently
    regular two-body potential. Furthermore, we prove the existence of a phase transition
    in this model and provide its phase diagram.
article_processing_charge: No
arxiv: 1
author:
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
- first_name: Robin
  full_name: Reuvers, Robin
  last_name: Reuvers
- first_name: Jan Philip
  full_name: Solovej, Jan Philip
  last_name: Solovej
citation:
  ama: 'Napiórkowski MM, Reuvers R, Solovej JP. The Bogoliubov free energy functional
    I: Existence of minimizers and phase diagram. <i>Archive for Rational Mechanics
    and Analysis</i>. 2018;229(3):1037-1090. doi:<a href="https://doi.org/10.1007/s00205-018-1232-6">10.1007/s00205-018-1232-6</a>'
  apa: 'Napiórkowski, M. M., Reuvers, R., &#38; Solovej, J. P. (2018). The Bogoliubov
    free energy functional I: Existence of minimizers and phase diagram. <i>Archive
    for Rational Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-018-1232-6">https://doi.org/10.1007/s00205-018-1232-6</a>'
  chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Philip Solovej. “The Bogoliubov
    Free Energy Functional I: Existence of Minimizers and Phase Diagram.” <i>Archive
    for Rational Mechanics and Analysis</i>. Springer Nature, 2018. <a href="https://doi.org/10.1007/s00205-018-1232-6">https://doi.org/10.1007/s00205-018-1232-6</a>.'
  ieee: 'M. M. Napiórkowski, R. Reuvers, and J. P. Solovej, “The Bogoliubov free energy
    functional I: Existence of minimizers and phase diagram,” <i>Archive for Rational
    Mechanics and Analysis</i>, vol. 229, no. 3. Springer Nature, pp. 1037–1090, 2018.'
  ista: 'Napiórkowski MM, Reuvers R, Solovej JP. 2018. The Bogoliubov free energy
    functional I: Existence of minimizers and phase diagram. Archive for Rational
    Mechanics and Analysis. 229(3), 1037–1090.'
  mla: 'Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional I:
    Existence of Minimizers and Phase Diagram.” <i>Archive for Rational Mechanics
    and Analysis</i>, vol. 229, no. 3, Springer Nature, 2018, pp. 1037–90, doi:<a
    href="https://doi.org/10.1007/s00205-018-1232-6">10.1007/s00205-018-1232-6</a>.'
  short: M.M. Napiórkowski, R. Reuvers, J.P. Solovej, Archive for Rational Mechanics
    and Analysis 229 (2018) 1037–1090.
date_created: 2019-02-14T13:40:53Z
date_published: 2018-09-01T00:00:00Z
date_updated: 2023-09-19T14:33:12Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00205-018-1232-6
external_id:
  arxiv:
  - '1511.05935'
  isi:
  - '000435367300003'
intvolume: '       229'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1511.05935
month: '09'
oa: 1
oa_version: Preprint
page: 1037-1090
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P27533_N27
  name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The Bogoliubov free energy functional I: Existence of minimizers and phase
  diagram'
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 229
year: '2018'
...