---
_id: '5856'
abstract:
- lang: eng
text: We give a bound on the ground-state energy of a system of N non-interacting
fermions in a three-dimensional cubic box interacting with an impurity particle
via point interactions. We show that the change in energy compared to the system
in the absence of the impurity is bounded in terms of the gas density and the
scattering length of the interaction, independently of N. Our bound holds as long
as the ratio of the mass of the impurity to the one of the gas particles is larger
than a critical value m∗ ∗≈ 0.36 , which is the same regime for which we recently
showed stability of the system.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Thomas
full_name: Moser, Thomas
id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87
last_name: Moser
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Moser T, Seiringer R. Energy contribution of a point-interacting impurity in
a Fermi gas. Annales Henri Poincare. 2019;20(4):1325–1365. doi:10.1007/s00023-018-00757-0
apa: Moser, T., & Seiringer, R. (2019). Energy contribution of a point-interacting
impurity in a Fermi gas. Annales Henri Poincare. Springer. https://doi.org/10.1007/s00023-018-00757-0
chicago: Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting
Impurity in a Fermi Gas.” Annales Henri Poincare. Springer, 2019. https://doi.org/10.1007/s00023-018-00757-0.
ieee: T. Moser and R. Seiringer, “Energy contribution of a point-interacting impurity
in a Fermi gas,” Annales Henri Poincare, vol. 20, no. 4. Springer, pp.
1325–1365, 2019.
ista: Moser T, Seiringer R. 2019. Energy contribution of a point-interacting impurity
in a Fermi gas. Annales Henri Poincare. 20(4), 1325–1365.
mla: Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting
Impurity in a Fermi Gas.” Annales Henri Poincare, vol. 20, no. 4, Springer,
2019, pp. 1325–1365, doi:10.1007/s00023-018-00757-0.
short: T. Moser, R. Seiringer, Annales Henri Poincare 20 (2019) 1325–1365.
date_created: 2019-01-20T22:59:17Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2023-09-07T12:37:42Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00023-018-00757-0
ec_funded: 1
external_id:
arxiv:
- '1807.00739'
isi:
- '000462444300008'
file:
- access_level: open_access
checksum: 255e42f957a8e2b10aad2499c750a8d6
content_type: application/pdf
creator: dernst
date_created: 2019-01-28T15:27:17Z
date_updated: 2020-07-14T12:47:12Z
file_id: '5894'
file_name: 2019_Annales_Moser.pdf
file_size: 859846
relation: main_file
file_date_updated: 2020-07-14T12:47:12Z
has_accepted_license: '1'
intvolume: ' 20'
isi: 1
issue: '4'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 1325–1365
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Annales Henri Poincare
publication_identifier:
issn:
- '14240637'
publication_status: published
publisher: Springer
quality_controlled: '1'
related_material:
record:
- id: '52'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Energy contribution of a point-interacting impurity in a 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: 20
year: '2019'
...
---
_id: '295'
abstract:
- lang: eng
text: We prove upper and lower bounds on the ground-state energy of the ideal two-dimensional
anyon gas. Our bounds are extensive in the particle number, as for fermions, and
linear in the statistics parameter (Formula presented.). The lower bounds extend
to Lieb–Thirring inequalities for all anyons except bosons.
acknowledgement: Financial support from the Swedish Research Council, grant no. 2013-4734
(D. L.), the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (grant agreement No 694227, R. S.), and by
the Austrian Science Fund (FWF), project Nr. P 27533-N27 (R. S.), is gratefully
acknowledged.
article_processing_charge: No
arxiv: 1
author:
- first_name: Douglas
full_name: Lundholm, Douglas
last_name: Lundholm
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Lundholm D, Seiringer R. Fermionic behavior of ideal anyons. Letters in
Mathematical Physics. 2018;108(11):2523-2541. doi:10.1007/s11005-018-1091-y
apa: Lundholm, D., & Seiringer, R. (2018). Fermionic behavior of ideal anyons.
Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-018-1091-y
chicago: Lundholm, Douglas, and Robert Seiringer. “Fermionic Behavior of Ideal Anyons.”
Letters in Mathematical Physics. Springer, 2018. https://doi.org/10.1007/s11005-018-1091-y.
ieee: D. Lundholm and R. Seiringer, “Fermionic behavior of ideal anyons,” Letters
in Mathematical Physics, vol. 108, no. 11. Springer, pp. 2523–2541, 2018.
ista: Lundholm D, Seiringer R. 2018. Fermionic behavior of ideal anyons. Letters
in Mathematical Physics. 108(11), 2523–2541.
mla: Lundholm, Douglas, and Robert Seiringer. “Fermionic Behavior of Ideal Anyons.”
Letters in Mathematical Physics, vol. 108, no. 11, Springer, 2018, pp.
2523–41, doi:10.1007/s11005-018-1091-y.
short: D. Lundholm, R. Seiringer, Letters in Mathematical Physics 108 (2018) 2523–2541.
date_created: 2018-12-11T11:45:40Z
date_published: 2018-05-11T00:00:00Z
date_updated: 2023-09-11T14:01:57Z
day: '11'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-018-1091-y
ec_funded: 1
external_id:
arxiv:
- '1712.06218'
isi:
- '000446491500008'
file:
- access_level: open_access
checksum: 8beb9632fa41bbd19452f55f31286a31
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T12:14:17Z
date_updated: 2020-07-14T12:45:55Z
file_id: '5698'
file_name: 2018_LettMathPhys_Lundholm.pdf
file_size: 551996
relation: main_file
file_date_updated: 2020-07-14T12:45:55Z
has_accepted_license: '1'
intvolume: ' 108'
isi: 1
issue: '11'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 2523-2541
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '7586'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fermionic behavior of ideal anyons
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: 108
year: '2018'
...
---
_id: '11'
abstract:
- lang: eng
text: We report on a novel strategy to derive mean-field limits of quantum mechanical
systems in which a large number of particles weakly couple to a second-quantized
radiation field. The technique combines the method of counting and the coherent
state approach to study the growth of the correlations among the particles and
in the radiation field. As an instructional example, we derive the Schrödinger–Klein–Gordon
system of equations from the Nelson model with ultraviolet cutoff and possibly
massless scalar field. In particular, we prove the convergence of the reduced
density matrices (of the nonrelativistic particles and the field bosons) associated
with the exact time evolution to the projectors onto the solutions of the Schrödinger–Klein–Gordon
equations in trace norm. Furthermore, we derive explicit bounds on the rate of
convergence of the one-particle reduced density matrix of the nonrelativistic
particles in Sobolev norm.
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: Peter
full_name: Pickl, Peter
last_name: Pickl
citation:
ama: 'Leopold NK, Pickl P. Mean-field limits of particles in interaction with quantised
radiation fields. In: Vol 270. Springer; 2018:185-214. doi:10.1007/978-3-030-01602-9_9'
apa: 'Leopold, N. K., & Pickl, P. (2018). Mean-field limits of particles in
interaction with quantised radiation fields (Vol. 270, pp. 185–214). Presented
at the MaLiQS: Macroscopic Limits of Quantum Systems, Munich, Germany: Springer.
https://doi.org/10.1007/978-3-030-01602-9_9'
chicago: Leopold, Nikolai K, and Peter Pickl. “Mean-Field Limits of Particles in
Interaction with Quantised Radiation Fields,” 270:185–214. Springer, 2018. https://doi.org/10.1007/978-3-030-01602-9_9.
ieee: 'N. K. Leopold and P. Pickl, “Mean-field limits of particles in interaction
with quantised radiation fields,” presented at the MaLiQS: Macroscopic Limits
of Quantum Systems, Munich, Germany, 2018, vol. 270, pp. 185–214.'
ista: 'Leopold NK, Pickl P. 2018. Mean-field limits of particles in interaction
with quantised radiation fields. MaLiQS: Macroscopic Limits of Quantum Systems
vol. 270, 185–214.'
mla: Leopold, Nikolai K., and Peter Pickl. Mean-Field Limits of Particles in
Interaction with Quantised Radiation Fields. Vol. 270, Springer, 2018, pp.
185–214, doi:10.1007/978-3-030-01602-9_9.
short: N.K. Leopold, P. Pickl, in:, Springer, 2018, pp. 185–214.
conference:
end_date: 2017-04-01
location: Munich, Germany
name: 'MaLiQS: Macroscopic Limits of Quantum Systems'
start_date: 2017-03-30
date_created: 2018-12-11T11:44:08Z
date_published: 2018-10-27T00:00:00Z
date_updated: 2021-01-12T06:48:16Z
day: '27'
department:
- _id: RoSe
doi: 10.1007/978-3-030-01602-9_9
ec_funded: 1
external_id:
arxiv:
- '1806.10843'
intvolume: ' 270'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1806.10843
month: '10'
oa: 1
oa_version: Preprint
page: 185 - 214
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication_status: published
publisher: Springer
publist_id: '8045'
quality_controlled: '1'
scopus_import: 1
status: public
title: Mean-field limits of particles in interaction with quantised radiation fields
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 270
year: '2018'
...
---
_id: '180'
abstract:
- lang: eng
text: In this paper we define and study the classical Uniform Electron Gas (UEG),
a system of infinitely many electrons whose density is constant everywhere in
space. The UEG is defined differently from Jellium, which has a positive constant
background but no constraint on the density. We prove that the UEG arises in Density
Functional Theory in the limit of a slowly varying density, minimizing the indirect
Coulomb energy. We also construct the quantum UEG and compare it to the classical
UEG at low density.
acknowledgement: "This project has received funding from the European Research Council
(ERC) under the European\r\nUnion’s Horizon 2020 research and innovation programme
(grant agreement 694227 for R.S. and MDFT 725528 for M.L.). Financial support by
the Austrian Science Fund (FWF), project No P 27533-N27 (R.S.) and by the US National
Science Foundation, grant No PHY12-1265118 (E.H.L.) are gratefully acknowledged."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
full_name: Lewi, Mathieu
last_name: Lewi
- first_name: Élliott
full_name: Lieb, Élliott
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: Lewi M, Lieb É, Seiringer R. Statistical mechanics of the uniform electron
gas. Journal de l’Ecole Polytechnique - Mathematiques. 2018;5:79-116. doi:10.5802/jep.64
apa: Lewi, M., Lieb, É., & Seiringer, R. (2018). Statistical mechanics of the
uniform electron gas. Journal de l’Ecole Polytechnique - Mathematiques.
Ecole Polytechnique. https://doi.org/10.5802/jep.64
chicago: Lewi, Mathieu, Élliott Lieb, and Robert Seiringer. “Statistical Mechanics
of the Uniform Electron Gas.” Journal de l’Ecole Polytechnique - Mathematiques.
Ecole Polytechnique, 2018. https://doi.org/10.5802/jep.64.
ieee: M. Lewi, É. Lieb, and R. Seiringer, “Statistical mechanics of the uniform
electron gas,” Journal de l’Ecole Polytechnique - Mathematiques, vol. 5.
Ecole Polytechnique, pp. 79–116, 2018.
ista: Lewi M, Lieb É, Seiringer R. 2018. Statistical mechanics of the uniform electron
gas. Journal de l’Ecole Polytechnique - Mathematiques. 5, 79–116.
mla: Lewi, Mathieu, et al. “Statistical Mechanics of the Uniform Electron Gas.”
Journal de l’Ecole Polytechnique - Mathematiques, vol. 5, Ecole Polytechnique,
2018, pp. 79–116, doi:10.5802/jep.64.
short: M. Lewi, É. Lieb, R. Seiringer, Journal de l’Ecole Polytechnique - Mathematiques
5 (2018) 79–116.
date_created: 2018-12-11T11:45:03Z
date_published: 2018-07-01T00:00:00Z
date_updated: 2023-10-17T08:05:28Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.5802/jep.64
ec_funded: 1
external_id:
arxiv:
- '1705.10676'
file:
- access_level: open_access
checksum: 1ba7cccdf3900f42c4f715ae75d6813c
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T16:38:18Z
date_updated: 2020-07-14T12:45:16Z
file_id: '5726'
file_name: 2018_JournaldeLecoleMath_Lewi.pdf
file_size: 843938
relation: main_file
file_date_updated: 2020-07-14T12:45:16Z
has_accepted_license: '1'
intvolume: ' 5'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 79 - 116
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Journal de l'Ecole Polytechnique - Mathematiques
publication_identifier:
eissn:
- 2270-518X
issn:
- 2429-7100
publication_status: published
publisher: Ecole Polytechnique
publist_id: '7741'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Statistical mechanics of the uniform electron gas
tmp:
image: /image/cc_by_nd.png
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)
short: CC BY-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2018'
...
---
_id: '52'
abstract:
- lang: eng
text: In this thesis we will discuss systems of point interacting fermions, their
stability and other spectral properties. Whereas for bosons a point interacting
system is always unstable this ques- tion is more subtle for a gas of two species
of fermions. In particular the answer depends on the mass ratio between these
two species. Most of this work will be focused on the N + M model which consists
of two species of fermions with N, M particles respectively which interact via
point interactions. We will introduce this model using a formal limit and discuss
the N + 1 system in more detail. In particular, we will show that for mass ratios
above a critical one, which does not depend on the particle number, the N + 1
system is stable. In the context of this model we will prove rigorous versions
of Tan relations which relate various quantities of the point-interacting model.
By restricting the N + 1 system to a box we define a finite density model with
point in- teractions. In the context of this system we will discuss the energy
change when introducing a point-interacting impurity into a system of non-interacting
fermions. We will see that this change in energy is bounded independently of the
particle number and in particular the bound only depends on the density and the
scattering length. As another special case of the N + M model we will show stability
of the 2 + 2 model for mass ratios in an interval around one. Further we will
investigate a different model of point interactions which was discussed before
in the literature and which is, contrary to the N + M model, not given by a limiting
procedure but is based on a Dirichlet form. We will show that this system behaves
trivially in the thermodynamic limit, i.e. the free energy per particle is the
same as the one of the non-interacting system.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Thomas
full_name: Moser, Thomas
id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87
last_name: Moser
citation:
ama: Moser T. Point interactions in systems of fermions. 2018. doi:10.15479/AT:ISTA:th_1043
apa: Moser, T. (2018). Point interactions in systems of fermions. Institute
of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1043
chicago: Moser, Thomas. “Point Interactions in Systems of Fermions.” Institute of
Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1043.
ieee: T. Moser, “Point interactions in systems of fermions,” Institute of Science
and Technology Austria, 2018.
ista: Moser T. 2018. Point interactions in systems of fermions. Institute of Science
and Technology Austria.
mla: Moser, Thomas. Point Interactions in Systems of Fermions. Institute
of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1043.
short: T. Moser, Point Interactions in Systems of Fermions, Institute of Science
and Technology Austria, 2018.
date_created: 2018-12-11T11:44:22Z
date_published: 2018-09-04T00:00:00Z
date_updated: 2023-09-27T12:34:14Z
day: '04'
ddc:
- '515'
- '530'
- '519'
degree_awarded: PhD
department:
- _id: RoSe
doi: 10.15479/AT:ISTA:th_1043
file:
- access_level: open_access
checksum: fbd8c747d148b468a21213b7cf175225
content_type: application/pdf
creator: dernst
date_created: 2019-04-09T07:45:38Z
date_updated: 2020-07-14T12:46:37Z
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file_name: 2018_Thesis_Moser.pdf
file_size: 851164
relation: main_file
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checksum: c28e16ecfc1126d3ce324ec96493c01e
content_type: application/zip
creator: dernst
date_created: 2019-04-09T07:45:38Z
date_updated: 2020-07-14T12:46:37Z
file_id: '6257'
file_name: 2018_Thesis_Moser_Source.zip
file_size: 1531516
relation: source_file
file_date_updated: 2020-07-14T12:46:37Z
has_accepted_license: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: '115'
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '8002'
pubrep_id: '1043'
related_material:
record:
- id: '5856'
relation: part_of_dissertation
status: public
- id: '154'
relation: part_of_dissertation
status: public
- id: '1198'
relation: part_of_dissertation
status: public
- id: '741'
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: Point interactions in systems of fermions
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...
---
_id: '554'
abstract:
- lang: eng
text: We analyse the canonical Bogoliubov free energy functional in three dimensions
at low temperatures in the dilute limit. We prove existence of a first-order phase
transition and, in the limit (Formula presented.), we determine the critical temperature
to be (Formula presented.) to leading order. Here, (Formula presented.) is the
critical temperature of the free Bose gas, ρ is the density of the gas and a is
the scattering length of the pair-interaction potential V. We also prove asymptotic
expansions for the free energy. In particular, we recover the Lee–Huang–Yang formula
in the limit (Formula presented.).
arxiv: 1
author:
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
- first_name: Robin
full_name: Reuvers, Robin
last_name: Reuvers
- first_name: Jan
full_name: Solovej, Jan
last_name: Solovej
citation:
ama: 'Napiórkowski MM, Reuvers R, Solovej J. The Bogoliubov free energy functional
II: The dilute Limit. Communications in Mathematical Physics. 2018;360(1):347-403.
doi:10.1007/s00220-017-3064-x'
apa: 'Napiórkowski, M. M., Reuvers, R., & Solovej, J. (2018). The Bogoliubov
free energy functional II: The dilute Limit. Communications in Mathematical
Physics. Springer. https://doi.org/10.1007/s00220-017-3064-x'
chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “The Bogoliubov
Free Energy Functional II: The Dilute Limit.” Communications in Mathematical
Physics. Springer, 2018. https://doi.org/10.1007/s00220-017-3064-x.'
ieee: 'M. M. Napiórkowski, R. Reuvers, and J. Solovej, “The Bogoliubov free energy
functional II: The dilute Limit,” Communications in Mathematical Physics,
vol. 360, no. 1. Springer, pp. 347–403, 2018.'
ista: 'Napiórkowski MM, Reuvers R, Solovej J. 2018. The Bogoliubov free energy functional
II: The dilute Limit. Communications in Mathematical Physics. 360(1), 347–403.'
mla: 'Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional II:
The Dilute Limit.” Communications in Mathematical Physics, vol. 360, no.
1, Springer, 2018, pp. 347–403, doi:10.1007/s00220-017-3064-x.'
short: M.M. Napiórkowski, R. Reuvers, J. Solovej, Communications in Mathematical
Physics 360 (2018) 347–403.
date_created: 2018-12-11T11:47:09Z
date_published: 2018-05-01T00:00:00Z
date_updated: 2021-01-12T08:02:35Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00220-017-3064-x
external_id:
arxiv:
- '1511.05953'
intvolume: ' 360'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1511.05953
month: '05'
oa: 1
oa_version: Submitted Version
page: 347-403
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- '00103616'
publication_status: published
publisher: Springer
publist_id: '7260'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'The Bogoliubov free energy functional II: The dilute Limit'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 360
year: '2018'
...
---
_id: '5983'
abstract:
- lang: eng
text: We study a quantum impurity possessing both translational and internal rotational
degrees of freedom interacting with a bosonic bath. Such a system corresponds
to a “rotating polaron,” which can be used to model, e.g., a rotating molecule
immersed in an ultracold Bose gas or superfluid helium. We derive the Hamiltonian
of the rotating polaron and study its spectrum in the weak- and strong-coupling
regimes using a combination of variational, diagrammatic, and mean-field approaches.
We reveal how the coupling between linear and angular momenta affects stable quasiparticle
states, and demonstrate that internal rotation leads to an enhanced self-localization
in the translational degrees of freedom.
article_number: '224506'
article_processing_charge: No
arxiv: 1
author:
- first_name: Enderalp
full_name: Yakaboylu, Enderalp
id: 38CB71F6-F248-11E8-B48F-1D18A9856A87
last_name: Yakaboylu
orcid: 0000-0001-5973-0874
- first_name: Bikashkali
full_name: Midya, Bikashkali
id: 456187FC-F248-11E8-B48F-1D18A9856A87
last_name: Midya
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- 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: Mikhail
full_name: Lemeshko, Mikhail
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
citation:
ama: 'Yakaboylu E, Midya B, Deuchert A, Leopold NK, Lemeshko M. Theory of the rotating
polaron: Spectrum and self-localization. Physical Review B. 2018;98(22).
doi:10.1103/physrevb.98.224506'
apa: 'Yakaboylu, E., Midya, B., Deuchert, A., Leopold, N. K., & Lemeshko, M.
(2018). Theory of the rotating polaron: Spectrum and self-localization. Physical
Review B. American Physical Society. https://doi.org/10.1103/physrevb.98.224506'
chicago: 'Yakaboylu, Enderalp, Bikashkali Midya, Andreas Deuchert, Nikolai K Leopold,
and Mikhail Lemeshko. “Theory of the Rotating Polaron: Spectrum and Self-Localization.”
Physical Review B. American Physical Society, 2018. https://doi.org/10.1103/physrevb.98.224506.'
ieee: 'E. Yakaboylu, B. Midya, A. Deuchert, N. K. Leopold, and M. Lemeshko, “Theory
of the rotating polaron: Spectrum and self-localization,” Physical Review B,
vol. 98, no. 22. American Physical Society, 2018.'
ista: 'Yakaboylu E, Midya B, Deuchert A, Leopold NK, Lemeshko M. 2018. Theory of
the rotating polaron: Spectrum and self-localization. Physical Review B. 98(22),
224506.'
mla: 'Yakaboylu, Enderalp, et al. “Theory of the Rotating Polaron: Spectrum and
Self-Localization.” Physical Review B, vol. 98, no. 22, 224506, American
Physical Society, 2018, doi:10.1103/physrevb.98.224506.'
short: E. Yakaboylu, B. Midya, A. Deuchert, N.K. Leopold, M. Lemeshko, Physical
Review B 98 (2018).
date_created: 2019-02-14T10:37:09Z
date_published: 2018-12-12T00:00:00Z
date_updated: 2023-09-19T14:29:03Z
day: '12'
department:
- _id: MiLe
- _id: RoSe
doi: 10.1103/physrevb.98.224506
ec_funded: 1
external_id:
arxiv:
- '1809.01204'
isi:
- '000452992700008'
intvolume: ' 98'
isi: 1
issue: '22'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1809.01204
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Physical Review B
publication_identifier:
eissn:
- 2469-9969
issn:
- 2469-9950
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Theory of the rotating polaron: Spectrum and self-localization'
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 98
year: '2018'
...
---
_id: '6002'
abstract:
- lang: eng
text: The Bogoliubov free energy functional is analysed. The functional serves as
a model of a translation-invariant Bose gas at positive temperature. We prove
the existence of minimizers in the case of repulsive interactions given by a sufficiently
regular two-body potential. Furthermore, we prove the existence of a phase transition
in this model and provide its phase diagram.
article_processing_charge: No
arxiv: 1
author:
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
- first_name: Robin
full_name: Reuvers, Robin
last_name: Reuvers
- first_name: Jan Philip
full_name: Solovej, Jan Philip
last_name: Solovej
citation:
ama: 'Napiórkowski MM, Reuvers R, Solovej JP. The Bogoliubov free energy functional
I: Existence of minimizers and phase diagram. Archive for Rational Mechanics
and Analysis. 2018;229(3):1037-1090. doi:10.1007/s00205-018-1232-6'
apa: 'Napiórkowski, M. M., Reuvers, R., & Solovej, J. P. (2018). The Bogoliubov
free energy functional I: Existence of minimizers and phase diagram. Archive
for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-018-1232-6'
chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Philip Solovej. “The Bogoliubov
Free Energy Functional I: Existence of Minimizers and Phase Diagram.” Archive
for Rational Mechanics and Analysis. Springer Nature, 2018. https://doi.org/10.1007/s00205-018-1232-6.'
ieee: 'M. M. Napiórkowski, R. Reuvers, and J. P. Solovej, “The Bogoliubov free energy
functional I: Existence of minimizers and phase diagram,” Archive for Rational
Mechanics and Analysis, vol. 229, no. 3. Springer Nature, pp. 1037–1090, 2018.'
ista: 'Napiórkowski MM, Reuvers R, Solovej JP. 2018. The Bogoliubov free energy
functional I: Existence of minimizers and phase diagram. Archive for Rational
Mechanics and Analysis. 229(3), 1037–1090.'
mla: 'Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional I:
Existence of Minimizers and Phase Diagram.” Archive for Rational Mechanics
and Analysis, vol. 229, no. 3, Springer Nature, 2018, pp. 1037–90, doi:10.1007/s00205-018-1232-6.'
short: M.M. Napiórkowski, R. Reuvers, J.P. Solovej, Archive for Rational Mechanics
and Analysis 229 (2018) 1037–1090.
date_created: 2019-02-14T13:40:53Z
date_published: 2018-09-01T00:00:00Z
date_updated: 2023-09-19T14:33:12Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00205-018-1232-6
external_id:
arxiv:
- '1511.05935'
isi:
- '000435367300003'
intvolume: ' 229'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1511.05935
month: '09'
oa: 1
oa_version: Preprint
page: 1037-1090
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The Bogoliubov free energy functional I: Existence of minimizers and phase
diagram'
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 229
year: '2018'
...
---
_id: '154'
abstract:
- lang: eng
text: We give a lower bound on the ground state energy of a system of two fermions
of one species interacting with two fermions of another species via point interactions.
We show that there is a critical mass ratio m2 ≈ 0.58 such that the system is
stable, i.e., the energy is bounded from below, for m∈[m2,m2−1]. So far it was
not known whether this 2 + 2 system exhibits a stable region at all or whether
the formation of four-body bound states causes an unbounded spectrum for all mass
ratios, similar to the Thomas effect. Our result gives further evidence for the
stability of the more general N + M system.
acknowledgement: Open access funding provided by Austrian Science Fund (FWF).
article_number: '19'
article_processing_charge: No
article_type: original
author:
- first_name: Thomas
full_name: Moser, Thomas
id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87
last_name: Moser
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Moser T, Seiringer R. Stability of the 2+2 fermionic system with point interactions.
Mathematical Physics Analysis and Geometry. 2018;21(3). doi:10.1007/s11040-018-9275-3
apa: Moser, T., & Seiringer, R. (2018). Stability of the 2+2 fermionic system
with point interactions. Mathematical Physics Analysis and Geometry. Springer.
https://doi.org/10.1007/s11040-018-9275-3
chicago: Moser, Thomas, and Robert Seiringer. “Stability of the 2+2 Fermionic System
with Point Interactions.” Mathematical Physics Analysis and Geometry. Springer,
2018. https://doi.org/10.1007/s11040-018-9275-3.
ieee: T. Moser and R. Seiringer, “Stability of the 2+2 fermionic system with point
interactions,” Mathematical Physics Analysis and Geometry, vol. 21, no.
3. Springer, 2018.
ista: Moser T, Seiringer R. 2018. Stability of the 2+2 fermionic system with point
interactions. Mathematical Physics Analysis and Geometry. 21(3), 19.
mla: Moser, Thomas, and Robert Seiringer. “Stability of the 2+2 Fermionic System
with Point Interactions.” Mathematical Physics Analysis and Geometry, vol.
21, no. 3, 19, Springer, 2018, doi:10.1007/s11040-018-9275-3.
short: T. Moser, R. Seiringer, Mathematical Physics Analysis and Geometry 21 (2018).
date_created: 2018-12-11T11:44:55Z
date_published: 2018-09-01T00:00:00Z
date_updated: 2023-09-19T09:31:15Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s11040-018-9275-3
ec_funded: 1
external_id:
isi:
- '000439639700001'
file:
- access_level: open_access
checksum: 411c4db5700d7297c9cd8ebc5dd29091
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T16:49:02Z
date_updated: 2020-07-14T12:45:01Z
file_id: '5729'
file_name: 2018_MathPhysics_Moser.pdf
file_size: 496973
relation: main_file
file_date_updated: 2020-07-14T12:45:01Z
has_accepted_license: '1'
intvolume: ' 21'
isi: 1
issue: '3'
language:
- iso: eng
month: '09'
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: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
- _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1
call_identifier: FWF
name: FWF Open Access Fund
publication: Mathematical Physics Analysis and Geometry
publication_identifier:
eissn:
- '15729656'
issn:
- '13850172'
publication_status: published
publisher: Springer
publist_id: '7767'
quality_controlled: '1'
related_material:
record:
- id: '52'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Stability of the 2+2 fermionic system with point 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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 21
year: '2018'
...
---
_id: '399'
abstract:
- lang: eng
text: Following an earlier calculation in 3D, we calculate the 2D critical temperature
of a dilute, translation-invariant Bose gas using a variational formulation of
the Bogoliubov approximation introduced by Critchley and Solomon in 1976. This
provides the first analytical calculation of the Kosterlitz-Thouless transition
temperature that includes the constant in the logarithm.
acknowledgement: We thank Robert Seiringer and Daniel Ueltschi for bringing the issue
of the change in critical temperature to our attention. We also thank the Erwin
Schrödinger Institute (all authors) and the Department of Mathematics, University
of Copenhagen (MN) for the hospitality during the period this work was carried out.
We gratefully acknowledge the financial support by the European Unions Seventh Framework
Programme under the ERC Grant Agreement Nos. 321029 (JPS and RR) and 337603 (RR)
as well as support by the VIL-LUM FONDEN via the QMATH Centre of Excellence (Grant
No. 10059) (JPS and RR), by the National Science Center (NCN) under grant No. 2016/21/D/ST1/02430
and the Austrian Science Fund (FWF) through project No. P 27533-N27 (MN).
article_number: '10007'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
- first_name: Robin
full_name: Reuvers, Robin
last_name: Reuvers
- first_name: Jan
full_name: Solovej, Jan
last_name: Solovej
citation:
ama: Napiórkowski MM, Reuvers R, Solovej J. Calculation of the critical temperature
of a dilute Bose gas in the Bogoliubov approximation. EPL. 2018;121(1).
doi:10.1209/0295-5075/121/10007
apa: Napiórkowski, M. M., Reuvers, R., & Solovej, J. (2018). Calculation of
the critical temperature of a dilute Bose gas in the Bogoliubov approximation.
EPL. IOP Publishing Ltd. https://doi.org/10.1209/0295-5075/121/10007
chicago: Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “Calculation of
the Critical Temperature of a Dilute Bose Gas in the Bogoliubov Approximation.”
EPL. IOP Publishing Ltd., 2018. https://doi.org/10.1209/0295-5075/121/10007.
ieee: M. M. Napiórkowski, R. Reuvers, and J. Solovej, “Calculation of the critical
temperature of a dilute Bose gas in the Bogoliubov approximation,” EPL,
vol. 121, no. 1. IOP Publishing Ltd., 2018.
ista: Napiórkowski MM, Reuvers R, Solovej J. 2018. Calculation of the critical temperature
of a dilute Bose gas in the Bogoliubov approximation. EPL. 121(1), 10007.
mla: Napiórkowski, Marcin M., et al. “Calculation of the Critical Temperature of
a Dilute Bose Gas in the Bogoliubov Approximation.” EPL, vol. 121, no.
1, 10007, IOP Publishing Ltd., 2018, doi:10.1209/0295-5075/121/10007.
short: M.M. Napiórkowski, R. Reuvers, J. Solovej, EPL 121 (2018).
date_created: 2018-12-11T11:46:15Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2023-09-08T13:30:51Z
day: '01'
department:
- _id: RoSe
doi: 10.1209/0295-5075/121/10007
external_id:
arxiv:
- '1706.01822'
isi:
- '000460003000003'
intvolume: ' 121'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1706.01822
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: EPL
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '7432'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov
approximation
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 121
year: '2018'
...
---
_id: '400'
abstract:
- lang: eng
text: We consider the two-dimensional BCS functional with a radial pair interaction.
We show that the translational symmetry is not broken in a certain temperature
interval below the critical temperature. In the case of vanishing angular momentum,
our results carry over to the three-dimensional case.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- first_name: Alissa
full_name: Geisinge, Alissa
last_name: Geisinge
- first_name: Christian
full_name: Hainzl, Christian
last_name: Hainzl
- first_name: Michael
full_name: Loss, Michael
last_name: Loss
citation:
ama: Deuchert A, Geisinge A, Hainzl C, Loss M. Persistence of translational symmetry
in the BCS model with radial pair interaction. Annales Henri Poincare.
2018;19(5):1507-1527. doi:10.1007/s00023-018-0665-7
apa: Deuchert, A., Geisinge, A., Hainzl, C., & Loss, M. (2018). Persistence
of translational symmetry in the BCS model with radial pair interaction. Annales
Henri Poincare. Springer. https://doi.org/10.1007/s00023-018-0665-7
chicago: Deuchert, Andreas, Alissa Geisinge, Christian Hainzl, and Michael Loss.
“Persistence of Translational Symmetry in the BCS Model with Radial Pair Interaction.”
Annales Henri Poincare. Springer, 2018. https://doi.org/10.1007/s00023-018-0665-7.
ieee: A. Deuchert, A. Geisinge, C. Hainzl, and M. Loss, “Persistence of translational
symmetry in the BCS model with radial pair interaction,” Annales Henri Poincare,
vol. 19, no. 5. Springer, pp. 1507–1527, 2018.
ista: Deuchert A, Geisinge A, Hainzl C, Loss M. 2018. Persistence of translational
symmetry in the BCS model with radial pair interaction. Annales Henri Poincare.
19(5), 1507–1527.
mla: Deuchert, Andreas, et al. “Persistence of Translational Symmetry in the BCS
Model with Radial Pair Interaction.” Annales Henri Poincare, vol. 19, no.
5, Springer, 2018, pp. 1507–27, doi:10.1007/s00023-018-0665-7.
short: A. Deuchert, A. Geisinge, C. Hainzl, M. Loss, Annales Henri Poincare 19 (2018)
1507–1527.
date_created: 2018-12-11T11:46:15Z
date_published: 2018-05-01T00:00:00Z
date_updated: 2023-09-15T12:04:15Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00023-018-0665-7
ec_funded: 1
external_id:
isi:
- '000429799900008'
file:
- access_level: open_access
checksum: 04d2c9bd7cbf3ca1d7acaaf4e7dca3e5
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:47Z
date_updated: 2020-07-14T12:46:22Z
file_id: '4966'
file_name: IST-2018-1011-v1+1_2018_Deuchert_Persistence.pdf
file_size: 582680
relation: main_file
file_date_updated: 2020-07-14T12:46:22Z
has_accepted_license: '1'
intvolume: ' 19'
isi: 1
issue: '5'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1507 - 1527
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Annales Henri Poincare
publication_status: published
publisher: Springer
publist_id: '7429'
pubrep_id: '1011'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Persistence of translational symmetry in the BCS model with radial pair interaction
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: 19
year: '2018'
...
---
_id: '446'
abstract:
- lang: eng
text: We prove that in Thomas–Fermi–Dirac–von Weizsäcker theory, a nucleus of charge
Z > 0 can bind at most Z + C electrons, where C is a universal constant. This
result is obtained through a comparison with Thomas-Fermi theory which, as a by-product,
gives bounds on the screened nuclear potential and the radius of the minimizer.
A key ingredient of the proof is a novel technique to control the particles in
the exterior region, which also applies to the liquid drop model with a nuclear
background potential.
acknowledgement: "We thank the referee for helpful suggestions that improved the presentation
of the paper. We also acknowledge partial support by National Science Foundation
Grant DMS-1363432 (R.L.F.), Austrian Science Fund (FWF) Project Nr. P 27533-N27
(P.T.N.), CONICYT (Chile) through CONICYT–PCHA/ Doctorado Nacional/2014, and Iniciativa
Científica Milenio (Chile) through Millenium Nucleus RC–120002 “Física Matemática”
(H.V.D.B.).\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rupert
full_name: Frank, Rupert
last_name: Frank
- first_name: Nam
full_name: Phan Thanh, Nam
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Phan Thanh
- first_name: Hanne
full_name: Van Den Bosch, Hanne
last_name: Van Den Bosch
citation:
ama: Frank R, Nam P, Van Den Bosch H. The ionization conjecture in Thomas–Fermi–Dirac–von
Weizsäcker theory. Communications on Pure and Applied Mathematics. 2018;71(3):577-614.
doi:10.1002/cpa.21717
apa: Frank, R., Nam, P., & Van Den Bosch, H. (2018). The ionization conjecture
in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied
Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21717
chicago: Frank, Rupert, Phan Nam, and Hanne Van Den Bosch. “The Ionization Conjecture
in Thomas–Fermi–Dirac–von Weizsäcker Theory.” Communications on Pure and Applied
Mathematics. Wiley-Blackwell, 2018. https://doi.org/10.1002/cpa.21717.
ieee: R. Frank, P. Nam, and H. Van Den Bosch, “The ionization conjecture in Thomas–Fermi–Dirac–von
Weizsäcker theory,” Communications on Pure and Applied Mathematics, vol.
71, no. 3. Wiley-Blackwell, pp. 577–614, 2018.
ista: Frank R, Nam P, Van Den Bosch H. 2018. The ionization conjecture in Thomas–Fermi–Dirac–von
Weizsäcker theory. Communications on Pure and Applied Mathematics. 71(3), 577–614.
mla: Frank, Rupert, et al. “The Ionization Conjecture in Thomas–Fermi–Dirac–von
Weizsäcker Theory.” Communications on Pure and Applied Mathematics, vol.
71, no. 3, Wiley-Blackwell, 2018, pp. 577–614, doi:10.1002/cpa.21717.
short: R. Frank, P. Nam, H. Van Den Bosch, Communications on Pure and Applied Mathematics
71 (2018) 577–614.
date_created: 2018-12-11T11:46:31Z
date_published: 2018-03-01T00:00:00Z
date_updated: 2023-09-19T10:09:40Z
day: '01'
department:
- _id: RoSe
doi: 10.1002/cpa.21717
external_id:
arxiv:
- '1606.07355'
isi:
- '000422675800004'
intvolume: ' 71'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1606.07355
month: '03'
oa: 1
oa_version: Preprint
page: 577 - 614
publication: Communications on Pure and Applied Mathematics
publication_status: published
publisher: Wiley-Blackwell
publist_id: '7377'
quality_controlled: '1'
status: public
title: The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 71
year: '2018'
...
---
_id: '455'
abstract:
- lang: eng
text: The derivation of effective evolution equations is central to the study of
non-stationary quantum many-body systems, and widely used in contexts such as
superconductivity, nuclear physics, Bose–Einstein condensation and quantum chemistry.
We reformulate the Dirac–Frenkel approximation principle in terms of reduced density
matrices and apply it to fermionic and bosonic many-body systems. We obtain the
Bogoliubov–de Gennes and Hartree–Fock–Bogoliubov equations, respectively. While
we do not prove quantitative error estimates, our formulation does show that the
approximation is optimal within the class of quasifree states. Furthermore, we
prove well-posedness of the Bogoliubov–de Gennes equations in energy space and
discuss conserved quantities
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). The authors acknowledge support by ERC Advanced Grant 321029 and
by VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059). The authors
would like to thank Sébastien Breteaux, Enno Lenzmann, Mathieu Lewin and Jochen
Schmid for comments and discussions about well-posedness of the Bogoliubov–de Gennes
equations.
alternative_title:
- Annales Henri Poincare
article_processing_charge: No
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: Jérémy
full_name: Sok, Jérémy
last_name: Sok
- first_name: Jan
full_name: Solovej, Jan
last_name: Solovej
citation:
ama: Benedikter NP, Sok J, Solovej J. The Dirac–Frenkel principle for reduced density
matrices and the Bogoliubov–de Gennes equations. Annales Henri Poincare.
2018;19(4):1167-1214. doi:10.1007/s00023-018-0644-z
apa: Benedikter, N. P., Sok, J., & Solovej, J. (2018). The Dirac–Frenkel principle
for reduced density matrices and the Bogoliubov–de Gennes equations. Annales
Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-018-0644-z
chicago: Benedikter, Niels P, Jérémy Sok, and Jan Solovej. “The Dirac–Frenkel Principle
for Reduced Density Matrices and the Bogoliubov–de Gennes Equations.” Annales
Henri Poincare. Birkhäuser, 2018. https://doi.org/10.1007/s00023-018-0644-z.
ieee: N. P. Benedikter, J. Sok, and J. Solovej, “The Dirac–Frenkel principle for
reduced density matrices and the Bogoliubov–de Gennes equations,” Annales Henri
Poincare, vol. 19, no. 4. Birkhäuser, pp. 1167–1214, 2018.
ista: Benedikter NP, Sok J, Solovej J. 2018. The Dirac–Frenkel principle for reduced
density matrices and the Bogoliubov–de Gennes equations. Annales Henri Poincare.
19(4), 1167–1214.
mla: Benedikter, Niels P., et al. “The Dirac–Frenkel Principle for Reduced Density
Matrices and the Bogoliubov–de Gennes Equations.” Annales Henri Poincare,
vol. 19, no. 4, Birkhäuser, 2018, pp. 1167–214, doi:10.1007/s00023-018-0644-z.
short: N.P. Benedikter, J. Sok, J. Solovej, Annales Henri Poincare 19 (2018) 1167–1214.
date_created: 2018-12-11T11:46:34Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2023-09-19T10:07:41Z
day: '01'
ddc:
- '510'
- '539'
department:
- _id: RoSe
doi: 10.1007/s00023-018-0644-z
external_id:
isi:
- '000427578900006'
file:
- access_level: open_access
checksum: 883eeccba8384ad7fcaa28761d99a0fa
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:11:57Z
date_updated: 2020-07-14T12:46:31Z
file_id: '4914'
file_name: IST-2018-993-v1+1_2018_Benedikter_Dirac.pdf
file_size: 923252
relation: main_file
file_date_updated: 2020-07-14T12:46:31Z
has_accepted_license: '1'
intvolume: ' 19'
isi: 1
issue: '4'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 1167 - 1214
publication: Annales Henri Poincare
publication_status: published
publisher: Birkhäuser
publist_id: '7367'
pubrep_id: '993'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de
Gennes 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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 19
year: '2018'
...
---
_id: '1079'
abstract:
- lang: eng
text: We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory
for atoms and molecules. We prove the nonexistence of minimizers for the energy
functional when the number of electrons is large and the total nuclear charge
is small. This nonexistence result also applies to external potentials decaying
faster than the Coulomb potential. In the case of arbitrary nuclear charges, we
obtain the nonexistence of stable minimizers and radial minimizers.
article_number: '6'
article_processing_charge: No
author:
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Hanne
full_name: Van Den Bosch, Hanne
last_name: Van Den Bosch
citation:
ama: Nam P, Van Den Bosch H. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory
with small nuclear charges. Mathematical Physics, Analysis and Geometry.
2017;20(2). doi:10.1007/s11040-017-9238-0
apa: Nam, P., & Van Den Bosch, H. (2017). Nonexistence in Thomas Fermi-Dirac-von
Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis
and Geometry. Springer. https://doi.org/10.1007/s11040-017-9238-0
chicago: Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von
Weizsäcker Theory with Small Nuclear Charges.” Mathematical Physics, Analysis
and Geometry. Springer, 2017. https://doi.org/10.1007/s11040-017-9238-0.
ieee: P. Nam and H. Van Den Bosch, “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker
theory with small nuclear charges,” Mathematical Physics, Analysis and Geometry,
vol. 20, no. 2. Springer, 2017.
ista: Nam P, Van Den Bosch H. 2017. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker
theory with small nuclear charges. Mathematical Physics, Analysis and Geometry.
20(2), 6.
mla: Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von
Weizsäcker Theory with Small Nuclear Charges.” Mathematical Physics, Analysis
and Geometry, vol. 20, no. 2, 6, Springer, 2017, doi:10.1007/s11040-017-9238-0.
short: P. Nam, H. Van Den Bosch, Mathematical Physics, Analysis and Geometry 20
(2017).
date_created: 2018-12-11T11:50:02Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2023-09-20T11:53:35Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s11040-017-9238-0
external_id:
isi:
- '000401270000004'
intvolume: ' 20'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1603.07368
month: '06'
oa: 1
oa_version: Submitted Version
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
issn:
- '13850172'
publication_status: published
publisher: Springer
publist_id: '6300'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear
charges
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 20
year: '2017'
...
---
_id: '1120'
abstract:
- lang: eng
text: 'The existence of a self-localization transition in the polaron problem has
been under an active debate ever since Landau suggested it 83 years ago. Here
we reveal the self-localization transition for the rotational analogue of the
polaron -- the angulon quasiparticle. We show that, unlike for the polarons, self-localization
of angulons occurs at finite impurity-bath coupling already at the mean-field
level. The transition is accompanied by the spherical-symmetry breaking of the
angulon ground state and a discontinuity in the first derivative of the ground-state
energy. Moreover, the type of the symmetry breaking is dictated by the symmetry
of the microscopic impurity-bath interaction, which leads to a number of distinct
self-localized states. The predicted effects can potentially be addressed in experiments
on cold molecules trapped in superfluid helium droplets and ultracold quantum
gases, as well as on electronic excitations in solids and Bose-Einstein condensates. '
article_number: '033608'
article_processing_charge: No
author:
- first_name: Xiang
full_name: Li, Xiang
id: 4B7E523C-F248-11E8-B48F-1D18A9856A87
last_name: Li
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Mikhail
full_name: Lemeshko, Mikhail
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
citation:
ama: Li X, Seiringer R, Lemeshko M. Angular self-localization of impurities rotating
in a bosonic bath. Physical Review A. 2017;95(3). doi:10.1103/PhysRevA.95.033608
apa: Li, X., Seiringer, R., & Lemeshko, M. (2017). Angular self-localization
of impurities rotating in a bosonic bath. Physical Review A. American Physical
Society. https://doi.org/10.1103/PhysRevA.95.033608
chicago: Li, Xiang, Robert Seiringer, and Mikhail Lemeshko. “Angular Self-Localization
of Impurities Rotating in a Bosonic Bath.” Physical Review A. American
Physical Society, 2017. https://doi.org/10.1103/PhysRevA.95.033608.
ieee: X. Li, R. Seiringer, and M. Lemeshko, “Angular self-localization of impurities
rotating in a bosonic bath,” Physical Review A, vol. 95, no. 3. American
Physical Society, 2017.
ista: Li X, Seiringer R, Lemeshko M. 2017. Angular self-localization of impurities
rotating in a bosonic bath. Physical Review A. 95(3), 033608.
mla: Li, Xiang, et al. “Angular Self-Localization of Impurities Rotating in a Bosonic
Bath.” Physical Review A, vol. 95, no. 3, 033608, American Physical Society,
2017, doi:10.1103/PhysRevA.95.033608.
short: X. Li, R. Seiringer, M. Lemeshko, Physical Review A 95 (2017).
date_created: 2018-12-11T11:50:15Z
date_published: 2017-03-06T00:00:00Z
date_updated: 2023-09-20T11:30:58Z
day: '06'
department:
- _id: MiLe
- _id: RoSe
doi: 10.1103/PhysRevA.95.033608
ec_funded: 1
external_id:
isi:
- '000395981900009'
intvolume: ' 95'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1610.04908
month: '03'
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: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
- _id: 26031614-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P29902
name: Quantum rotations in the presence of a many-body environment
publication: Physical Review A
publication_identifier:
issn:
- '24699926'
publication_status: published
publisher: American Physical Society
publist_id: '6242'
quality_controlled: '1'
related_material:
record:
- id: '8958'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Angular self-localization of impurities rotating in a bosonic bath
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 95
year: '2017'
...
---
_id: '739'
abstract:
- lang: eng
text: We study the norm approximation to the Schrödinger dynamics of N bosons in
with an interaction potential of the form . Assuming that in the initial state
the particles outside of the condensate form a quasi-free state with finite kinetic
energy, we show that in the large N limit, the fluctuations around the condensate
can be effectively described using Bogoliubov approximation for all . The range
of β is expected to be optimal for this large class of initial states.
article_processing_charge: No
author:
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
citation:
ama: Nam P, Napiórkowski MM. A note on the validity of Bogoliubov correction to
mean field dynamics. Journal de Mathématiques Pures et Appliquées. 2017;108(5):662-688.
doi:10.1016/j.matpur.2017.05.013
apa: Nam, P., & Napiórkowski, M. M. (2017). A note on the validity of Bogoliubov
correction to mean field dynamics. Journal de Mathématiques Pures et Appliquées.
Elsevier. https://doi.org/10.1016/j.matpur.2017.05.013
chicago: Nam, Phan, and Marcin M Napiórkowski. “A Note on the Validity of Bogoliubov
Correction to Mean Field Dynamics.” Journal de Mathématiques Pures et Appliquées.
Elsevier, 2017. https://doi.org/10.1016/j.matpur.2017.05.013.
ieee: P. Nam and M. M. Napiórkowski, “A note on the validity of Bogoliubov correction
to mean field dynamics,” Journal de Mathématiques Pures et Appliquées,
vol. 108, no. 5. Elsevier, pp. 662–688, 2017.
ista: Nam P, Napiórkowski MM. 2017. A note on the validity of Bogoliubov correction
to mean field dynamics. Journal de Mathématiques Pures et Appliquées. 108(5),
662–688.
mla: Nam, Phan, and Marcin M. Napiórkowski. “A Note on the Validity of Bogoliubov
Correction to Mean Field Dynamics.” Journal de Mathématiques Pures et Appliquées,
vol. 108, no. 5, Elsevier, 2017, pp. 662–88, doi:10.1016/j.matpur.2017.05.013.
short: P. Nam, M.M. Napiórkowski, Journal de Mathématiques Pures et Appliquées 108
(2017) 662–688.
date_created: 2018-12-11T11:48:15Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-09-27T12:52:07Z
day: '01'
department:
- _id: RoSe
doi: 10.1016/j.matpur.2017.05.013
external_id:
isi:
- '000414113600003'
intvolume: ' 108'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1604.05240
month: '11'
oa: 1
oa_version: Submitted Version
page: 662 - 688
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Journal de Mathématiques Pures et Appliquées
publication_identifier:
issn:
- '00217824'
publication_status: published
publisher: Elsevier
publist_id: '6928'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A note on the validity of Bogoliubov correction to mean field dynamics
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 108
year: '2017'
...
---
_id: '741'
abstract:
- lang: eng
text: We prove that a system of N fermions interacting with an additional particle
via point interactions is stable if the ratio of the mass of the additional particle
to the one of the fermions is larger than some critical m*. The value of m* is
independent of N and turns out to be less than 1. This fact has important implications
for the stability of the unitary Fermi gas. We also characterize the domain of
the Hamiltonian of this model, and establish the validity of the Tan relations
for all wave functions in the domain.
article_processing_charge: No
author:
- first_name: Thomas
full_name: Moser, Thomas
id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87
last_name: Moser
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Moser T, Seiringer R. Stability of a fermionic N+1 particle system with point
interactions. Communications in Mathematical Physics. 2017;356(1):329-355.
doi:10.1007/s00220-017-2980-0
apa: Moser, T., & Seiringer, R. (2017). Stability of a fermionic N+1 particle
system with point interactions. Communications in Mathematical Physics.
Springer. https://doi.org/10.1007/s00220-017-2980-0
chicago: Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle
System with Point Interactions.” Communications in Mathematical Physics.
Springer, 2017. https://doi.org/10.1007/s00220-017-2980-0.
ieee: T. Moser and R. Seiringer, “Stability of a fermionic N+1 particle system with
point interactions,” Communications in Mathematical Physics, vol. 356,
no. 1. Springer, pp. 329–355, 2017.
ista: Moser T, Seiringer R. 2017. Stability of a fermionic N+1 particle system with
point interactions. Communications in Mathematical Physics. 356(1), 329–355.
mla: Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle
System with Point Interactions.” Communications in Mathematical Physics,
vol. 356, no. 1, Springer, 2017, pp. 329–55, doi:10.1007/s00220-017-2980-0.
short: T. Moser, R. Seiringer, Communications in Mathematical Physics 356 (2017)
329–355.
date_created: 2018-12-11T11:48:15Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-09-27T12:34:15Z
day: '01'
ddc:
- '539'
department:
- _id: RoSe
doi: 10.1007/s00220-017-2980-0
ec_funded: 1
external_id:
isi:
- '000409821300010'
file:
- access_level: open_access
checksum: 0fd9435400f91e9b3c5346319a2d24e3
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:50Z
date_updated: 2020-07-14T12:47:57Z
file_id: '4841'
file_name: IST-2017-880-v1+1_s00220-017-2980-0.pdf
file_size: 952639
relation: main_file
file_date_updated: 2020-07-14T12:47:57Z
has_accepted_license: '1'
intvolume: ' 356'
isi: 1
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 329 - 355
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- '00103616'
publication_status: published
publisher: Springer
publist_id: '6926'
pubrep_id: '880'
quality_controlled: '1'
related_material:
record:
- id: '52'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Stability of a fermionic N+1 particle system with point 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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 356
year: '2017'
...
---
_id: '484'
abstract:
- lang: eng
text: We consider the dynamics of a large quantum system of N identical bosons in
3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed
0 = β < 1/3 and large N, we obtain a norm approximation to the many-body evolution
in the Nparticle Hilbert space. The leading order behaviour of the dynamics is
determined by Hartree theory while the second order is given by Bogoliubov theory.
author:
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
citation:
ama: Nam P, Napiórkowski MM. Bogoliubov correction to the mean-field dynamics of
interacting bosons. Advances in Theoretical and Mathematical Physics. 2017;21(3):683-738.
doi:10.4310/ATMP.2017.v21.n3.a4
apa: Nam, P., & Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field
dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a4
chicago: Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field
Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics.
International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a4.
ieee: P. Nam and M. M. Napiórkowski, “Bogoliubov correction to the mean-field dynamics
of interacting bosons,” Advances in Theoretical and Mathematical Physics,
vol. 21, no. 3. International Press, pp. 683–738, 2017.
ista: Nam P, Napiórkowski MM. 2017. Bogoliubov correction to the mean-field dynamics
of interacting bosons. Advances in Theoretical and Mathematical Physics. 21(3),
683–738.
mla: Nam, Phan, and Marcin M. Napiórkowski. “Bogoliubov Correction to the Mean-Field
Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics,
vol. 21, no. 3, International Press, 2017, pp. 683–738, doi:10.4310/ATMP.2017.v21.n3.a4.
short: P. Nam, M.M. Napiórkowski, Advances in Theoretical and Mathematical Physics
21 (2017) 683–738.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:00:58Z
day: '01'
department:
- _id: RoSe
doi: 10.4310/ATMP.2017.v21.n3.a4
ec_funded: 1
intvolume: ' 21'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1509.04631
month: '01'
oa: 1
oa_version: Submitted Version
page: 683 - 738
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- '10950761'
publication_status: published
publisher: International Press
publist_id: '7336'
quality_controlled: '1'
scopus_import: 1
status: public
title: Bogoliubov correction to the mean-field dynamics of interacting bosons
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2017'
...
---
_id: '632'
abstract:
- lang: eng
text: 'We consider a 2D quantum system of N bosons in a trapping potential |x|s,
interacting via a pair potential of the form N2β−1 w(Nβ x). We show that for all
0 < β < (s + 1)/(s + 2), the leading order behavior of ground states of
the many-body system is described in the large N limit by the corresponding cubic
nonlinear Schrödinger energy functional. Our result covers the focusing case (w
< 0) where even the stability of the many-body system is not obvious. This
answers an open question mentioned by X. Chen and J. Holmer for harmonic traps
(s = 2). Together with the BBGKY hierarchy approach used by these authors, our
result implies the convergence of the many-body quantum dynamics to the focusing
NLS equation with harmonic trap for all 0 < β < 3/4. '
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Nicolas
full_name: Rougerie, Nicolas
last_name: Rougerie
citation:
ama: Lewin M, Nam P, Rougerie N. A note on 2D focusing many boson systems. Proceedings
of the American Mathematical Society. 2017;145(6):2441-2454. doi:10.1090/proc/13468
apa: Lewin, M., Nam, P., & Rougerie, N. (2017). A note on 2D focusing many boson
systems. Proceedings of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/proc/13468
chicago: Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “A Note on 2D Focusing
Many Boson Systems.” Proceedings of the American Mathematical Society.
American Mathematical Society, 2017. https://doi.org/10.1090/proc/13468.
ieee: M. Lewin, P. Nam, and N. Rougerie, “A note on 2D focusing many boson systems,”
Proceedings of the American Mathematical Society, vol. 145, no. 6. American
Mathematical Society, pp. 2441–2454, 2017.
ista: Lewin M, Nam P, Rougerie N. 2017. A note on 2D focusing many boson systems.
Proceedings of the American Mathematical Society. 145(6), 2441–2454.
mla: Lewin, Mathieu, et al. “A Note on 2D Focusing Many Boson Systems.” Proceedings
of the American Mathematical Society, vol. 145, no. 6, American Mathematical
Society, 2017, pp. 2441–54, doi:10.1090/proc/13468.
short: M. Lewin, P. Nam, N. Rougerie, Proceedings of the American Mathematical Society
145 (2017) 2441–2454.
date_created: 2018-12-11T11:47:36Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:07:03Z
day: '01'
department:
- _id: RoSe
doi: 10.1090/proc/13468
ec_funded: 1
intvolume: ' 145'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1509.09045
month: '01'
oa: 1
oa_version: Submitted Version
page: 2441 - 2454
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '7160'
quality_controlled: '1'
scopus_import: 1
status: public
title: A note on 2D focusing many boson systems
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 145
year: '2017'
...
---
_id: '912'
abstract:
- lang: eng
text: "We consider a many-body system of fermionic atoms interacting via a local
pair potential and subject to an external potential within the framework of Bardeen-Cooper-Schrieffer
(BCS) theory. We measure the free energy of the whole sample with respect to the
free energy of a reference state which allows us to define a BCS functional with
boundary conditions at infinity. Our main result is a lower bound for this energy
functional in terms of expressions that typically appear in Ginzburg-Landau functionals.\r\n"
article_number: '081901'
article_processing_charge: No
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
citation:
ama: Deuchert A. A lower bound for the BCS functional with boundary conditions at
infinity. Journal of Mathematical Physics. 2017;58(8). doi:10.1063/1.4996580
apa: Deuchert, A. (2017). A lower bound for the BCS functional with boundary conditions
at infinity. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/1.4996580
chicago: Deuchert, Andreas. “A Lower Bound for the BCS Functional with Boundary
Conditions at Infinity.” Journal of Mathematical Physics. AIP Publishing,
2017. https://doi.org/10.1063/1.4996580.
ieee: A. Deuchert, “A lower bound for the BCS functional with boundary conditions
at infinity,” Journal of Mathematical Physics, vol. 58, no. 8. AIP Publishing,
2017.
ista: Deuchert A. 2017. A lower bound for the BCS functional with boundary conditions
at infinity. Journal of Mathematical Physics. 58(8), 081901.
mla: Deuchert, Andreas. “A Lower Bound for the BCS Functional with Boundary Conditions
at Infinity.” Journal of Mathematical Physics, vol. 58, no. 8, 081901,
AIP Publishing, 2017, doi:10.1063/1.4996580.
short: A. Deuchert, Journal of Mathematical Physics 58 (2017).
date_created: 2018-12-11T11:49:10Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2024-02-28T13:07:56Z
day: '01'
department:
- _id: RoSe
doi: 10.1063/1.4996580
ec_funded: 1
external_id:
isi:
- '000409197200015'
intvolume: ' 58'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1703.04616
month: '08'
oa: 1
oa_version: Submitted Version
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:
- '00222488'
publication_status: published
publisher: AIP Publishing
publist_id: '6531'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A lower bound for the BCS functional with boundary conditions at infinity
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2017'
...