---
_id: '9225'
abstract:
- lang: eng
text: "The Landau–Pekar equations describe the dynamics of a strongly coupled polaron.\r\nHere,
we provide a class of initial data for which the associated effective Hamiltonian\r\nhas
a uniform spectral gap for all times. For such initial data, this allows us to
extend the\r\nresults on the adiabatic theorem for the Landau–Pekar equations
and their derivation\r\nfrom the Fröhlich model obtained in previous works to
larger times."
acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation
programme under the ERC Grant Agreement No 694227 (D.F. and R.S.) and under the
Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.
Open Access funding provided by Institute of Science and Technology (IST Austria)
article_number: '19'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
- 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, Rademacher SAE, Seiringer R. Persistence of the spectral gap
for the Landau–Pekar equations. Letters in Mathematical Physics. 2021;111.
doi:10.1007/s11005-020-01350-5
apa: Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2021). Persistence
of the spectral gap for the Landau–Pekar equations. Letters in Mathematical
Physics. Springer Nature. https://doi.org/10.1007/s11005-020-01350-5
chicago: Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
“Persistence of the Spectral Gap for the Landau–Pekar Equations.” Letters in
Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s11005-020-01350-5.
ieee: D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “Persistence of the
spectral gap for the Landau–Pekar equations,” Letters in Mathematical Physics,
vol. 111. Springer Nature, 2021.
ista: Feliciangeli D, Rademacher SAE, Seiringer R. 2021. Persistence of the spectral
gap for the Landau–Pekar equations. Letters in Mathematical Physics. 111, 19.
mla: Feliciangeli, Dario, et al. “Persistence of the Spectral Gap for the Landau–Pekar
Equations.” Letters in Mathematical Physics, vol. 111, 19, Springer Nature,
2021, doi:10.1007/s11005-020-01350-5.
short: D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Letters in Mathematical
Physics 111 (2021).
date_created: 2021-03-07T23:01:25Z
date_published: 2021-02-11T00:00:00Z
date_updated: 2026-04-08T06:59:49Z
day: '11'
ddc:
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department:
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doi: 10.1007/s11005-020-01350-5
ec_funded: 1
external_id:
isi:
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creator: dernst
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month: '02'
oa: 1
oa_version: Published Version
project:
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call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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publication: Letters in Mathematical Physics
publication_identifier:
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issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Persistence of the spectral gap for the Landau–Pekar equations
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)
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type: journal_article
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year: '2021'
...
---
_id: '9246'
abstract:
- lang: eng
text: We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic
particles weakly couple to the quantized phonon field. For large particle numbers
and a suitably small coupling, we show that the dynamics of the system is approximately
described by the Landau–Pekar equations. These describe a Bose–Einstein condensate
interacting with a classical polarization field, whose dynamics is effected by
the condensate, i.e., the back-reaction of the phonons that are created by the
particles during the time evolution is of leading order.
acknowledgement: "Financial support by the European Research Council (ERC) under the\r\nEuropean
Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo 694227;
N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the\r\nDeutsche
Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral\r\nTheory
and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.\r\ngratefully
acknowledges support from the NCCRSwissMAP and would like to thank Simone\r\nRademacher
and Benjamin Schlein for interesting discussions about the time-evolution of\r\nthe
polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for\r\nextensive
discussions about the Fröhlich polaron."
article_processing_charge: No
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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: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Leopold NK, Mitrouskas DJ, Seiringer R. Derivation of the Landau–Pekar equations
in a many-body mean-field limit. Archive for Rational Mechanics and Analysis.
2021;240:383-417. doi:10.1007/s00205-021-01616-9
apa: Leopold, N. K., Mitrouskas, D. J., & Seiringer, R. (2021). Derivation of
the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational
Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01616-9
chicago: Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation
of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” Archive for
Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01616-9.
ieee: N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar
equations in a many-body mean-field limit,” Archive for Rational Mechanics
and Analysis, vol. 240. Springer Nature, pp. 383–417, 2021.
ista: Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar
equations in a many-body mean-field limit. Archive for Rational Mechanics and
Analysis. 240, 383–417.
mla: Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a
Many-Body Mean-Field Limit.” Archive for Rational Mechanics and Analysis,
vol. 240, Springer Nature, 2021, pp. 383–417, doi:10.1007/s00205-021-01616-9.
short: N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics
and Analysis 240 (2021) 383–417.
date_created: 2021-03-14T23:01:34Z
date_published: 2021-02-26T00:00:00Z
date_updated: 2025-06-12T06:35:22Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-021-01616-9
ec_funded: 1
external_id:
arxiv:
- '2001.03993'
isi:
- '000622226200001'
pmid:
- '33785964'
file:
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checksum: 23449e44dc5132501a5c86e70638800f
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T08:31:29Z
date_updated: 2021-03-22T08:31:29Z
file_id: '9270'
file_name: 2021_ArchRationalMechAnal_Leopold.pdf
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oa_version: Published Version
page: 383-417
pmid: 1
project:
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call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
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issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivation of the Landau–Pekar equations in a many-body mean-field limit
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: 240
year: '2021'
...
---
_id: '9256'
abstract:
- lang: eng
text: We consider the ferromagnetic quantum Heisenberg model in one dimension, for
any spin S≥1/2. We give upper and lower bounds on the free energy, proving that
at low temperature it is asymptotically equal to the one of an ideal Bose gas
of magnons, as predicted by the spin-wave approximation. The trial state used
in the upper bound yields an analogous estimate also in the case of two spatial
dimensions, which is believed to be sharp at low temperature.
acknowledgement: "The work of MN was supported by the National Science Centre (NCN)
Project Nr. 2016/21/D/ST1/02430. The work of RS was supported by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No. 694227).\r\nOpen access funding provided by Institute of Science
and Technology (IST Austria)."
article_number: '31'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Napiórkowski MM, Seiringer R. Free energy asymptotics of the quantum Heisenberg
spin chain. Letters in Mathematical Physics. 2021;111(2). doi:10.1007/s11005-021-01375-4
apa: Napiórkowski, M. M., & Seiringer, R. (2021). Free energy asymptotics of
the quantum Heisenberg spin chain. Letters in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s11005-021-01375-4
chicago: Napiórkowski, Marcin M, and Robert Seiringer. “Free Energy Asymptotics
of the Quantum Heisenberg Spin Chain.” Letters in Mathematical Physics.
Springer Nature, 2021. https://doi.org/10.1007/s11005-021-01375-4.
ieee: M. M. Napiórkowski and R. Seiringer, “Free energy asymptotics of the quantum
Heisenberg spin chain,” Letters in Mathematical Physics, vol. 111, no.
2. Springer Nature, 2021.
ista: Napiórkowski MM, Seiringer R. 2021. Free energy asymptotics of the quantum
Heisenberg spin chain. Letters in Mathematical Physics. 111(2), 31.
mla: Napiórkowski, Marcin M., and Robert Seiringer. “Free Energy Asymptotics of
the Quantum Heisenberg Spin Chain.” Letters in Mathematical Physics, vol.
111, no. 2, 31, Springer Nature, 2021, doi:10.1007/s11005-021-01375-4.
short: M.M. Napiórkowski, R. Seiringer, Letters in Mathematical Physics 111 (2021).
date_created: 2021-03-21T23:01:19Z
date_published: 2021-03-09T00:00:00Z
date_updated: 2026-04-02T14:06:48Z
day: '09'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-021-01375-4
external_id:
isi:
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pmid:
- '33785980'
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creator: dernst
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file_id: '9273'
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month: '03'
oa: 1
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pmid: 1
publication: Letters in Mathematical Physics
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issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Free energy asymptotics of the quantum Heisenberg spin chain
tmp:
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name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 111
year: '2021'
...
---
_id: '9318'
abstract:
- lang: eng
text: We consider a system of N bosons in the mean-field scaling regime for a class
of interactions including the repulsive Coulomb potential. We derive an asymptotic
expansion of the low-energy eigenstates and the corresponding energies, which
provides corrections to Bogoliubov theory to any order in 1/N.
acknowledgement: The first author gratefully acknowledges funding from the European
Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie
Grant Agreement No. 754411. The third author was supported by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No. 694227).
article_number: e28
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lea
full_name: Bossmann, Lea
id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
last_name: Bossmann
orcid: 0000-0002-6854-1343
- first_name: Sören P
full_name: Petrat, Sören P
id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
last_name: Petrat
orcid: 0000-0002-9166-5889
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Bossmann L, Petrat SP, Seiringer R. Asymptotic expansion of low-energy excitations
for weakly interacting bosons. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.22
apa: Bossmann, L., Petrat, S. P., & Seiringer, R. (2021). Asymptotic expansion
of low-energy excitations for weakly interacting bosons. Forum of Mathematics,
Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.22
chicago: Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion
of Low-Energy Excitations for Weakly Interacting Bosons.” Forum of Mathematics,
Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.22.
ieee: L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy
excitations for weakly interacting bosons,” Forum of Mathematics, Sigma,
vol. 9. Cambridge University Press, 2021.
ista: Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy
excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28.
mla: Bossmann, Lea, et al. “Asymptotic Expansion of Low-Energy Excitations for Weakly
Interacting Bosons.” Forum of Mathematics, Sigma, vol. 9, e28, Cambridge
University Press, 2021, doi:10.1017/fms.2021.22.
short: L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).
date_created: 2021-04-11T22:01:15Z
date_published: 2021-03-26T00:00:00Z
date_updated: 2026-04-02T14:02:29Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1017/fms.2021.22
ec_funded: 1
external_id:
isi:
- '000634006900001'
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language:
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month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Asymptotic expansion of low-energy excitations for weakly interacting 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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 9
year: '2021'
...
---
_id: '9333'
abstract:
- lang: eng
text: We revise a previous result about the Fröhlich dynamics in the strong coupling
limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter
it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα,
where φ0 is the electron ground state of the Pekar energy functional and ξα the
associated coherent state of the phonons, can be approximated by a global phase
for times small compared to α2. In the present note we prove that a similar approximation
holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons
that is generated by an operator proportional to α−2 and quadratic in creation
and annihilation operators. Our result implies that the electron ground state
remains close to its initial state for times of order α2, while the phonon fluctuations
around the coherent state ξα can be described by a time-dependent Bogoliubov transformation.
acknowledgement: 'I thank Marcel Griesemer for many interesting discussions about
the Fröhlich polaron and also for valuable comments on this manuscript. Helpful
discussions with Nikolai Leopold and Robert Seiringer are also gratefully acknowledged.
This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG) through
the Research Training Group 1838: Spectral Theory and Dynamics of Quantum Systems.
Open Access funding enabled and organized by Projekt DEAL.'
article_number: '45'
article_processing_charge: No
article_type: original
author:
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
citation:
ama: Mitrouskas DJ. A note on the Fröhlich dynamics in the strong coupling limit.
Letters in Mathematical Physics. 2021;111. doi:10.1007/s11005-021-01380-7
apa: Mitrouskas, D. J. (2021). A note on the Fröhlich dynamics in the strong coupling
limit. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01380-7
chicago: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong
Coupling Limit.” Letters in Mathematical Physics. Springer Nature, 2021.
https://doi.org/10.1007/s11005-021-01380-7.
ieee: D. J. Mitrouskas, “A note on the Fröhlich dynamics in the strong coupling
limit,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021.
ista: Mitrouskas DJ. 2021. A note on the Fröhlich dynamics in the strong coupling
limit. Letters in Mathematical Physics. 111, 45.
mla: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong
Coupling Limit.” Letters in Mathematical Physics, vol. 111, 45, Springer
Nature, 2021, doi:10.1007/s11005-021-01380-7.
short: D.J. Mitrouskas, Letters in Mathematical Physics 111 (2021).
date_created: 2021-04-18T22:01:41Z
date_published: 2021-04-05T00:00:00Z
date_updated: 2026-04-02T13:58:00Z
day: '05'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-021-01380-7
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- '000637359300002'
file:
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checksum: be56c0845a43c0c5c772ee0b5053f7d7
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oa: 1
oa_version: Published Version
publication: Letters in Mathematical Physics
publication_identifier:
eissn:
- 1573-0530
issn:
- 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A note on the Fröhlich dynamics in the strong coupling limit
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type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 111
year: '2021'
...
---
_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. Journal of Functional Analysis. 2021;281(3). doi:10.1016/j.jfa.2021.109029
apa: Brooks, M., & Di Gesù, G. (2021). Sharp tunneling estimates for a double-well
model in infinite dimension. Journal of Functional Analysis. Elsevier.
https://doi.org/10.1016/j.jfa.2021.109029
chicago: Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well
Model in Infinite Dimension.” Journal of Functional Analysis. Elsevier,
2021. https://doi.org/10.1016/j.jfa.2021.109029.
ieee: M. Brooks and G. Di Gesù, “Sharp tunneling estimates for a double-well model
in infinite dimension,” Journal of Functional Analysis, 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.” Journal of Functional Analysis, vol. 281,
no. 3, 109029, Elsevier, 2021, doi:10.1016/j.jfa.2021.109029.
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: '9351'
abstract:
- lang: eng
text: 'We consider the many-body quantum evolution of a factorized initial data,
in the mean-field regime. We show that fluctuations around the limiting Hartree
dynamics satisfy large deviation estimates that are consistent with central limit
theorems that have been established in the last years. '
acknowledgement: The authors gratefully acknowledge Gérard Ben Arous for suggesting
this kind of result. K.L.K. was partially supported by NSF CAREER Award DMS-125479
and a Simons Sabbatical Fellowship. S.R. acknowledges funding from the European
Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411. B. S. gratefully acknowledges partial 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. Funding Open access funding provided by Institute
of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Kay
full_name: Kirkpatrick, Kay
last_name: Kirkpatrick
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
citation:
ama: Kirkpatrick K, Rademacher SAE, Schlein B. A large deviation principle in many-body
quantum dynamics. Annales Henri Poincare. 2021;22:2595-2618. doi:10.1007/s00023-021-01044-1
apa: Kirkpatrick, K., Rademacher, S. A. E., & Schlein, B. (2021). A large deviation
principle in many-body quantum dynamics. Annales Henri Poincare. Springer
Nature. https://doi.org/10.1007/s00023-021-01044-1
chicago: Kirkpatrick, Kay, Simone Anna Elvira Rademacher, and Benjamin Schlein.
“A Large Deviation Principle in Many-Body Quantum Dynamics.” Annales Henri
Poincare. Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01044-1.
ieee: K. Kirkpatrick, S. A. E. Rademacher, and B. Schlein, “A large deviation principle
in many-body quantum dynamics,” Annales Henri Poincare, vol. 22. Springer
Nature, pp. 2595–2618, 2021.
ista: Kirkpatrick K, Rademacher SAE, Schlein B. 2021. A large deviation principle
in many-body quantum dynamics. Annales Henri Poincare. 22, 2595–2618.
mla: Kirkpatrick, Kay, et al. “A Large Deviation Principle in Many-Body Quantum
Dynamics.” Annales Henri Poincare, vol. 22, Springer Nature, 2021, pp.
2595–618, doi:10.1007/s00023-021-01044-1.
short: K. Kirkpatrick, S.A.E. Rademacher, B. Schlein, Annales Henri Poincare 22
(2021) 2595–2618.
date_created: 2021-04-25T22:01:30Z
date_published: 2021-04-08T00:00:00Z
date_updated: 2025-06-12T06:39:59Z
day: '08'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00023-021-01044-1
ec_funded: 1
external_id:
arxiv:
- '2010.13754'
isi:
- '000638022600001'
pmid:
- '34776771'
file:
- access_level: open_access
checksum: 1a0fb963f2f415ba470881a794f20eb6
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-15T11:15:40Z
date_updated: 2021-10-15T11:15:40Z
file_id: '10143'
file_name: 2021_Annales_Kirkpatrick.pdf
file_size: 522669
relation: main_file
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file_date_updated: 2021-10-15T11:15:40Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 2595-2618
pmid: 1
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: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A large deviation principle in many-body quantum dynamics
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: 22
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. Journal of Functional Analysis.
2021;281(6). doi:10.1016/j.jfa.2021.109096
apa: Deuchert, A., & Seiringer, R. (2021). Semiclassical approximation and critical
temperature shift for weakly interacting trapped bosons. Journal of Functional
Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2021.109096
chicago: Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and
Critical Temperature Shift for Weakly Interacting Trapped Bosons.” Journal
of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109096.
ieee: A. Deuchert and R. Seiringer, “Semiclassical approximation and critical temperature
shift for weakly interacting trapped bosons,” Journal of Functional Analysis,
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.” Journal of Functional
Analysis, vol. 281, no. 6, 109096, Elsevier, 2021, doi:10.1016/j.jfa.2021.109096.
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: 2025-04-14T07:26:53Z
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: '9787'
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. 4.1.\r\n"
article_number: '2101.12566'
article_processing_charge: No
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. arXiv. doi:10.48550/arXiv.2101.12566'
apa: 'Feliciangeli, D., & Seiringer, R. (n.d.). The strongly coupled polaron
on the torus: Quantum corrections to the Pekar asymptotics. arXiv. https://doi.org/10.48550/arXiv.2101.12566'
chicago: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron
on the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, n.d.
https://doi.org/10.48550/arXiv.2101.12566.'
ieee: 'D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus:
Quantum corrections to the Pekar asymptotics,” arXiv. .'
ista: 'Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum
corrections to the Pekar asymptotics. arXiv, 2101.12566.'
mla: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on
the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, 2101.12566,
doi:10.48550/arXiv.2101.12566.'
short: D. Feliciangeli, R. Seiringer, ArXiv (n.d.).
corr_author: '1'
date_created: 2021-08-06T08:25:57Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2026-04-08T06:59:49Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.48550/arXiv.2101.12566
ec_funded: 1
external_id:
arxiv:
- '2101.12566'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2101.12566
month: '02'
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: arXiv
publication_status: draft
related_material:
record:
- id: '10224'
relation: later_version
status: public
- id: '9733'
relation: dissertation_contains
status: public
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: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
OA_place: repository
_id: '9791'
abstract:
- lang: eng
text: We provide a definition of the effective mass for the classical polaron described
by the Landau-Pekar equations. It is based on a novel variational principle, minimizing
the energy functional over states with given (initial) velocity. The resulting
formula for the polaron's effective mass agrees with the prediction by Landau
and Pekar.
acknowledgement: We thank Herbert Spohn for helpful comments. Funding from the European
Union’s Horizon 2020 research and innovation programme under the ERC grant agreement
No. 694227 (D.F. and R.S.) and under the Marie Skłodowska-Curie Grant Agreement
No. 754411 (S.R.) is gratefully acknowledged..
article_number: '2107.03720 '
article_processing_charge: No
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: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
- 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, Rademacher SAE, Seiringer R. The effective mass problem for
the Landau-Pekar equations. arXiv. doi:10.48550/arXiv.2107.03720
apa: Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (n.d.). The effective
mass problem for the Landau-Pekar equations. arXiv. https://doi.org/10.48550/arXiv.2107.03720
chicago: Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
“The Effective Mass Problem for the Landau-Pekar Equations.” ArXiv, n.d.
https://doi.org/10.48550/arXiv.2107.03720.
ieee: D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass
problem for the Landau-Pekar equations,” arXiv. .
ista: Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for
the Landau-Pekar equations. arXiv, 2107.03720.
mla: Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar
Equations.” ArXiv, 2107.03720, doi:10.48550/arXiv.2107.03720.
short: D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, ArXiv (n.d.).
corr_author: '1'
date_created: 2021-08-06T08:49:45Z
date_published: 2021-07-08T00:00:00Z
date_updated: 2026-04-08T06:59:49Z
day: '08'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.48550/arXiv.2107.03720
ec_funded: 1
external_id:
arxiv:
- '2107.03720'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2107.03720
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: arXiv
publication_status: draft
related_material:
record:
- id: '10755'
relation: later_version
status: public
- id: '9733'
relation: dissertation_contains
status: public
status: public
title: The effective mass problem for the Landau-Pekar equations
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9792'
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 careful 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 thanks 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. Finally, the authors
also thanks J. Maas and R. Seiringer for their feedback and useful comments to a
first draft of the article. L.P. acknowledges support by the Austrian Science Fund
(FWF), grants No W1245 and NoF65. D.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 European
Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942].'
article_number: '2106.11217'
article_processing_charge: No
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. arXiv.
doi:10.48550/arXiv.2106.11217
apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (n.d.). A non-commutative
entropic optimal transport approach to quantum composite systems at positive temperature.
arXiv. https://doi.org/10.48550/arXiv.2106.11217
chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative
Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2106.11217.
ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic
optimal transport approach to quantum composite systems at positive temperature,”
arXiv. .
ista: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal
transport approach to quantum composite systems at positive temperature. arXiv,
2106.11217.
mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach
to Quantum Composite Systems at Positive Temperature.” ArXiv, 2106.11217,
doi:10.48550/arXiv.2106.11217.
short: D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.).
date_created: 2021-08-06T09:07:12Z
date_published: 2021-07-21T00:00:00Z
date_updated: 2026-04-08T07:00:03Z
day: '21'
ddc:
- '510'
department:
- _id: RoSe
- _id: JaMa
doi: 10.48550/arXiv.2106.11217
ec_funded: 1
external_id:
arxiv:
- '2106.11217'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2106.11217
month: '07'
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
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
related_material:
record:
- id: '12911'
relation: later_version
status: public
- id: '9733'
relation: dissertation_contains
status: public
- id: '10030'
relation: dissertation_contains
status: public
status: public
title: A non-commutative entropic optimal transport approach to quantum composite
systems 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: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9891'
abstract:
- lang: eng
text: 'Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127
(2019)], we present a modified “floating crystal” trial state for jellium (also
known as the classical homogeneous electron gas) with density equal to a characteristic
function. This allows us to show that three definitions of the jellium energy
coincide in dimensions d ≥ 2, thus extending the result of Cotar and Petrache
[“Equality of the Jellium and uniform electron gas next-order asymptotic terms
for Coulomb and Riesz potentials,” arXiv: 1707.07664 (2019)] and Lewin, Lieb,
and Seiringer [Phys. Rev. B 100, 035127 (2019)] that the three definitions coincide
in dimension d ≥ 3. We show that the jellium energy is also equivalent to a “renormalized
energy” studied in a series of papers by Serfaty and others, and thus, by the
work of Bétermin and Sandier [Constr. Approximation 47, 39–74 (2018)], we relate
the jellium energy to the order n term in the logarithmic energy of n points on
the unit 2-sphere. We improve upon known lower bounds for this renormalized energy.
Additionally, we derive formulas for the jellium energy of periodic configurations.'
acknowledgement: The author would like to thank Robert Seiringer for guidance and
many helpful comments on this project. The author would also like to thank Mathieu
Lewin for his comments on the manuscript and Lorenzo Portinale for providing his
lecture notes for the course “Mathematics of quantum many-body systems” in spring
2020, taught by Robert Seiringer. The Proof of Theorem III.1 is inspired by these
lecture notes.
article_number: '083305'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
citation:
ama: Lauritsen AB. Floating Wigner crystal and periodic jellium configurations.
Journal of Mathematical Physics. 2021;62(8). doi:10.1063/5.0053494
apa: Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations.
Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0053494
chicago: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium
Configurations.” Journal of Mathematical Physics. AIP Publishing, 2021.
https://doi.org/10.1063/5.0053494.
ieee: A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,”
Journal of Mathematical Physics, vol. 62, no. 8. AIP Publishing, 2021.
ista: Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations.
Journal of Mathematical Physics. 62(8), 083305.
mla: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium
Configurations.” Journal of Mathematical Physics, vol. 62, no. 8, 083305,
AIP Publishing, 2021, doi:10.1063/5.0053494.
short: A.B. Lauritsen, Journal of Mathematical Physics 62 (2021).
corr_author: '1'
date_created: 2021-08-12T07:08:36Z
date_published: 2021-08-01T00:00:00Z
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title: Floating Wigner crystal and periodic jellium configurations
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abstract:
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text: This thesis is the result of the research carried out by the author during
his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich
polaron model, specifically to its regime of strong coupling. This model, which
is rigorously introduced and discussed in the introduction, has been of great
interest in condensed matter physics and field theory for more than eighty years.
It is used to describe an electron interacting with the atoms of a solid material
(the strength of this interaction is modeled by the presence of a coupling constant
α in the Hamiltonian of the system). The particular regime examined here, which
is mathematically described by considering the limit α →∞, displays many interesting
features related to the emergence of classical behavior, which allows for a simplified
effective description of the system under analysis. The properties, the range
of validity and a quantitative analysis of the precision of such classical approximations
are the main object of the present work. We specify our investigation to the study
of the ground state energy of the system, its dynamics and its effective mass.
For each of these problems, we provide in the introduction an overview of the
previously known results and a detailed account of the original contributions
by the author.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
citation:
ama: Feliciangeli D. The polaron at strong coupling. 2021. doi:10.15479/at:ista:9733
apa: Feliciangeli, D. (2021). The polaron at strong coupling. Institute of
Science and Technology Austria. https://doi.org/10.15479/at:ista:9733
chicago: Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science
and Technology Austria, 2021. https://doi.org/10.15479/at:ista:9733.
ieee: D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and
Technology Austria, 2021.
ista: Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science
and Technology Austria.
mla: Feliciangeli, Dario. The Polaron at Strong Coupling. Institute of Science
and Technology Austria, 2021, doi:10.15479/at:ista:9733.
short: D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and
Technology Austria, 2021.
corr_author: '1'
date_created: 2021-07-27T15:48:30Z
date_published: 2021-08-20T00:00:00Z
date_updated: 2026-07-06T14:02:25Z
day: '20'
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name: Optimal Transport and Stochastic Dynamics
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issn:
- 2663-337X
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publisher: Institute of Science and Technology Austria
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supervisor:
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full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: The polaron at strong coupling
tmp:
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legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
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type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2021'
...
---
_id: '14891'
abstract:
- lang: eng
text: We give the first mathematically rigorous justification of the local density
approximation in density functional theory. We provide a quantitative estimate
on the difference between the grand-canonical Levy–Lieb energy of a given density
(the lowest possible energy of all quantum states having this density) and the
integral over the uniform electron gas energy of this density. The error involves
gradient terms and justifies the use of the local density approximation in the
situation where the density is very flat on sufficiently large regions in space.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Elliott H.
full_name: Lieb, Elliott H.
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Lewin M, Lieb EH, Seiringer R. The local density approximation in density
functional theory. Pure and Applied Analysis. 2020;2(1):35-73. doi:10.2140/paa.2020.2.35
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2020). The local density approximation
in density functional theory. Pure and Applied Analysis. Mathematical Sciences
Publishers. https://doi.org/10.2140/paa.2020.2.35
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “ The Local Density
Approximation in Density Functional Theory.” Pure and Applied Analysis.
Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/paa.2020.2.35.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “ The local density approximation
in density functional theory,” Pure and Applied Analysis, vol. 2, no. 1.
Mathematical Sciences Publishers, pp. 35–73, 2020.
ista: Lewin M, Lieb EH, Seiringer R. 2020. The local density approximation in density
functional theory. Pure and Applied Analysis. 2(1), 35–73.
mla: Lewin, Mathieu, et al. “ The Local Density Approximation in Density Functional
Theory.” Pure and Applied Analysis, vol. 2, no. 1, Mathematical Sciences
Publishers, 2020, pp. 35–73, doi:10.2140/paa.2020.2.35.
short: M. Lewin, E.H. Lieb, R. Seiringer, Pure and Applied Analysis 2 (2020) 35–73.
corr_author: '1'
date_created: 2024-01-28T23:01:44Z
date_published: 2020-01-01T00:00:00Z
date_updated: 2024-10-09T21:08:02Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2020.2.35
external_id:
arxiv:
- '1903.04046'
intvolume: ' 2'
issue: '1'
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.48550/arXiv.1903.04046
month: '01'
oa: 1
oa_version: Preprint
page: 35-73
publication: Pure and Applied Analysis
publication_identifier:
eissn:
- 2578-5885
issn:
- 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' The local density approximation in density functional theory'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2020'
...
---
_id: '7611'
abstract:
- lang: eng
text: We consider a system of N bosons in the limit N→∞, interacting through singular
potentials. For initial data exhibiting Bose–Einstein condensation, the many-body
time evolution is well approximated through a quadratic fluctuation dynamics around
a cubic nonlinear Schrödinger equation of the condensate wave function. We show
that these fluctuations satisfy a (multi-variate) central limit theorem.
acknowledgement: "Simone Rademacher acknowledges partial support from the NCCR SwissMAP.
This project has received\r\nfunding from the European Union’s Horizon 2020 research
and innovation program under the Marie\r\nSkłodowska-Curie Grant Agreement No. 754411.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria).\r\nS.R.
would like to thank Benjamin Schlein for many fruitful discussions."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
citation:
ama: Rademacher SAE. Central limit theorem for Bose gases interacting through singular
potentials. Letters in Mathematical Physics. 2020;110:2143-2174. doi:10.1007/s11005-020-01286-w
apa: Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting
through singular potentials. Letters in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s11005-020-01286-w
chicago: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
through Singular Potentials.” Letters in Mathematical Physics. Springer
Nature, 2020. https://doi.org/10.1007/s11005-020-01286-w.
ieee: S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through
singular potentials,” Letters in Mathematical Physics, vol. 110. Springer
Nature, pp. 2143–2174, 2020.
ista: Rademacher SAE. 2020. Central limit theorem for Bose gases interacting through
singular potentials. Letters in Mathematical Physics. 110, 2143–2174.
mla: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
through Singular Potentials.” Letters in Mathematical Physics, vol. 110,
Springer Nature, 2020, pp. 2143–74, doi:10.1007/s11005-020-01286-w.
short: S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174.
corr_author: '1'
date_created: 2020-03-23T11:11:47Z
date_published: 2020-03-12T00:00:00Z
date_updated: 2025-04-14T07:44:03Z
day: '12'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-020-01286-w
ec_funded: 1
external_id:
isi:
- '000551556000006'
file:
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checksum: 3bdd41f10ad947b67a45b98f507a7d4a
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creator: dernst
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date_updated: 2020-11-20T12:04:26Z
file_id: '8784'
file_name: 2020_LettersMathPhysics_Rademacher.pdf
file_size: 478683
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language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 2143-2174
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: Letters in Mathematical Physics
publication_identifier:
eissn:
- 1573-0530
issn:
- 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Central limit theorem for Bose gases interacting through singular potentials
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: 110
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. Archive for Rational Mechanics and Analysis. 2020;236(6):1217-1271.
doi:10.1007/s00205-020-01489-4
apa: Deuchert, A., & Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous
Bose gas at positive temperature. Archive for Rational Mechanics and Analysis.
Springer Nature. https://doi.org/10.1007/s00205-020-01489-4
chicago: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous
Bose Gas at Positive Temperature.” Archive for Rational Mechanics and Analysis.
Springer Nature, 2020. https://doi.org/10.1007/s00205-020-01489-4.
ieee: A. Deuchert and R. Seiringer, “Gross-Pitaevskii limit of a homogeneous Bose
gas at positive temperature,” Archive for Rational Mechanics and Analysis,
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.” Archive for Rational Mechanics and Analysis,
vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:10.1007/s00205-020-01489-4.
short: A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236
(2020) 1217–1271.
corr_author: '1'
date_created: 2020-04-08T15:18:03Z
date_published: 2020-03-09T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
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: '7790'
abstract:
- lang: eng
text: "We prove a lower bound for the free energy (per unit volume) of the two-dimensional
Bose gas in the thermodynamic limit. We show that the free energy at density \U0001D70C
and inverse temperature \U0001D6FD differs from the one of the noninteracting
system by the correction term \U0001D70B\U0001D70C\U0001D70C\U0001D6FD\U0001D6FD
. Here, is the scattering length of the interaction potential, and \U0001D6FD
is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity.
The result is valid in the dilute limit \U0001D70C and if \U0001D6FD\U0001D70C
."
article_number: e20
article_processing_charge: No
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: Simon
full_name: Mayer, Simon
id: 30C4630A-F248-11E8-B48F-1D18A9856A87
last_name: Mayer
- 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, Mayer S, Seiringer R. The free energy of the two-dimensional dilute
Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 2020;8. doi:10.1017/fms.2020.17
apa: Deuchert, A., Mayer, S., & Seiringer, R. (2020). The free energy of the
two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma.
Cambridge University Press. https://doi.org/10.1017/fms.2020.17
chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy
of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” Forum of Mathematics,
Sigma. Cambridge University Press, 2020. https://doi.org/10.1017/fms.2020.17.
ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional
dilute Bose gas. I. Lower bound,” Forum of Mathematics, Sigma, vol. 8.
Cambridge University Press, 2020.
ista: Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional
dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20.
mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose
Gas. I. Lower Bound.” Forum of Mathematics, Sigma, vol. 8, e20, Cambridge
University Press, 2020, doi:10.1017/fms.2020.17.
short: A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020).
corr_author: '1'
date_created: 2020-05-03T22:00:48Z
date_published: 2020-03-14T00:00:00Z
date_updated: 2026-04-03T09:30:21Z
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ddc:
- '510'
department:
- _id: RoSe
doi: 10.1017/fms.2020.17
ec_funded: 1
external_id:
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name: Analysis of quantum many-body systems
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publisher: Cambridge University Press
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status: public
title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 8
year: '2020'
...
---
_id: '8091'
abstract:
- lang: eng
text: In the setting of the fractional quantum Hall effect we study the effects
of strong, repulsive two-body interaction potentials of short range. We prove
that Haldane’s pseudo-potential operators, including their pre-factors, emerge
as mathematically rigorous limits of such interactions when the range of the potential
tends to zero while its strength tends to infinity. In a common approach the interaction
potential is expanded in angular momentum eigenstates in the lowest Landau level,
which amounts to taking the pre-factors to be the moments of the potential. Such
a procedure is not appropriate for very strong interactions, however, in particular
not in the case of hard spheres. We derive the formulas valid in the short-range
case, which involve the scattering lengths of the interaction potential in different
angular momentum channels rather than its moments. Our results hold for bosons
and fermions alike and generalize previous results in [6], which apply to bosons
in the lowest angular momentum channel. Our main theorem asserts the convergence
in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after
appropriate energy scalings, to Hamiltonians with contact interactions in the
lowest Landau level.
acknowledgement: "Open access funding provided by Institute of Science and Technology
(IST Austria).\r\nThe work of R.S. was supported by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No 694227). J.Y. gratefully acknowledges hospitality at the LPMMC
Grenoble and valuable discussions with Alessandro Olgiati and Nicolas Rougerie. "
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: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems
with short-range interactions. Journal of Statistical Physics. 2020;181:448-464.
doi:10.1007/s10955-020-02586-0
apa: Seiringer, R., & Yngvason, J. (2020). Emergence of Haldane pseudo-potentials
in systems with short-range interactions. Journal of Statistical Physics.
Springer. https://doi.org/10.1007/s10955-020-02586-0
chicago: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials
in Systems with Short-Range Interactions.” Journal of Statistical Physics.
Springer, 2020. https://doi.org/10.1007/s10955-020-02586-0.
ieee: R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems
with short-range interactions,” Journal of Statistical Physics, vol. 181.
Springer, pp. 448–464, 2020.
ista: Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems
with short-range interactions. Journal of Statistical Physics. 181, 448–464.
mla: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials
in Systems with Short-Range Interactions.” Journal of Statistical Physics,
vol. 181, Springer, 2020, pp. 448–64, doi:10.1007/s10955-020-02586-0.
short: R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464.
corr_author: '1'
date_created: 2020-07-05T22:00:46Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2025-07-10T11:55:04Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s10955-020-02586-0
ec_funded: 1
external_id:
arxiv:
- '2001.07144'
isi:
- '000543030000002'
file:
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creator: dernst
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file_name: 2020_JourStatPhysics_Seiringer.pdf
file_size: 404778
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oa: 1
oa_version: Published Version
page: 448-464
project:
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name: IST Austria Open Access Fund
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Emergence of Haldane pseudo-potentials in systems with short-range interactions
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: 181
year: '2020'
...
---
_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. Archive for Rational Mechanics and Analysis. 2020;238(11):541-606.
doi:10.1007/s00205-020-01548-w
apa: Bossmann, L. (2020). Derivation of the 2d Gross–Pitaevskii equation for strongly
confined 3d Bosons. Archive for Rational Mechanics and Analysis. Springer
Nature. https://doi.org/10.1007/s00205-020-01548-w
chicago: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly
Confined 3d Bosons.” Archive for Rational Mechanics and Analysis. Springer
Nature, 2020. https://doi.org/10.1007/s00205-020-01548-w.
ieee: L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly
confined 3d Bosons,” Archive for Rational Mechanics and Analysis, 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.” Archive for Rational Mechanics and Analysis, vol.
238, no. 11, Springer Nature, 2020, pp. 541–606, doi:10.1007/s00205-020-01548-w.
short: L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.
corr_author: '1'
date_created: 2020-07-18T15:06:35Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2025-04-14T07:44:05Z
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
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isi: 1
issue: '11'
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- 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: '8134'
abstract:
- lang: eng
text: We prove an upper bound on the free energy of a two-dimensional homogeneous
Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the
free energy per unit volume differs from the one of the non-interacting system
by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]2+) to leading order, where a is the scattering
length of the two-body interaction potential, ρ is the density, β is the inverse
temperature, and βc is the inverse Berezinskii–Kosterlitz–Thouless critical temperature
for superfluidity. In combination with the corresponding matching lower bound
proved by Deuchert et al. [Forum Math. Sigma 8, e20 (2020)], this shows equality
in the asymptotic expansion.
article_number: '061901'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Simon
full_name: Mayer, Simon
id: 30C4630A-F248-11E8-B48F-1D18A9856A87
last_name: Mayer
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas.
II. Upper bound. Journal of Mathematical Physics. 2020;61(6). doi:10.1063/5.0005950
apa: Mayer, S., & Seiringer, R. (2020). The free energy of the two-dimensional
dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. AIP
Publishing. https://doi.org/10.1063/5.0005950
chicago: Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional
Dilute Bose Gas. II. Upper Bound.” Journal of Mathematical Physics. AIP
Publishing, 2020. https://doi.org/10.1063/5.0005950.
ieee: S. Mayer and R. Seiringer, “The free energy of the two-dimensional dilute
Bose gas. II. Upper bound,” Journal of Mathematical Physics, vol. 61, no.
6. AIP Publishing, 2020.
ista: Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute
Bose gas. II. Upper bound. Journal of Mathematical Physics. 61(6), 061901.
mla: Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional
Dilute Bose Gas. II. Upper Bound.” Journal of Mathematical Physics, vol.
61, no. 6, 061901, AIP Publishing, 2020, doi:10.1063/5.0005950.
short: S. Mayer, R. Seiringer, Journal of Mathematical Physics 61 (2020).
corr_author: '1'
date_created: 2020-07-19T22:00:59Z
date_published: 2020-06-22T00:00:00Z
date_updated: 2025-07-10T11:55:05Z
day: '22'
department:
- _id: RoSe
doi: 10.1063/5.0005950
ec_funded: 1
external_id:
arxiv:
- '2002.08281'
isi:
- '000544595100001'
intvolume: ' 61'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
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url: https://arxiv.org/abs/2002.08281
month: '06'
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 Mathematical Physics
publication_identifier:
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The free energy of the two-dimensional dilute Bose gas. II. Upper bound
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 61
year: '2020'
...