---
_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
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: '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: '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: '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: '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
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'
...