---
_id: '10850'
abstract:
- lang: eng
text: "We study two interacting quantum particles forming a bound state in d-dimensional
free\r\nspace, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with
Neumann boundary\r\nconditions. First, we prove that the ground state energy strictly
decreases upon going from k\r\nto k+1. This shows that the particles stick to
the corner where all boundary planes intersect.\r\nSecond, we show that for all
k the resulting Hamiltonian, after removing the free part of the\r\nkinetic energy,
has only finitely many eigenvalues below the essential spectrum. This paper\r\ngeneralizes
the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444,\r\n2020)
to dimensions d > 1."
acknowledgement: We thank Rupert Frank for contributing Appendix B. Funding from the
European Union's Horizon 2020 research and innovation programme under the ERC grant
agreement No. 694227 is gratefully acknowledged.
article_number: '109455'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Barbara
full_name: Roos, Barbara
id: 5DA90512-D80F-11E9-8994-2E2EE6697425
last_name: Roos
orcid: 0000-0002-9071-5880
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Roos B, Seiringer R. Two-particle bound states at interfaces and corners. Journal
of Functional Analysis. 2022;282(12). doi:10.1016/j.jfa.2022.109455
apa: Roos, B., & Seiringer, R. (2022). Two-particle bound states at interfaces
and corners. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109455
chicago: Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces
and Corners.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109455.
ieee: B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,”
Journal of Functional Analysis, vol. 282, no. 12. Elsevier, 2022.
ista: Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners.
Journal of Functional Analysis. 282(12), 109455.
mla: Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces
and Corners.” Journal of Functional Analysis, vol. 282, no. 12, 109455,
Elsevier, 2022, doi:10.1016/j.jfa.2022.109455.
short: B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022).
date_created: 2022-03-16T08:41:53Z
date_published: 2022-06-15T00:00:00Z
date_updated: 2023-10-27T10:37:29Z
day: '15'
ddc:
- '510'
department:
- _id: GradSch
- _id: RoSe
doi: 10.1016/j.jfa.2022.109455
ec_funded: 1
external_id:
arxiv:
- '2105.04874'
isi:
- '000795160200009'
file:
- access_level: open_access
checksum: 63efcefaa1f2717244ef5407bd564426
content_type: application/pdf
creator: dernst
date_created: 2022-08-02T10:37:55Z
date_updated: 2022-08-02T10:37:55Z
file_id: '11720'
file_name: 2022_JourFunctionalAnalysis_Roos.pdf
file_size: 631391
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success: 1
file_date_updated: 2022-08-02T10:37:55Z
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intvolume: ' 282'
isi: 1
issue: '12'
keyword:
- Analysis
language:
- iso: eng
month: '06'
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: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '14374'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Two-particle bound states at interfaces and corners
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 282
year: '2022'
...
---
_id: '11473'
abstract:
- lang: eng
text: "The polaron model is a basic model of quantum field theory describing a single
particle\r\ninteracting with a bosonic field. It arises in many physical contexts.
We are mostly concerned\r\nwith models applicable in the context of an impurity
atom in a Bose-Einstein condensate as\r\nwell as the problem of electrons moving
in polar crystals.\r\nThe model has a simple structure in which the interaction
of the particle with the field is given\r\nby a term linear in the field’s creation
and annihilation operators. In this work, we investigate\r\nthe properties of
this model by providing rigorous estimates on various energies relevant to the\r\nproblem.
The estimates are obtained, for the most part, by suitable operator techniques
which\r\nconstitute the principal mathematical substance of the thesis.\r\nThe
first application of these techniques is to derive the polaron model rigorously
from first\r\nprinciples, i.e., from a full microscopic quantum-mechanical many-body
problem involving an\r\nimpurity in an otherwise homogeneous system. We accomplish
this for the N + 1 Bose gas\r\nin the mean-field regime by showing that a suitable
polaron-type Hamiltonian arises at weak\r\ninteractions as a low-energy effective
theory for this problem.\r\nIn the second part, we investigate rigorously the
ground state of the model at fixed momentum\r\nand for large values of the coupling
constant. Qualitatively, the system is expected to display\r\na transition from
the quasi-particle behavior at small momenta, where the dispersion relation\r\nis
parabolic and the particle moves through the medium dragging along a cloud of
phonons, to\r\nthe radiative behavior at larger momenta where the polaron decelerates
and emits free phonons.\r\nAt the same time, in the strong coupling regime, the
bosonic field is expected to behave purely\r\nclassically. Accordingly, the effective
mass of the polaron at strong coupling is conjectured to\r\nbe asymptotically
equal to the one obtained from the semiclassical counterpart of the problem,\r\nfirst
studied by Landau and Pekar in the 1940s. For polaron models with regularized
form\r\nfactors and phonon dispersion relations of superfluid type, i.e., bounded
below by a linear\r\nfunction of the wavenumbers for all phonon momenta as in
the interacting Bose gas, we prove\r\nthat for a large window of momenta below
the radiation threshold, the energy-momentum\r\nrelation at strong coupling is
indeed essentially a parabola with semi-latus rectum equal to the\r\nLandau–Pekar
effective mass, as expected.\r\nFor the Fröhlich polaron describing electrons
in polar crystals where the dispersion relation is\r\nof the optical type and
the form factor is formally UV–singular due to the nature of the point\r\ncharge-dipole
interaction, we are able to give the corresponding upper bound. In contrast to\r\nthe
regular case, this requires the inclusion of the quantum fluctuations of the phonon
field,\r\nwhich makes the problem considerably more difficult.\r\nThe results
are supplemented by studies on the absolute ground-state energy at strong coupling,\r\na
proof of the divergence of the effective mass with the coupling constant for a
wide class of\r\npolaron models, as well as the discussion of the apparent UV
singularity of the Fröhlich model\r\nand the application of the techniques used
for its removal for the energy estimates.\r\n"
acknowledged_ssus:
- _id: SSU
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Krzysztof
full_name: Mysliwy, Krzysztof
id: 316457FC-F248-11E8-B48F-1D18A9856A87
last_name: Mysliwy
citation:
ama: 'Mysliwy K. Polarons in Bose gases and polar crystals: Some rigorous energy
estimates. 2022. doi:10.15479/at:ista:11473'
apa: 'Mysliwy, K. (2022). Polarons in Bose gases and polar crystals: Some rigorous
energy estimates. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:11473'
chicago: 'Mysliwy, Krzysztof. “Polarons in Bose Gases and Polar Crystals: Some Rigorous
Energy Estimates.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:11473.'
ieee: 'K. Mysliwy, “Polarons in Bose gases and polar crystals: Some rigorous energy
estimates,” Institute of Science and Technology Austria, 2022.'
ista: 'Mysliwy K. 2022. Polarons in Bose gases and polar crystals: Some rigorous
energy estimates. Institute of Science and Technology Austria.'
mla: 'Mysliwy, Krzysztof. Polarons in Bose Gases and Polar Crystals: Some Rigorous
Energy Estimates. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:11473.'
short: 'K. Mysliwy, Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy
Estimates, Institute of Science and Technology Austria, 2022.'
date_created: 2022-06-30T12:15:03Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-09-07T13:43:52Z
day: '01'
ddc:
- '515'
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: RoSe
doi: 10.15479/at:ista:11473
ec_funded: 1
file:
- access_level: open_access
checksum: 7970714a20a6052f75fb27a6c3e9976e
content_type: application/pdf
creator: kmysliwy
date_created: 2022-07-05T08:12:56Z
date_updated: 2022-07-05T08:12:56Z
file_id: '11486'
file_name: thes1_no_isbn_2_1b.pdf
file_size: 1830973
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creator: kmysliwy
date_created: 2022-07-05T08:15:52Z
date_updated: 2022-07-05T08:17:12Z
file_id: '11487'
file_name: thes_source.zip
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file_date_updated: 2022-07-05T08:17:12Z
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language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '138'
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10564'
relation: part_of_dissertation
status: public
- id: '8705'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
title: 'Polarons in Bose gases and polar crystals: Some rigorous energy estimates'
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2022'
...
---
_id: '11732'
abstract:
- lang: eng
text: We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic
formula, which strongly depends on the strength of the interaction potential V
on the Fermi surface. In combination with the recent result by one of us (Math.
Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities,
we prove the universality of the ratio of the energy gap and the critical temperature.
acknowledgement: "We are grateful to Robert Seiringer for helpful discussions and
many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges
partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open
access funding provided by Institute of Science and Technology (IST Austria)"
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- 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: Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of
Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9
apa: Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density.
Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9
chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap
at High Density.” Journal of Statistical Physics. Springer Nature, 2022.
https://doi.org/10.1007/s10955-022-02965-9.
ieee: S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal
of Statistical Physics, vol. 189. Springer Nature, 2022.
ista: Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal
of Statistical Physics. 189, 5.
mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at
High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature,
2022, doi:10.1007/s10955-022-02965-9.
short: S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).
date_created: 2022-08-05T11:36:56Z
date_published: 2022-07-29T00:00:00Z
date_updated: 2023-09-05T14:57:49Z
day: '29'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
- _id: RoSe
doi: 10.1007/s10955-022-02965-9
ec_funded: 1
external_id:
isi:
- '000833007200002'
file:
- access_level: open_access
checksum: b398c4dbf65f71d417981d6e366427e9
content_type: application/pdf
creator: dernst
date_created: 2022-08-08T07:36:34Z
date_updated: 2022-08-08T07:36:34Z
file_id: '11746'
file_name: 2022_JourStatisticalPhysics_Henheik.pdf
file_size: 419563
relation: main_file
success: 1
file_date_updated: 2022-08-08T07:36:34Z
has_accepted_license: '1'
intvolume: ' 189'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The BCS energy gap at high density
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: 189
year: '2022'
...
---
_id: '11783'
abstract:
- lang: eng
text: We consider a gas of N bosons with interactions in the mean-field scaling
regime. We review the proof of an asymptotic expansion of its low-energy spectrum,
eigenstates, and dynamics, which provides corrections to Bogoliubov theory to
all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer,
and Soffer. In addition, we derive a full asymptotic expansion of the ground state
one-body reduced density matrix.
acknowledgement: "The author thanks Nataˇsa Pavlovic, Sören Petrat, Peter Pickl, Robert
Seiringer, and Avy Soffer for the collaboration on Refs. 1, 2 and 21. Funding from
the European Union’s Horizon 2020 Research and Innovation Programme under Marie
Skℓodowska-Curie Grant Agreement\r\nNo. 754411 is gratefully acknowledged."
article_number: '061102'
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. Low-energy spectrum and dynamics of the weakly interacting Bose
gas. Journal of Mathematical Physics. 2022;63(6). doi:10.1063/5.0089983
apa: Bossmann, L. (2022). Low-energy spectrum and dynamics of the weakly interacting
Bose gas. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0089983
chicago: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting
Bose Gas.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0089983.
ieee: L. Bossmann, “Low-energy spectrum and dynamics of the weakly interacting Bose
gas,” Journal of Mathematical Physics, vol. 63, no. 6. AIP Publishing,
2022.
ista: Bossmann L. 2022. Low-energy spectrum and dynamics of the weakly interacting
Bose gas. Journal of Mathematical Physics. 63(6), 061102.
mla: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting
Bose Gas.” Journal of Mathematical Physics, vol. 63, no. 6, 061102, AIP
Publishing, 2022, doi:10.1063/5.0089983.
short: L. Bossmann, Journal of Mathematical Physics 63 (2022).
date_created: 2022-08-11T06:37:52Z
date_published: 2022-06-10T00:00:00Z
date_updated: 2023-08-03T12:46:28Z
day: '10'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1063/5.0089983
ec_funded: 1
external_id:
arxiv:
- '2203.00730'
isi:
- '000809648100002'
file:
- access_level: open_access
checksum: d0d32c338c1896680174be88c70968fa
content_type: application/pdf
creator: dernst
date_created: 2022-08-11T07:03:02Z
date_updated: 2022-08-11T07:03:02Z
file_id: '11784'
file_name: 2022_JourMathPhysics_Bossmann.pdf
file_size: 5957888
relation: main_file
success: 1
file_date_updated: 2022-08-11T07:03:02Z
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '6'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Low-energy spectrum and dynamics of the weakly interacting Bose gas
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: 63
year: '2022'
...
---
_id: '10564'
abstract:
- lang: eng
text: We study a class of polaron-type Hamiltonians with sufficiently regular form
factor in the interaction term. We investigate the strong-coupling limit of the
model, and prove suitable bounds on the ground state energy as a function of the
total momentum of the system. These bounds agree with the semiclassical approximation
to leading order. The latter corresponds here to the situation when the particle
undergoes harmonic motion in a potential well whose frequency is determined by
the corresponding Pekar functional. We show that for all such models the effective
mass diverges in the strong coupling limit, in all spatial dimensions. Moreover,
for the case when the phonon dispersion relation grows at least linearly with
momentum, the bounds result in an asymptotic formula for the effective mass quotient,
a quantity generalizing the usual notion of the effective mass. This asymptotic
form agrees with the semiclassical Landau–Pekar formula and can be regarded as
the first rigorous confirmation, in a slightly weaker sense than usually considered,
of the validity of the semiclassical formula for the effective mass.
acknowledgement: Financial support through the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme Grant Agreement
No. 694227 (R.S.) and the Maria Skłodowska-Curie Grant Agreement No. 665386 (K.M.)
is gratefully acknowledged. Open access funding provided by Institute of Science
and Technology (IST Austria).
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Krzysztof
full_name: Mysliwy, Krzysztof
id: 316457FC-F248-11E8-B48F-1D18A9856A87
last_name: Mysliwy
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Mysliwy K, Seiringer R. Polaron models with regular interactions at strong
coupling. Journal of Statistical Physics. 2022;186(1). doi:10.1007/s10955-021-02851-w
apa: Mysliwy, K., & Seiringer, R. (2022). Polaron models with regular interactions
at strong coupling. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-021-02851-w
chicago: Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular
Interactions at Strong Coupling.” Journal of Statistical Physics. Springer
Nature, 2022. https://doi.org/10.1007/s10955-021-02851-w.
ieee: K. Mysliwy and R. Seiringer, “Polaron models with regular interactions at
strong coupling,” Journal of Statistical Physics, vol. 186, no. 1. Springer
Nature, 2022.
ista: Mysliwy K, Seiringer R. 2022. Polaron models with regular interactions at
strong coupling. Journal of Statistical Physics. 186(1), 5.
mla: Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions
at Strong Coupling.” Journal of Statistical Physics, vol. 186, no. 1, 5,
Springer Nature, 2022, doi:10.1007/s10955-021-02851-w.
short: K. Mysliwy, R. Seiringer, Journal of Statistical Physics 186 (2022).
date_created: 2021-12-19T23:01:32Z
date_published: 2022-01-01T00:00:00Z
date_updated: 2023-09-07T13:43:51Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s10955-021-02851-w
ec_funded: 1
external_id:
arxiv:
- '2106.09328'
isi:
- '000726275600001'
file:
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checksum: da03f6d293c4b9802091bce9471b1d29
content_type: application/pdf
creator: cchlebak
date_created: 2022-02-02T14:24:41Z
date_updated: 2022-02-02T14:24:41Z
file_id: '10716'
file_name: 2022_JournalStatPhys_Myśliwy.pdf
file_size: 434957
relation: main_file
success: 1
file_date_updated: 2022-02-02T14:24:41Z
has_accepted_license: '1'
intvolume: ' 186'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
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
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '11473'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Polaron models with regular interactions at strong coupling
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: 186
year: '2022'
...
---
_id: '11917'
abstract:
- lang: eng
text: We study the many-body dynamics of an initially factorized bosonic wave function
in the mean-field regime. We prove large deviation estimates for the fluctuations
around the condensate. We derive an upper bound extending a recent result to more
general interactions. Furthermore, we derive a new lower bound which agrees with
the upper bound in leading order.
acknowledgement: "The authors thank Gérard Ben Arous for pointing out the question
of a lower bound. 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 Skłodowska-Curie
Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.\r\nOpen access funding
provided by IST Austria."
article_number: '9'
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
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Rademacher SAE, Seiringer R. Large deviation estimates for weakly interacting
bosons. Journal of Statistical Physics. 2022;188. doi:10.1007/s10955-022-02940-4
apa: Rademacher, S. A. E., & Seiringer, R. (2022). Large deviation estimates
for weakly interacting bosons. Journal of Statistical Physics. Springer
Nature. https://doi.org/10.1007/s10955-022-02940-4
chicago: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation
Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics.
Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02940-4.
ieee: S. A. E. Rademacher and R. Seiringer, “Large deviation estimates for weakly
interacting bosons,” Journal of Statistical Physics, vol. 188. Springer
Nature, 2022.
ista: Rademacher SAE, Seiringer R. 2022. Large deviation estimates for weakly interacting
bosons. Journal of Statistical Physics. 188, 9.
mla: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates
for Weakly Interacting Bosons.” Journal of Statistical Physics, vol. 188,
9, Springer Nature, 2022, doi:10.1007/s10955-022-02940-4.
short: S.A.E. Rademacher, R. Seiringer, Journal of Statistical Physics 188 (2022).
date_created: 2022-08-18T07:23:26Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-08-03T12:55:58Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s10955-022-02940-4
ec_funded: 1
external_id:
isi:
- '000805175000001'
file:
- access_level: open_access
checksum: 44418cb44f07fa21ed3907f85abf7f39
content_type: application/pdf
creator: dernst
date_created: 2022-08-18T08:09:00Z
date_updated: 2022-08-18T08:09:00Z
file_id: '11922'
file_name: 2022_JournalStatisticalPhysics_Rademacher.pdf
file_size: 483481
relation: main_file
success: 1
file_date_updated: 2022-08-18T08:09:00Z
has_accepted_license: '1'
intvolume: ' 188'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '07'
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
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Large deviation estimates 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 188
year: '2022'
...
---
_id: '12083'
abstract:
- lang: eng
text: We consider the many-body time evolution of weakly interacting bosons in the
mean field regime for initial coherent states. We show that bounded k-particle
operators, corresponding to dependent random variables, satisfy both a law of
large numbers and a central limit theorem.
acknowledgement: S.R. would like to thank Robert Seiringer and Benedikt Stufler for
helpful discussions. Funding from the European Union’s Horizon 2020 Research and
Innovation Program under the ERC grant (Grant Agreement No. 694227) and under the
Marie Skłodowska-Curie grant (Agreement No. 754411) is acknowledged.
article_number: '081902'
article_processing_charge: No
article_type: original
arxiv: 1
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. Dependent random variables in quantum dynamics. Journal
of Mathematical Physics. 2022;63(8). doi:10.1063/5.0086712
apa: Rademacher, S. A. E. (2022). Dependent random variables in quantum dynamics.
Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0086712
chicago: Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum
Dynamics.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0086712.
ieee: S. A. E. Rademacher, “Dependent random variables in quantum dynamics,” Journal
of Mathematical Physics, vol. 63, no. 8. AIP Publishing, 2022.
ista: Rademacher SAE. 2022. Dependent random variables in quantum dynamics. Journal
of Mathematical Physics. 63(8), 081902.
mla: Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.”
Journal of Mathematical Physics, vol. 63, no. 8, 081902, AIP Publishing,
2022, doi:10.1063/5.0086712.
short: S.A.E. Rademacher, Journal of Mathematical Physics 63 (2022).
date_created: 2022-09-11T22:01:56Z
date_published: 2022-08-25T00:00:00Z
date_updated: 2023-08-03T13:57:19Z
day: '25'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1063/5.0086712
ec_funded: 1
external_id:
arxiv:
- '2112.04817'
isi:
- '000844402500001'
file:
- access_level: open_access
checksum: e6fb0cf3f0327739c5e69a2cfc4020eb
content_type: application/pdf
creator: dernst
date_created: 2022-09-12T07:35:34Z
date_updated: 2022-09-12T07:35:34Z
file_id: '12089'
file_name: 2022_JourMathPhysics_Rademacher.pdf
file_size: 4552261
relation: main_file
success: 1
file_date_updated: 2022-09-12T07:35:34Z
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '8'
language:
- iso: eng
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
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Dependent random variables in 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2022'
...
---
_id: '12246'
abstract:
- lang: eng
text: The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of
a classical system of N identical charges only in terms of their one-particle
density. We prove here a new estimate on the best constant in this inequality.
Numerical evaluation provides the value 1.58, which is a significant improvement
to the previously known value 1.64. The best constant has recently been shown
to be larger than 1.44. In a second part, we prove that the constant can be reduced
to 1.25 when the inequality is restricted to Hartree–Fock states. This is the
first proof that the exchange term is always much lower than the full indirect
Coulomb energy.
acknowledgement: We would like to thank David Gontier for useful advice on the numerical
simulations. This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation program (Grant
Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful
for the hospitality of the Institut Henri Poincaré in Paris, where part of this
work was done.
article_number: '92'
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. Improved Lieb–Oxford bound on the indirect and
exchange energies. Letters in Mathematical Physics. 2022;112(5). doi:10.1007/s11005-022-01584-5
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2022). Improved Lieb–Oxford bound
on the indirect and exchange energies. Letters in Mathematical Physics.
Springer Nature. https://doi.org/10.1007/s11005-022-01584-5
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford
Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics.
Springer Nature, 2022. https://doi.org/10.1007/s11005-022-01584-5.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the
indirect and exchange energies,” Letters in Mathematical Physics, vol.
112, no. 5. Springer Nature, 2022.
ista: Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect
and exchange energies. Letters in Mathematical Physics. 112(5), 92.
mla: Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange
Energies.” Letters in Mathematical Physics, vol. 112, no. 5, 92, Springer
Nature, 2022, doi:10.1007/s11005-022-01584-5.
short: M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022).
date_created: 2023-01-16T09:53:54Z
date_published: 2022-09-15T00:00:00Z
date_updated: 2023-09-05T15:17:34Z
day: '15'
department:
- _id: RoSe
doi: 10.1007/s11005-022-01584-5
ec_funded: 1
external_id:
arxiv:
- '2203.12473'
isi:
- '000854762600001'
intvolume: ' 112'
isi: 1
issue: '5'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2203.12473
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: 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: Improved Lieb–Oxford bound on the indirect and exchange energies
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 112
year: '2022'
...
---
_id: '12276'
abstract:
- lang: eng
text: Ongoing development of quantum simulators allows for a progressively finer
degree of control of quantum many-body systems. This motivates the development
of efficient approaches to facilitate the control of such systems and enable the
preparation of nontrivial quantum states. Here we formulate an approach to control
quantum systems based on matrix product states (MPSs). We compare counterdiabatic
and leakage minimization approaches to the so-called local steering problem that
consists in finding the best value of the control parameters for generating a
unitary evolution of the specific MPS in a given direction. In order to benchmark
the different approaches, we apply them to the generalization of the PXP model
known to exhibit coherent quantum dynamics due to quantum many-body scars. We
find that the leakage-based approach generally outperforms the counterdiabatic
framework and use it to construct a Floquet model with quantum scars. We perform
the first steps towards global trajectory optimization and demonstrate entanglement
steering capabilities in the generalized PXP model. Finally, we apply our leakage
minimization approach to construct quantum scars in the periodically driven nonintegrable
Ising model.
acknowledgement: We thank A. A. Michailidis for insightful discussions. M.L. and M.S.
acknowledge support from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 850899).
D.A. is supported by the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (Grant Agreement No. 864597) and
by the Swiss National Science Foundation. The infinite TEBD simulations were performed
using the ITensor library [67].
article_number: '030343'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marko
full_name: Ljubotina, Marko
id: F75EE9BE-5C90-11EA-905D-16643DDC885E
last_name: Ljubotina
- first_name: Barbara
full_name: Roos, Barbara
id: 5DA90512-D80F-11E9-8994-2E2EE6697425
last_name: Roos
orcid: 0000-0002-9071-5880
- first_name: Dmitry A.
full_name: Abanin, Dmitry A.
last_name: Abanin
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
citation:
ama: Ljubotina M, Roos B, Abanin DA, Serbyn M. Optimal steering of matrix product
states and quantum many-body scars. PRX Quantum. 2022;3(3). doi:10.1103/prxquantum.3.030343
apa: Ljubotina, M., Roos, B., Abanin, D. A., & Serbyn, M. (2022). Optimal steering
of matrix product states and quantum many-body scars. PRX Quantum. American
Physical Society. https://doi.org/10.1103/prxquantum.3.030343
chicago: Ljubotina, Marko, Barbara Roos, Dmitry A. Abanin, and Maksym Serbyn. “Optimal
Steering of Matrix Product States and Quantum Many-Body Scars.” PRX Quantum.
American Physical Society, 2022. https://doi.org/10.1103/prxquantum.3.030343.
ieee: M. Ljubotina, B. Roos, D. A. Abanin, and M. Serbyn, “Optimal steering of matrix
product states and quantum many-body scars,” PRX Quantum, vol. 3, no. 3.
American Physical Society, 2022.
ista: Ljubotina M, Roos B, Abanin DA, Serbyn M. 2022. Optimal steering of matrix
product states and quantum many-body scars. PRX Quantum. 3(3), 030343.
mla: Ljubotina, Marko, et al. “Optimal Steering of Matrix Product States and Quantum
Many-Body Scars.” PRX Quantum, vol. 3, no. 3, 030343, American Physical
Society, 2022, doi:10.1103/prxquantum.3.030343.
short: M. Ljubotina, B. Roos, D.A. Abanin, M. Serbyn, PRX Quantum 3 (2022).
date_created: 2023-01-16T10:01:56Z
date_published: 2022-09-23T00:00:00Z
date_updated: 2023-01-30T11:05:23Z
day: '23'
ddc:
- '530'
department:
- _id: MaSe
- _id: RoSe
doi: 10.1103/prxquantum.3.030343
ec_funded: 1
external_id:
arxiv:
- '2204.02899'
file:
- access_level: open_access
checksum: ef8f0a1b5a019b3958009162de0fa4c3
content_type: application/pdf
creator: dernst
date_created: 2023-01-30T11:02:50Z
date_updated: 2023-01-30T11:02:50Z
file_id: '12457'
file_name: 2022_PRXQuantum_Ljubotina.pdf
file_size: 7661905
relation: main_file
success: 1
file_date_updated: 2023-01-30T11:02:50Z
has_accepted_license: '1'
intvolume: ' 3'
issue: '3'
keyword:
- General Medicine
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
call_identifier: H2020
grant_number: '850899'
name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication: PRX Quantum
publication_identifier:
eissn:
- 2691-3399
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal steering of matrix product states and quantum many-body scars
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: 3
year: '2022'
...
---
_id: '12390'
abstract:
- lang: eng
text: "The scope of this thesis is to study quantum systems exhibiting a continuous
symmetry that\r\nis broken on the level of the corresponding effective theory.
In particular we are going to\r\ninvestigate translation-invariant Bose gases
in the mean field limit, effectively described by\r\nthe Hartree functional, and
the Fröhlich Polaron in the regime of strong coupling, effectively\r\ndescribed
by the Pekar functional. The latter is a model describing the interaction between
a\r\ncharged particle and the optical modes of a polar crystal. Regarding the
former, we assume in\r\naddition that the particles in the gas are unconfined,
and typically we will consider particles\r\nthat are subject to an attractive
interaction. In both cases the ground state energy of the\r\nHamiltonian is not
a proper eigenvalue due to the underlying translation-invariance, while on\r\nthe
contrary there exists a whole invariant orbit of minimizers for the corresponding
effective\r\nfunctionals. Both, the absence of proper eigenstates and the broken
symmetry of the effective\r\ntheory, make the study significantly more involved
and it is the content of this thesis to\r\ndevelop a frameworks which allows for
a systematic way to circumvent these issues.\r\nIt is a well-established result
that the ground state energy of Bose gases in the mean field limit,\r\nas well
as the ground state energy of the Fröhlich Polaron in the regime of strong coupling,
is\r\nto leading order given by the minimal energy of the corresponding effective
theory. As part\r\nof this thesis we identify the sub-leading term in the expansion
of the ground state energy,\r\nwhich can be interpreted as the quantum correction
to the classical energy, since the effective\r\ntheories under consideration can
be seen as classical counterparts.\r\nWe are further going to establish an asymptotic
expression for the energy-momentum relation\r\nof the Fröhlich Polaron in the
strong coupling limit. In the regime of suitably small momenta,\r\nthis asymptotic
expression agrees with the energy-momentum relation of a free particle having\r\nan
effectively increased mass, and we find that this effectively increased mass agrees
with the\r\nconjectured value in the physics literature.\r\nIn addition we will
discuss two unrelated papers written by the author during his stay at ISTA\r\nin
the appendix. The first one concerns the realization of anyons, which are quasi-particles\r\nacquiring
a non-trivial phase under the exchange of two particles, as molecular impurities.\r\nThe
second one provides a classification of those vector fields defined on a given
manifold\r\nthat can be written as the gradient of a given functional with respect
to a suitable metric,\r\nprovided that some mild smoothness assumptions hold.
This classification is subsequently\r\nused to identify those quantum Markov semigroups
that can be written as a gradient flow of\r\nthe relative entropy.\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Morris
full_name: Brooks, Morris
id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
last_name: Brooks
orcid: 0000-0002-6249-0928
citation:
ama: Brooks M. Translation-invariant quantum systems with effectively broken symmetry.
2022. doi:10.15479/at:ista:12390
apa: Brooks, M. (2022). Translation-invariant quantum systems with effectively
broken symmetry. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:12390
chicago: Brooks, Morris. “Translation-Invariant Quantum Systems with Effectively
Broken Symmetry.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:12390.
ieee: M. Brooks, “Translation-invariant quantum systems with effectively broken
symmetry,” Institute of Science and Technology Austria, 2022.
ista: Brooks M. 2022. Translation-invariant quantum systems with effectively broken
symmetry. Institute of Science and Technology Austria.
mla: Brooks, Morris. Translation-Invariant Quantum Systems with Effectively Broken
Symmetry. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:12390.
short: M. Brooks, Translation-Invariant Quantum Systems with Effectively Broken
Symmetry, Institute of Science and Technology Austria, 2022.
date_created: 2023-01-26T10:00:42Z
date_published: 2022-12-15T00:00:00Z
date_updated: 2023-08-07T13:32:09Z
day: '15'
ddc:
- '500'
degree_awarded: PhD
department:
- _id: GradSch
- _id: RoSe
doi: 10.15479/at:ista:12390
ec_funded: 1
file:
- access_level: open_access
checksum: b31460e937f33b557abb40ebef02b567
content_type: application/pdf
creator: cchlebak
date_created: 2023-01-26T10:02:34Z
date_updated: 2023-01-26T10:02:34Z
file_id: '12391'
file_name: Brooks_Thesis.pdf
file_size: 3095225
relation: main_file
success: 1
- access_level: closed
checksum: 9751869fa5e7981588ad4228f4fd4bd6
content_type: application/octet-stream
creator: cchlebak
date_created: 2023-01-26T10:02:42Z
date_updated: 2023-01-26T10:02:42Z
file_id: '12392'
file_name: Brooks_Thesis.tex
file_size: 809842
relation: source_file
file_date_updated: 2023-01-26T10:02:42Z
has_accepted_license: '1'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: '196'
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '9005'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
title: Translation-invariant quantum systems with effectively broken symmetry
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2022'
...
---
_id: '10738'
abstract:
- lang: eng
text: We prove an adiabatic theorem for the Landau–Pekar equations. This allows
us to derive new results on the accuracy of their use as effective equations for
the time evolution generated by the Fröhlich Hamiltonian with large coupling constant
α. In particular, we show that the time evolution of Pekar product states with
coherent phonon field and the electron being trapped by the phonons is well approximated
by the Landau–Pekar equations until times short compared to α2.
acknowledgement: "N. L. and R. S. gratefully acknowledge financial support by the
European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research
and innovation programme (grant\r\nagreement No 694227). B. S. acknowledges support
from the Swiss National Science Foundation (grant 200020_172623) and from the NCCR
SwissMAP. N. L. would like to thank\r\nAndreas Deuchert and David Mitrouskas for
interesting discussions. B. S. and R. S. would\r\nlike to thank Rupert Frank for
stimulating discussions about the time-evolution of a polaron.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nikolai K
full_name: Leopold, Nikolai K
id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
last_name: Leopold
orcid: 0000-0002-0495-6822
- first_name: 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
- 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, Rademacher SAE, Schlein B, Seiringer R. The Landau–Pekar equations:
Adiabatic theorem and accuracy. Analysis and PDE. 2021;14(7):2079-2100.
doi:10.2140/APDE.2021.14.2079'
apa: 'Leopold, N. K., Rademacher, S. A. E., Schlein, B., & Seiringer, R. (2021). The
Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE.
Mathematical Sciences Publishers. https://doi.org/10.2140/APDE.2021.14.2079'
chicago: 'Leopold, Nikolai K, Simone Anna Elvira Rademacher, Benjamin Schlein, and
Robert Seiringer. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.”
Analysis and PDE. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/APDE.2021.14.2079.'
ieee: 'N. K. Leopold, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “ The Landau–Pekar
equations: Adiabatic theorem and accuracy,” Analysis and PDE, vol. 14,
no. 7. Mathematical Sciences Publishers, pp. 2079–2100, 2021.'
ista: 'Leopold NK, Rademacher SAE, Schlein B, Seiringer R. 2021. The Landau–Pekar
equations: Adiabatic theorem and accuracy. Analysis and PDE. 14(7), 2079–2100.'
mla: 'Leopold, Nikolai K., et al. “ The Landau–Pekar Equations: Adiabatic Theorem
and Accuracy.” Analysis and PDE, vol. 14, no. 7, Mathematical Sciences
Publishers, 2021, pp. 2079–100, doi:10.2140/APDE.2021.14.2079.'
short: N.K. Leopold, S.A.E. Rademacher, B. Schlein, R. Seiringer, Analysis and PDE
14 (2021) 2079–2100.
date_created: 2022-02-06T23:01:33Z
date_published: 2021-11-10T00:00:00Z
date_updated: 2023-10-17T11:26:45Z
day: '10'
department:
- _id: RoSe
doi: 10.2140/APDE.2021.14.2079
ec_funded: 1
external_id:
arxiv:
- '1904.12532'
isi:
- '000733976600004'
intvolume: ' 14'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1904.12532
month: '11'
oa: 1
oa_version: Preprint
page: 2079-2100
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Analysis and PDE
publication_identifier:
eissn:
- 1948-206X
issn:
- 2157-5045
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' The Landau–Pekar equations: Adiabatic theorem and accuracy'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2021'
...
---
_id: '10852'
abstract:
- lang: eng
text: ' We review old and new results on the Fröhlich polaron model. The discussion
includes the validity of the (classical) Pekar approximation in the strong coupling
limit, quantum corrections to this limit, as well as the divergence of the effective
polaron mass.'
acknowledgement: This work was supported by the European Research Council (ERC) under
the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo.
694227).
article_number: '2060012'
article_processing_charge: No
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
citation:
ama: Seiringer R. The polaron at strong coupling. Reviews in Mathematical Physics.
2021;33(01). doi:10.1142/s0129055x20600120
apa: Seiringer, R. (2021). The polaron at strong coupling. Reviews in Mathematical
Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600120
chicago: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical
Physics. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600120.
ieee: R. Seiringer, “The polaron at strong coupling,” Reviews in Mathematical
Physics, vol. 33, no. 01. World Scientific Publishing, 2021.
ista: Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical
Physics. 33(01), 2060012.
mla: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical
Physics, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600120.
short: R. Seiringer, Reviews in Mathematical Physics 33 (2021).
date_created: 2022-03-18T08:11:34Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-09-05T16:08:02Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600120
ec_funded: 1
external_id:
arxiv:
- '1912.12509'
isi:
- '000613313200013'
intvolume: ' 33'
isi: 1
issue: '01'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1912.12509
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: Reviews in Mathematical Physics
publication_identifier:
eissn:
- 1793-6659
issn:
- 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The polaron at strong coupling
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...
---
_id: '7900'
abstract:
- lang: eng
text: Hartree–Fock theory has been justified as a mean-field approximation for fermionic
systems. However, it suffers from some defects in predicting physical properties,
making necessary a theory of quantum correlations. Recently, bosonization of many-body
correlations has been rigorously justified as an upper bound on the correlation
energy at high density with weak interactions. We review the bosonic approximation,
deriving an effective Hamiltonian. We then show that for systems with Coulomb
interaction this effective theory predicts collective excitations (plasmons) in
accordance with the random phase approximation of Bohm and Pines, and with experimental
observation.
article_number: '2060009'
article_processing_charge: No
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
citation:
ama: Benedikter NP. Bosonic collective excitations in Fermi gases. Reviews in
Mathematical Physics. 2021;33(1). doi:10.1142/s0129055x20600090
apa: Benedikter, N. P. (2021). Bosonic collective excitations in Fermi gases. Reviews
in Mathematical Physics. World Scientific. https://doi.org/10.1142/s0129055x20600090
chicago: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews
in Mathematical Physics. World Scientific, 2021. https://doi.org/10.1142/s0129055x20600090.
ieee: N. P. Benedikter, “Bosonic collective excitations in Fermi gases,” Reviews
in Mathematical Physics, vol. 33, no. 1. World Scientific, 2021.
ista: Benedikter NP. 2021. Bosonic collective excitations in Fermi gases. Reviews
in Mathematical Physics. 33(1), 2060009.
mla: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews
in Mathematical Physics, vol. 33, no. 1, 2060009, World Scientific, 2021,
doi:10.1142/s0129055x20600090.
short: N.P. Benedikter, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-05-28T16:47:55Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-09-05T16:07:40Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600090
ec_funded: 1
external_id:
arxiv:
- '1910.08190'
isi:
- '000613313200010'
intvolume: ' 33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.08190
month: '01'
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: Reviews in Mathematical Physics
publication_identifier:
eissn:
- 1793-6659
issn:
- 0129-055X
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bosonic collective excitations in Fermi gases
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...
---
_id: '7901'
abstract:
- lang: eng
text: We derive rigorously the leading order of the correlation energy of a Fermi
gas in a scaling regime of high density and weak interaction. The result verifies
the prediction of the random-phase approximation. Our proof refines the method
of collective bosonization in three dimensions. We approximately diagonalize an
effective Hamiltonian describing approximately bosonic collective excitations
around the Hartree–Fock state, while showing that gapless and non-collective excitations
have only a negligible effect on the ground state energy.
acknowledgement: We thank Christian Hainzl for helpful discussions and a referee for
very careful reading of the paper and many helpful suggestions. NB and RS were supported
by the European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation programme (grant agreement No. 694227). Part of the research of NB
was conducted on the RZD18 Nice–Milan–Vienna–Moscow. NB thanks Elliott H. Lieb and
Peter Otte for explanations about the Luttinger model. PTN has received funding
from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under
Germany’s Excellence Strategy (EXC-2111-390814868). MP acknowledges financial support
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (ERC StG MaMBoQ, grant agreement No. 802901).
BS gratefully 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). All authors acknowledge support for
workshop participation from Mathematisches Forschungsinstitut Oberwolfach (Leibniz
Association). NB, PTN, BS, and RS acknowledge support for workshop participation
from Fondation des Treilles.
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: Phan Thành
full_name: Nam, Phan Thành
last_name: Nam
- 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, Nam PT, Porta M, Schlein B, Seiringer R. Correlation energy
of a weakly interacting Fermi gas. Inventiones Mathematicae. 2021;225:885-979.
doi:10.1007/s00222-021-01041-5
apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R.
(2021). Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae.
Springer. https://doi.org/10.1007/s00222-021-01041-5
chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas.”
Inventiones Mathematicae. Springer, 2021. https://doi.org/10.1007/s00222-021-01041-5.
ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Correlation
energy of a weakly interacting Fermi gas,” Inventiones Mathematicae, vol.
225. Springer, pp. 885–979, 2021.
ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Correlation
energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 225, 885–979.
mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi
Gas.” Inventiones Mathematicae, vol. 225, Springer, 2021, pp. 885–979,
doi:10.1007/s00222-021-01041-5.
short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Inventiones
Mathematicae 225 (2021) 885–979.
date_created: 2020-05-28T16:48:20Z
date_published: 2021-05-03T00:00:00Z
date_updated: 2023-08-21T06:30:30Z
day: '03'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00222-021-01041-5
ec_funded: 1
external_id:
arxiv:
- '2005.08933'
isi:
- '000646573600001'
file:
- access_level: open_access
checksum: f38c79dfd828cdc7f49a34b37b83d376
content_type: application/pdf
creator: dernst
date_created: 2022-05-16T12:23:40Z
date_updated: 2022-05-16T12:23:40Z
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language:
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oa: 1
oa_version: Published Version
page: 885-979
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
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: Inventiones Mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
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publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Correlation energy of a weakly interacting Fermi gas
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: 225
year: '2021'
...
---
_id: '8603'
abstract:
- lang: eng
text: We consider the Fröhlich polaron model in the strong coupling limit. It is
well‐known that to leading order the ground state energy is given by the (classical)
Pekar energy. In this work, we establish the subleading correction, describing
quantum fluctuation about the classical limit. Our proof applies to a model of
a confined polaron, where both the electron and the polarization field are restricted
to a set of finite volume, with linear size determined by the natural length scale
of the Pekar problem.
acknowledgement: Partial support through National Science Foundation GrantDMS-1363432
(R.L.F.) and the European Research Council (ERC) under the Euro-pean Union’s Horizon
2020 research and innovation programme (grant agreementNo 694227; R.S.), is acknowledged.
Open access funding enabled and organizedby Projekt DEAL.
article_processing_charge: No
article_type: original
author:
- first_name: Rupert
full_name: Frank, Rupert
last_name: Frank
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Frank R, Seiringer R. Quantum corrections to the Pekar asymptotics of a strongly
coupled polaron. Communications on Pure and Applied Mathematics. 2021;74(3):544-588.
doi:10.1002/cpa.21944
apa: Frank, R., & Seiringer, R. (2021). Quantum corrections to the Pekar asymptotics
of a strongly coupled polaron. Communications on Pure and Applied Mathematics.
Wiley. https://doi.org/10.1002/cpa.21944
chicago: Frank, Rupert, and Robert Seiringer. “Quantum Corrections to the Pekar
Asymptotics of a Strongly Coupled Polaron.” Communications on Pure and Applied
Mathematics. Wiley, 2021. https://doi.org/10.1002/cpa.21944.
ieee: R. Frank and R. Seiringer, “Quantum corrections to the Pekar asymptotics of
a strongly coupled polaron,” Communications on Pure and Applied Mathematics,
vol. 74, no. 3. Wiley, pp. 544–588, 2021.
ista: Frank R, Seiringer R. 2021. Quantum corrections to the Pekar asymptotics of
a strongly coupled polaron. Communications on Pure and Applied Mathematics. 74(3),
544–588.
mla: Frank, Rupert, and Robert Seiringer. “Quantum Corrections to the Pekar Asymptotics
of a Strongly Coupled Polaron.” Communications on Pure and Applied Mathematics,
vol. 74, no. 3, Wiley, 2021, pp. 544–88, doi:10.1002/cpa.21944.
short: R. Frank, R. Seiringer, Communications on Pure and Applied Mathematics 74
(2021) 544–588.
date_created: 2020-10-04T22:01:37Z
date_published: 2021-03-01T00:00:00Z
date_updated: 2023-08-04T11:02:16Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1002/cpa.21944
ec_funded: 1
external_id:
isi:
- '000572991500001'
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checksum: 5f665ffa6e6dd958aec5c3040cbcfa84
content_type: application/pdf
creator: dernst
date_created: 2021-03-11T10:03:30Z
date_updated: 2021-03-11T10:03:30Z
file_id: '9236'
file_name: 2021_CommPureApplMath_Frank.pdf
file_size: 334987
relation: main_file
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file_date_updated: 2021-03-11T10:03:30Z
has_accepted_license: '1'
intvolume: ' 74'
isi: 1
issue: '3'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 544-588
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications on Pure and Applied Mathematics
publication_identifier:
eissn:
- '10970312'
issn:
- '00103640'
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantum corrections to the Pekar asymptotics of a strongly coupled polaron
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: 74
year: '2021'
...
---
_id: '7685'
abstract:
- lang: eng
text: We consider a gas of interacting bosons trapped in a box of side length one
in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s
prediction for the ground state energy and the low-energy excitation spectrum.
This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.
article_number: '2060006'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
full_name: Boccato, Chiara
id: 342E7E22-F248-11E8-B48F-1D18A9856A87
last_name: Boccato
citation:
ama: Boccato C. The excitation spectrum of the Bose gas in the Gross-Pitaevskii
regime. Reviews in Mathematical Physics. 2021;33(1). doi:10.1142/S0129055X20600065
apa: Boccato, C. (2021). The excitation spectrum of the Bose gas in the Gross-Pitaevskii
regime. Reviews in Mathematical Physics. World Scientific. https://doi.org/10.1142/S0129055X20600065
chicago: Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii
Regime.” Reviews in Mathematical Physics. World Scientific, 2021. https://doi.org/10.1142/S0129055X20600065.
ieee: C. Boccato, “The excitation spectrum of the Bose gas in the Gross-Pitaevskii
regime,” Reviews in Mathematical Physics, vol. 33, no. 1. World Scientific,
2021.
ista: Boccato C. 2021. The excitation spectrum of the Bose gas in the Gross-Pitaevskii
regime. Reviews in Mathematical Physics. 33(1), 2060006.
mla: Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii
Regime.” Reviews in Mathematical Physics, vol. 33, no. 1, 2060006, World
Scientific, 2021, doi:10.1142/S0129055X20600065.
short: C. Boccato, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-04-26T22:00:45Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-04T10:50:13Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/S0129055X20600065
ec_funded: 1
external_id:
arxiv:
- '2001.00497'
isi:
- '000613313200007'
intvolume: ' 33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2001.00497
month: '01'
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: Reviews in Mathematical Physics
publication_identifier:
issn:
- 0129-055X
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2021'
...
---
_id: '14889'
abstract:
- lang: eng
text: We consider the Fröhlich Hamiltonian with large coupling constant α. For initial
data of Pekar product form with coherent phonon field and with the electron minimizing
the corresponding energy, we provide a norm approximation of the evolution, valid
up to times of order α2. The approximation is given in terms of a Pekar product
state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics
taking quantum fluctuations into account. This allows us to show that the Landau-Pekar
equations approximately describe the evolution of the electron- and one-phonon
reduced density matrices under the Fröhlich dynamics up to times of order α2.
acknowledgement: "Financial support by the European Union’s Horizon 2020 research
and innovation programme\r\nunder the Marie Skłodowska-Curie grant agreement No.
754411 (S.R.) and the European\r\nResearch Council under grant agreement No. 694227
(N.L. and R.S.), as well as by the SNSF\r\nEccellenza project PCEFP2 181153 (N.L.),
the NCCR SwissMAP (N.L. and B.S.) and by the\r\nDeutsche Forschungsgemeinschaft
(DFG) through the Research Training Group 1838: Spectral\r\nTheory and Dynamics
of Quantum Systems (D.M.) is gratefully acknowledged. B.S. gratefully\r\nacknowledges
financial support from the Swiss National Science Foundation through the Grant\r\n“Dynamical
and energetic properties of Bose-Einstein condensates” and from the European\r\nResearch
Council through the ERC-AdG CLaQS (grant agreement No 834782). D.M. thanks\r\nMarcel
Griesemer for helpful discussions."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nikolai K
full_name: Leopold, Nikolai K
id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
last_name: Leopold
orcid: 0000-0002-0495-6822
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- 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
- 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, Rademacher SAE, Schlein B, Seiringer R. Landau–Pekar
equations and quantum fluctuations for the dynamics of a strongly coupled polaron.
Pure and Applied Analysis. 2021;3(4):653-676. doi:10.2140/paa.2021.3.653
apa: Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., &
Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the
dynamics of a strongly coupled polaron. Pure and Applied Analysis. Mathematical
Sciences Publishers. https://doi.org/10.2140/paa.2021.3.653
chicago: Leopold, Nikolai K, David Johannes Mitrouskas, Simone Anna Elvira Rademacher,
Benjamin Schlein, and Robert Seiringer. “Landau–Pekar Equations and Quantum Fluctuations
for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis.
Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/paa.2021.3.653.
ieee: N. K. Leopold, D. J. Mitrouskas, S. A. E. Rademacher, B. Schlein, and R. Seiringer,
“Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly
coupled polaron,” Pure and Applied Analysis, vol. 3, no. 4. Mathematical
Sciences Publishers, pp. 653–676, 2021.
ista: Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. 2021. Landau–Pekar
equations and quantum fluctuations for the dynamics of a strongly coupled polaron.
Pure and Applied Analysis. 3(4), 653–676.
mla: Leopold, Nikolai K., et al. “Landau–Pekar Equations and Quantum Fluctuations
for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis,
vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:10.2140/paa.2021.3.653.
short: N.K. Leopold, D.J. Mitrouskas, S.A.E. Rademacher, B. Schlein, R. Seiringer,
Pure and Applied Analysis 3 (2021) 653–676.
date_created: 2024-01-28T23:01:43Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2024-02-05T10:02:45Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2021.3.653
ec_funded: 1
external_id:
arxiv:
- '2005.02098'
intvolume: ' 3'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2005.02098
month: '10'
oa: 1
oa_version: Preprint
page: 653-676
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: 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: Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly
coupled polaron
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2021'
...
---
_id: '14890'
abstract:
- lang: eng
text: We consider a system of N interacting bosons in the mean-field scaling regime
and construct corrections to the Bogoliubov dynamics that approximate the true
N-body dynamics in norm to arbitrary precision. The N-independent corrections
are given in terms of the solutions of the Bogoliubov and Hartree equations and
satisfy a generalized form of Wick's theorem. We determine the n-point correlation
functions of the excitations around the condensate, as well as the reduced densities
of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point
functions of a quasi-free state and the solution of the Hartree equation. In this
way, the complex problem of computing all n-point correlation functions for an
interacting N-body system is essentially reduced to the problem of solving the
Hartree equation and the PDEs for the Bogoliubov two-point functions.
acknowledgement: "We are grateful for the hospitality of Central China Normal University
(CCNU),\r\nwhere parts of this work were done, and thank Phan Th`anh Nam, Simone\r\nRademacher,
Robert Seiringer and Stefan Teufel for helpful discussions. L.B. gratefully acknowledges
the support by the German Research Foundation (DFG) within the Research\r\nTraining
Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and the funding\r\nfrom
the European Union’s Horizon 2020 research and innovation programme under the Marie\r\nSk
lodowska-Curie Grant Agreement No. 754411."
article_processing_charge: No
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
- 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: Peter
full_name: Pickl, Peter
last_name: Pickl
- first_name: Avy
full_name: Soffer, Avy
last_name: Soffer
citation:
ama: Bossmann L, Petrat SP, Pickl P, Soffer A. Beyond Bogoliubov dynamics. Pure
and Applied Analysis. 2021;3(4):677-726. doi:10.2140/paa.2021.3.677
apa: Bossmann, L., Petrat, S. P., Pickl, P., & Soffer, A. (2021). Beyond Bogoliubov
dynamics. Pure and Applied Analysis. Mathematical Sciences Publishers.
https://doi.org/10.2140/paa.2021.3.677
chicago: Bossmann, Lea, Sören P Petrat, Peter Pickl, and Avy Soffer. “Beyond Bogoliubov
Dynamics.” Pure and Applied Analysis. Mathematical Sciences Publishers,
2021. https://doi.org/10.2140/paa.2021.3.677.
ieee: L. Bossmann, S. P. Petrat, P. Pickl, and A. Soffer, “Beyond Bogoliubov dynamics,”
Pure and Applied Analysis, vol. 3, no. 4. Mathematical Sciences Publishers,
pp. 677–726, 2021.
ista: Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics.
Pure and Applied Analysis. 3(4), 677–726.
mla: Bossmann, Lea, et al. “Beyond Bogoliubov Dynamics.” Pure and Applied Analysis,
vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 677–726, doi:10.2140/paa.2021.3.677.
short: L. Bossmann, S.P. Petrat, P. Pickl, A. Soffer, Pure and Applied Analysis
3 (2021) 677–726.
date_created: 2024-01-28T23:01:43Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2024-02-05T09:26:31Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2021.3.677
ec_funded: 1
external_id:
arxiv:
- '1912.11004'
intvolume: ' 3'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1912.11004
month: '10'
oa: 1
oa_version: Preprint
page: 677-726
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Beyond Bogoliubov dynamics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2021'
...
---
_id: '9005'
abstract:
- lang: eng
text: Studies on the experimental realization of two-dimensional anyons in terms
of quasiparticles have been restricted, so far, to only anyons on the plane. It
is known, however, that the geometry and topology of space can have significant
effects on quantum statistics for particles moving on it. Here, we have undertaken
the first step toward realizing the emerging fractional statistics for particles
restricted to move on the sphere instead of on the plane. We show that such a
model arises naturally in the context of quantum impurity problems. In particular,
we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic
or fermionic molecules immersed in a quantum many-particle environment can coincide
with the anyonic spectrum on the sphere. This paves the way toward the experimental
realization of anyons on the sphere using molecular impurities. Furthermore, since
a change in the alignment of the molecules corresponds to the exchange of the
particles on the sphere, such a realization reveals a novel type of exclusion
principle for molecular impurities, which could also be of use as a powerful technique
to measure the statistics parameter. Finally, our approach opens up a simple numerical
route to investigate the spectra of many anyons on the sphere. Accordingly, we
present the spectrum of two anyons on the sphere in the presence of a Dirac monopole
field.
acknowledgement: "We are grateful to A. Ghazaryan for valuable discussions and also
thank the anonymous referees for comments. D.L. acknowledges financial support from
the G¨oran Gustafsson Foundation (grant no. 1804) and LMU Munich. M.L. gratefully
acknowledges financial support\r\nby the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (grant agreements
No 801770)."
article_number: '015301'
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: Mikhail
full_name: Lemeshko, Mikhail
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
- first_name: D.
full_name: Lundholm, D.
last_name: Lundholm
- first_name: Enderalp
full_name: Yakaboylu, Enderalp
id: 38CB71F6-F248-11E8-B48F-1D18A9856A87
last_name: Yakaboylu
orcid: 0000-0001-5973-0874
citation:
ama: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Molecular impurities as a realization
of anyons on the two-sphere. Physical Review Letters. 2021;126(1). doi:10.1103/PhysRevLett.126.015301
apa: Brooks, M., Lemeshko, M., Lundholm, D., & Yakaboylu, E. (2021). Molecular
impurities as a realization of anyons on the two-sphere. Physical Review Letters.
American Physical Society. https://doi.org/10.1103/PhysRevLett.126.015301
chicago: Brooks, Morris, Mikhail Lemeshko, D. Lundholm, and Enderalp Yakaboylu.
“Molecular Impurities as a Realization of Anyons on the Two-Sphere.” Physical
Review Letters. American Physical Society, 2021. https://doi.org/10.1103/PhysRevLett.126.015301.
ieee: M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Molecular impurities
as a realization of anyons on the two-sphere,” Physical Review Letters,
vol. 126, no. 1. American Physical Society, 2021.
ista: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Molecular impurities
as a realization of anyons on the two-sphere. Physical Review Letters. 126(1),
015301.
mla: Brooks, Morris, et al. “Molecular Impurities as a Realization of Anyons on
the Two-Sphere.” Physical Review Letters, vol. 126, no. 1, 015301, American
Physical Society, 2021, doi:10.1103/PhysRevLett.126.015301.
short: M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Physical Review Letters
126 (2021).
date_created: 2021-01-17T23:01:10Z
date_published: 2021-01-08T00:00:00Z
date_updated: 2023-08-07T13:32:10Z
day: '08'
department:
- _id: MiLe
- _id: RoSe
doi: 10.1103/PhysRevLett.126.015301
ec_funded: 1
external_id:
arxiv:
- '2009.05948'
isi:
- '000606325000003'
intvolume: ' 126'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2009.05948
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: 2688CF98-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '801770'
name: 'Angulon: physics and applications of a new quasiparticle'
publication: Physical Review Letters
publication_identifier:
eissn:
- '10797114'
issn:
- '00319007'
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
related_material:
link:
- description: News on IST Homepage
relation: press_release
url: https://ist.ac.at/en/news/dancing-molecules-and-two-dimensional-particles/
record:
- id: '12390'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Molecular impurities as a realization of anyons on the two-sphere
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 126
year: '2021'
...
---
_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: 2023-09-07T13:30:11Z
day: '11'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-020-01350-5
ec_funded: 1
external_id:
isi:
- '000617195700001'
file:
- access_level: open_access
checksum: ffbfe1aad623bce7ff529c207e343b53
content_type: application/pdf
creator: dernst
date_created: 2021-03-09T11:44:34Z
date_updated: 2021-03-09T11:44:34Z
file_id: '9232'
file_name: 2021_LettersMathPhysics_Feliciangeli.pdf
file_size: 391205
relation: main_file
success: 1
file_date_updated: 2021-03-09T11:44:34Z
has_accepted_license: '1'
intvolume: ' 111'
isi: 1
language:
- iso: eng
month: '02'
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
- _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:
- '15730530'
issn:
- '03779017'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '9733'
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)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 111
year: '2021'
...