---
_id: '14891'
abstract:
- lang: eng
text: We give the first mathematically rigorous justification of the local density
approximation in density functional theory. We provide a quantitative estimate
on the difference between the grand-canonical Levy–Lieb energy of a given density
(the lowest possible energy of all quantum states having this density) and the
integral over the uniform electron gas energy of this density. The error involves
gradient terms and justifies the use of the local density approximation in the
situation where the density is very flat on sufficiently large regions in space.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Elliott H.
full_name: Lieb, Elliott H.
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Lewin M, Lieb EH, Seiringer R. The local density approximation in density functional
theory. Pure and Applied Analysis. 2020;2(1):35-73. doi:10.2140/paa.2020.2.35
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2020). The local density approximation
in density functional theory. Pure and Applied Analysis. Mathematical Sciences
Publishers. https://doi.org/10.2140/paa.2020.2.35
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “The Local Density
Approximation in Density Functional Theory.” Pure and Applied Analysis.
Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/paa.2020.2.35.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “The local density approximation in
density functional theory,” Pure and Applied Analysis, vol. 2, no. 1. Mathematical
Sciences Publishers, pp. 35–73, 2020.
ista: Lewin M, Lieb EH, Seiringer R. 2020. The local density approximation in density
functional theory. Pure and Applied Analysis. 2(1), 35–73.
mla: Lewin, Mathieu, et al. “The Local Density Approximation in Density Functional
Theory.” Pure and Applied Analysis, vol. 2, no. 1, Mathematical Sciences
Publishers, 2020, pp. 35–73, doi:10.2140/paa.2020.2.35.
short: M. Lewin, E.H. Lieb, R. Seiringer, Pure and Applied Analysis 2 (2020) 35–73.
corr_author: '1'
date_created: 2024-01-28T23:01:44Z
date_published: 2020-01-01T00:00:00Z
date_updated: 2026-08-12T08:47:14Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2020.2.35
external_id:
arxiv:
- '1903.04046'
intvolume: ' 2'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1903.04046
month: '01'
oa: 1
oa_version: Preprint
page: 35-73
publication: Pure and Applied Analysis
publication_identifier:
eissn:
- 2578-5885
issn:
- 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: The local density approximation in density functional theory
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2020'
...
---
_id: '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: 2026-04-08T14:12:30Z
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:
- 1424-0637
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 20
year: '2019'
...
---
_id: '80'
abstract:
- lang: eng
text: 'We consider an interacting, dilute Bose gas trapped in a harmonic potential
at a positive temperature. The system is analyzed in a combination of a thermodynamic
and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature
T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering
length is so small that the interaction energy per particle around the center
of the trap is of the same order of magnitude as the spectral gap in the trap.
We prove that the difference between the canonical free energy of the interacting
gas and the one of the noninteracting system can be obtained by minimizing the
GP energy functional. We also prove Bose–Einstein condensation in the following
sense: The one-particle density matrix of any approximate minimizer of the canonical
free energy functional is to leading order given by that of the noninteracting
gas but with the free condensate wavefunction replaced by the GP minimizer.'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: Deuchert A, Seiringer R, Yngvason J. Bose–Einstein condensation in a dilute,
trapped gas at positive temperature. Communications in Mathematical Physics.
2019;368(2):723-776. doi:10.1007/s00220-018-3239-0
apa: Deuchert, A., Seiringer, R., & Yngvason, J. (2019). Bose–Einstein condensation
in a dilute, trapped gas at positive temperature. Communications in Mathematical
Physics. Springer. https://doi.org/10.1007/s00220-018-3239-0
chicago: Deuchert, Andreas, Robert Seiringer, and Jakob Yngvason. “Bose–Einstein
Condensation in a Dilute, Trapped Gas at Positive Temperature.” Communications
in Mathematical Physics. Springer, 2019. https://doi.org/10.1007/s00220-018-3239-0.
ieee: A. Deuchert, R. Seiringer, and J. Yngvason, “Bose–Einstein condensation in
a dilute, trapped gas at positive temperature,” Communications in Mathematical
Physics, vol. 368, no. 2. Springer, pp. 723–776, 2019.
ista: Deuchert A, Seiringer R, Yngvason J. 2019. Bose–Einstein condensation in a
dilute, trapped gas at positive temperature. Communications in Mathematical Physics.
368(2), 723–776.
mla: Deuchert, Andreas, et al. “Bose–Einstein Condensation in a Dilute, Trapped
Gas at Positive Temperature.” Communications in Mathematical Physics, vol.
368, no. 2, Springer, 2019, pp. 723–76, doi:10.1007/s00220-018-3239-0.
short: A. Deuchert, R. Seiringer, J. Yngvason, Communications in Mathematical Physics
368 (2019) 723–776.
date_created: 2018-12-11T11:44:31Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00220-018-3239-0
ec_funded: 1
external_id:
isi:
- '000467796800007'
file:
- access_level: open_access
checksum: c7e9880b43ac726712c1365e9f2f73a6
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T10:34:06Z
date_updated: 2020-07-14T12:48:07Z
file_id: '5688'
file_name: 2018_CommunMathPhys_Deuchert.pdf
file_size: 893902
relation: main_file
file_date_updated: 2020-07-14T12:48:07Z
has_accepted_license: '1'
intvolume: ' 368'
isi: 1
issue: '2'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 723-776
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_status: published
publisher: Springer
publist_id: '7974'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bose–Einstein condensation in a dilute, trapped gas at positive temperature
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 368
year: '2019'
...
---
_id: '6840'
abstract:
- lang: eng
text: "We discuss thermodynamic properties of harmonically trapped\r\nimperfect
quantum gases. The spatial inhomogeneity of these systems imposes\r\na redefinition
of the mean-field interparticle potential energy as compared\r\nto the homogeneous
case. In our approach, it takes the form a\r\n2N2 ωd, where\r\nN is the number
of particles, ω—the harmonic trap frequency, d—system’s\r\ndimensionality, and
a is a parameter characterizing the interparticle interaction.\r\nWe provide arguments
that this model corresponds to the limiting case of\r\na long-ranged interparticle
potential of vanishingly small amplitude. This\r\nconclusion is drawn from a computation
similar to the well-known Kac scaling\r\nprocedure, which is presented here in
a form adapted to the case of an isotropic\r\nharmonic trap. We show that within
the model, the imperfect gas of trapped\r\nrepulsive bosons undergoes the Bose–Einstein
condensation provided d > 1.\r\nThe main result of our analysis is that in d =
1 the gas of attractive imperfect\r\nfermions with a = −aF < 0 is thermodynamically
equivalent to the gas of\r\nrepulsive bosons with a = aB > 0 provided the parameters
aF and aB fulfill\r\nthe relation aB + aF = \x1F. This result supplements similar
recent conclusion\r\nabout thermodynamic equivalence of two-dimensional (2D) uniform
imperfect\r\nrepulsive Bose and attractive Fermi gases."
article_number: '063101'
article_processing_charge: No
arxiv: 1
author:
- first_name: Krzysztof
full_name: Mysliwy, Krzysztof
id: 316457FC-F248-11E8-B48F-1D18A9856A87
last_name: Mysliwy
- first_name: Marek
full_name: Napiórkowski, Marek
last_name: Napiórkowski
citation:
ama: 'Mysliwy K, Napiórkowski M. Thermodynamics of inhomogeneous imperfect quantum
gases in harmonic traps. Journal of Statistical Mechanics: Theory and Experiment.
2019;2019(6). doi:10.1088/1742-5468/ab190d'
apa: 'Mysliwy, K., & Napiórkowski, M. (2019). Thermodynamics of inhomogeneous
imperfect quantum gases in harmonic traps. Journal of Statistical Mechanics:
Theory and Experiment. IOP Publishing. https://doi.org/10.1088/1742-5468/ab190d'
chicago: 'Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous
Imperfect Quantum Gases in Harmonic Traps.” Journal of Statistical Mechanics:
Theory and Experiment. IOP Publishing, 2019. https://doi.org/10.1088/1742-5468/ab190d.'
ieee: 'K. Mysliwy and M. Napiórkowski, “Thermodynamics of inhomogeneous imperfect
quantum gases in harmonic traps,” Journal of Statistical Mechanics: Theory
and Experiment, vol. 2019, no. 6. IOP Publishing, 2019.'
ista: 'Mysliwy K, Napiórkowski M. 2019. Thermodynamics of inhomogeneous imperfect
quantum gases in harmonic traps. Journal of Statistical Mechanics: Theory and
Experiment. 2019(6), 063101.'
mla: 'Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous
Imperfect Quantum Gases in Harmonic Traps.” Journal of Statistical Mechanics:
Theory and Experiment, vol. 2019, no. 6, 063101, IOP Publishing, 2019, doi:10.1088/1742-5468/ab190d.'
short: 'K. Mysliwy, M. Napiórkowski, Journal of Statistical Mechanics: Theory and
Experiment 2019 (2019).'
date_created: 2019-09-01T22:00:59Z
date_published: 2019-06-13T00:00:00Z
date_updated: 2025-03-31T16:01:18Z
day: '13'
department:
- _id: RoSe
doi: 10.1088/1742-5468/ab190d
ec_funded: 1
external_id:
arxiv:
- '1810.02209'
isi:
- '000471650100001'
intvolume: ' 2019'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1810.02209
month: '06'
oa: 1
oa_version: Preprint
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
eissn:
- 1742-5468
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2019
year: '2019'
...
---
_id: '7015'
abstract:
- lang: eng
text: We modify the "floating crystal" trial state for the classical homogeneous
electron gas (also known as jellium), in order to suppress the boundary charge
fluctuations that are known to lead to a macroscopic increase of the energy. The
argument is to melt a thin layer of the crystal close to the boundary and consequently
replace it by an incompressible fluid. With the aid of this trial state we show
that three different definitions of the ground-state energy of jellium coincide.
In the first point of view the electrons are placed in a neutralizing uniform
background. In the second definition there is no background but the electrons
are submitted to the constraint that their density is constant, as is appropriate
in density functional theory. Finally, in the third system each electron interacts
with a periodic image of itself; that is, periodic boundary conditions are imposed
on the interaction potential.
article_number: '035127'
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. Floating Wigner crystal with no boundary charge
fluctuations. Physical Review B. 2019;100(3). doi:10.1103/physrevb.100.035127
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2019). Floating Wigner crystal
with no boundary charge fluctuations. Physical Review B. American Physical
Society. https://doi.org/10.1103/physrevb.100.035127
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Floating Wigner
Crystal with No Boundary Charge Fluctuations.” Physical Review B. American
Physical Society, 2019. https://doi.org/10.1103/physrevb.100.035127.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Floating Wigner crystal with no boundary
charge fluctuations,” Physical Review B, vol. 100, no. 3. American Physical
Society, 2019.
ista: Lewin M, Lieb EH, Seiringer R. 2019. Floating Wigner crystal with no boundary
charge fluctuations. Physical Review B. 100(3), 035127.
mla: Lewin, Mathieu, et al. “Floating Wigner Crystal with No Boundary Charge Fluctuations.”
Physical Review B, vol. 100, no. 3, 035127, American Physical Society,
2019, doi:10.1103/physrevb.100.035127.
short: M. Lewin, E.H. Lieb, R. Seiringer, Physical Review B 100 (2019).
date_created: 2019-11-13T08:41:48Z
date_published: 2019-07-25T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
day: '25'
department:
- _id: RoSe
doi: 10.1103/physrevb.100.035127
ec_funded: 1
external_id:
arxiv:
- '1905.09138'
isi:
- '000477888200001'
intvolume: ' 100'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1905.09138
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
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: Floating Wigner crystal with no boundary charge fluctuations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 100
year: '2019'
...
---
_id: '7226'
article_number: '123504'
article_processing_charge: No
article_type: letter_note
author:
- first_name: Vojkan
full_name: Jaksic, Vojkan
last_name: Jaksic
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Jaksic V, Seiringer R. Introduction to the Special Collection: International
Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical Physics.
2019;60(12). doi:10.1063/1.5138135'
apa: 'Jaksic, V., & Seiringer, R. (2019). Introduction to the Special Collection:
International Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical
Physics. AIP Publishing. https://doi.org/10.1063/1.5138135'
chicago: 'Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection:
International Congress on Mathematical Physics (ICMP) 2018.” Journal of Mathematical
Physics. AIP Publishing, 2019. https://doi.org/10.1063/1.5138135.'
ieee: 'V. Jaksic and R. Seiringer, “Introduction to the Special Collection: International
Congress on Mathematical Physics (ICMP) 2018,” Journal of Mathematical Physics,
vol. 60, no. 12. AIP Publishing, 2019.'
ista: 'Jaksic V, Seiringer R. 2019. Introduction to the Special Collection: International
Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical Physics.
60(12), 123504.'
mla: 'Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection:
International Congress on Mathematical Physics (ICMP) 2018.” Journal of Mathematical
Physics, vol. 60, no. 12, 123504, AIP Publishing, 2019, doi:10.1063/1.5138135.'
short: V. Jaksic, R. Seiringer, Journal of Mathematical Physics 60 (2019).
date_created: 2020-01-05T23:00:46Z
date_published: 2019-12-01T00:00:00Z
date_updated: 2025-07-10T11:54:25Z
day: '01'
ddc:
- '500'
department:
- _id: RoSe
doi: 10.1063/1.5138135
external_id:
isi:
- '000505529800002'
file:
- access_level: open_access
checksum: bbd12ad1999a9ad7ba4d3c6f2e579c22
content_type: application/pdf
creator: dernst
date_created: 2020-01-07T14:59:13Z
date_updated: 2020-07-14T12:47:54Z
file_id: '7244'
file_name: 2019_JournalMathPhysics_Jaksic.pdf
file_size: 1025015
relation: main_file
file_date_updated: 2020-07-14T12:47:54Z
has_accepted_license: '1'
intvolume: ' 60'
isi: 1
issue: '12'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
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: 'Introduction to the Special Collection: International Congress on Mathematical
Physics (ICMP) 2018'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 60
year: '2019'
...
---
_id: '7413'
abstract:
- lang: eng
text: We consider Bose gases consisting of N particles trapped in a box with volume
one and interacting through a repulsive potential with scattering length of order
N−1 (Gross–Pitaevskii regime). We determine the ground state energy and the low-energy
excitation spectrum, up to errors vanishing as N→∞. Our results confirm Bogoliubov’s
predictions.
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
- first_name: Christian
full_name: Brennecke, Christian
last_name: Brennecke
- first_name: Serena
full_name: Cenatiempo, Serena
last_name: Cenatiempo
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
citation:
ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. Bogoliubov theory in the Gross–Pitaevskii
limit. Acta Mathematica. 2019;222(2):219-335. doi:10.4310/acta.2019.v222.n2.a1
apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2019). Bogoliubov
theory in the Gross–Pitaevskii limit. Acta Mathematica. International Press
of Boston. https://doi.org/10.4310/acta.2019.v222.n2.a1
chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
“Bogoliubov Theory in the Gross–Pitaevskii Limit.” Acta Mathematica. International
Press of Boston, 2019. https://doi.org/10.4310/acta.2019.v222.n2.a1.
ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Bogoliubov theory
in the Gross–Pitaevskii limit,” Acta Mathematica, vol. 222, no. 2. International
Press of Boston, pp. 219–335, 2019.
ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2019. Bogoliubov theory in
the Gross–Pitaevskii limit. Acta Mathematica. 222(2), 219–335.
mla: Boccato, Chiara, et al. “Bogoliubov Theory in the Gross–Pitaevskii Limit.”
Acta Mathematica, vol. 222, no. 2, International Press of Boston, 2019,
pp. 219–335, doi:10.4310/acta.2019.v222.n2.a1.
short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Acta Mathematica 222
(2019) 219–335.
date_created: 2020-01-30T09:30:41Z
date_published: 2019-06-07T00:00:00Z
date_updated: 2023-09-06T15:24:31Z
day: '07'
department:
- _id: RoSe
doi: 10.4310/acta.2019.v222.n2.a1
external_id:
arxiv:
- '1801.01389'
isi:
- '000495865300001'
intvolume: ' 222'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1801.01389
month: '06'
oa: 1
oa_version: Preprint
page: 219-335
publication: Acta Mathematica
publication_identifier:
eissn:
- 1871-2509
issn:
- 0001-5962
publication_status: published
publisher: International Press of Boston
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bogoliubov theory in the Gross–Pitaevskii limit
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 222
year: '2019'
...
---
OA_place: repository
OA_type: green
_id: '7524'
abstract:
- lang: eng
text: "We prove a lower bound for the free energy (per unit volume) of the two-dimensional
Bose gas in the thermodynamic limit. We show that the free energy at density $\\rho$
and inverse temperature $\\beta$ differs from the one of the non-interacting system
by the correction term $4 \\pi \\rho^2 |\\ln a^2 \\rho|^{-1} (2 - [1 - \\beta_{\\mathrm{c}}/\\beta]_+^2)$.
Here $a$ is the scattering length of the interaction potential, $[\\cdot]_+ =
\\max\\{ 0, \\cdot \\}$ and $\\beta_{\\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless
critical temperature for superfluidity. The result is valid in the dilute limit\r\n$a^2\\rho
\\ll 1$ and if $\\beta \\rho \\gtrsim 1$."
article_number: '1910.03372'
article_processing_charge: No
arxiv: 1
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- first_name: Simon
full_name: Mayer, Simon
id: 30C4630A-F248-11E8-B48F-1D18A9856A87
last_name: Mayer
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute
Bose gas. I. Lower bound. arXiv. doi:10.48550/arXiv.1910.03372
apa: Deuchert, A., Mayer, S., & Seiringer, R. (n.d.). The free energy of the
two-dimensional dilute Bose gas. I. Lower bound. arXiv. https://doi.org/10.48550/arXiv.1910.03372
chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy
of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1910.03372.
ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional
dilute Bose gas. I. Lower bound,” arXiv. .
ista: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute
Bose gas. I. Lower bound. arXiv, 1910.03372.
mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose
Gas. I. Lower Bound.” ArXiv, 1910.03372, doi:10.48550/arXiv.1910.03372.
short: A. Deuchert, S. Mayer, R. Seiringer, ArXiv (n.d.).
corr_author: '1'
date_created: 2020-02-26T08:46:40Z
date_published: 2019-10-08T00:00:00Z
date_updated: 2026-04-08T07:25:40Z
day: '08'
department:
- _id: RoSe
doi: 10.48550/arXiv.1910.03372
ec_funded: 1
external_id:
arxiv:
- '1910.03372'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.03372
month: '10'
oa: 1
oa_version: Preprint
page: '61'
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: arXiv
publication_status: draft
related_material:
record:
- id: '7790'
relation: later_version
status: public
- id: '7514'
relation: dissertation_contains
status: public
status: public
title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
OA_place: publisher
OA_type: hybrid
_id: '6788'
abstract:
- lang: eng
text: We consider the Nelson model with ultraviolet cutoff, which describes the
interaction between non-relativistic particles and a positive or zero mass quantized
scalar field. We take the non-relativistic particles to obey Fermi statistics
and discuss the time evolution in a mean-field limit of many fermions. In this
case, the limit is known to be also a semiclassical limit. We prove convergence
in terms of reduced density matrices of the many-body state to a tensor product
of a Slater determinant with semiclassical structure and a coherent state, which
evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations.
acknowledgement: 'Open access funding provided by Institute of Science and Technology
(IST Austria). We would like to thank Peter Pickl and Robert Seiringer for fruitful
discussions, and the anonymous referees for their valuable comments and suggestions.
Moreover, we would like to thank Niels Benedikter and László Erdős for helpful remarks
about the semiclassical structure and the Schrödinger–Klein–Gordon equations. N.
L. gratefully acknowledges financial support by the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation program (Grant Agreement
No. 694227) and funding for his stay at Princeton University from the project “Effective
One-Particle Equations for Correlated Many-Particle-(Coulomb) Systems: Derivation
and Properties” (Project No. 318342445) of the German Research Foundation (DFG).
S. P. gratefully acknowledges support from the German Academic Exchange Service
(DAAD) and the National Science Foundation under Agreement No. DMS-1128155. Moreover,
we would like to thank Princeton University and the Institute for Advanced Study
for their hospitality. S. P. would additionally like to thank the University of
Washington for hospitality.'
article_processing_charge: Yes (via OA deal)
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: Sören P
full_name: Petrat, Sören P
id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
last_name: Petrat
orcid: 0000-0002-9166-5889
citation:
ama: Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions.
Annales Henri Poincare. 2019;20(10):3471–3508. doi:10.1007/s00023-019-00828-w
apa: Leopold, N. K., & Petrat, S. P. (2019). Mean-field dynamics for the Nelson
model with fermions. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-019-00828-w
chicago: Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson
Model with Fermions.” Annales Henri Poincare. Springer Nature, 2019. https://doi.org/10.1007/s00023-019-00828-w.
ieee: N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model
with fermions,” Annales Henri Poincare, vol. 20, no. 10. Springer Nature,
pp. 3471–3508, 2019.
ista: Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with
fermions. Annales Henri Poincare. 20(10), 3471–3508.
mla: Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson
Model with Fermions.” Annales Henri Poincare, vol. 20, no. 10, Springer
Nature, 2019, pp. 3471–3508, doi:10.1007/s00023-019-00828-w.
short: N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 3471–3508.
corr_author: '1'
date_created: 2019-08-11T21:59:21Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2026-07-28T13:24:14Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00023-019-00828-w
ec_funded: 1
external_id:
arxiv:
- '1807.06781'
isi:
- '000487036900008'
file:
- access_level: open_access
checksum: b6dbf0d837d809293d449adf77138904
content_type: application/pdf
creator: dernst
date_created: 2019-08-12T12:05:58Z
date_updated: 2020-07-14T12:47:40Z
file_id: '6801'
file_name: 2019_AnnalesHenriPoincare_Leopold.pdf
file_size: 681139
relation: main_file
file_date_updated: 2020-07-14T12:47:40Z
has_accepted_license: '1'
intvolume: ' 20'
isi: 1
issue: '10'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 3471–3508
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Annales Henri Poincare
publication_identifier:
eissn:
- 1424-0661
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mean-field dynamics for the Nelson model with fermions
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: 20
year: '2019'
...
---
OA_place: publisher
OA_type: hybrid
_id: '7100'
abstract:
- lang: eng
text: We present microscopic derivations of the defocusing two-dimensional cubic
nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman
interacting N-particle system of bosons. We consider the interaction potential
to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx),
for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R).
In both cases we prove the convergence of the reduced density corresponding to
the exact time evolution to the projector onto the solution of the corresponding
nonlinear Schrödinger equation in trace norm. For the latter potential VN we show
that it is crucial to take the microscopic structure of the condensate into account
in order to obtain the correct dynamics.
acknowledgement: OA fund by IST Austria
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Maximilian
full_name: Jeblick, Maximilian
last_name: Jeblick
- 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: Jeblick M, Leopold NK, Pickl P. Derivation of the time dependent Gross–Pitaevskii
equation in two dimensions. Communications in Mathematical Physics. 2019;372(1):1-69.
doi:10.1007/s00220-019-03599-x
apa: Jeblick, M., Leopold, N. K., & Pickl, P. (2019). Derivation of the time
dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical
Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03599-x
chicago: Jeblick, Maximilian, Nikolai K Leopold, and Peter Pickl. “Derivation of
the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” Communications
in Mathematical Physics. Springer Nature, 2019. https://doi.org/10.1007/s00220-019-03599-x.
ieee: M. Jeblick, N. K. Leopold, and P. Pickl, “Derivation of the time dependent
Gross–Pitaevskii equation in two dimensions,” Communications in Mathematical
Physics, vol. 372, no. 1. Springer Nature, pp. 1–69, 2019.
ista: Jeblick M, Leopold NK, Pickl P. 2019. Derivation of the time dependent Gross–Pitaevskii
equation in two dimensions. Communications in Mathematical Physics. 372(1), 1–69.
mla: Jeblick, Maximilian, et al. “Derivation of the Time Dependent Gross–Pitaevskii
Equation in Two Dimensions.” Communications in Mathematical Physics, vol.
372, no. 1, Springer Nature, 2019, pp. 1–69, doi:10.1007/s00220-019-03599-x.
short: M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics
372 (2019) 1–69.
corr_author: '1'
date_created: 2019-11-25T08:08:02Z
date_published: 2019-11-08T00:00:00Z
date_updated: 2026-07-28T13:04:54Z
day: '08'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00220-019-03599-x
ec_funded: 1
external_id:
isi:
- '000495193700002'
file:
- access_level: open_access
checksum: cd283b475dd739e04655315abd46f528
content_type: application/pdf
creator: dernst
date_created: 2019-11-25T08:11:11Z
date_updated: 2020-07-14T12:47:49Z
file_id: '7101'
file_name: 2019_CommMathPhys_Jeblick.pdf
file_size: 884469
relation: main_file
file_date_updated: 2020-07-14T12:47:49Z
has_accepted_license: '1'
intvolume: ' 372'
isi: 1
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 1-69
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivation of the time dependent Gross–Pitaevskii equation in two dimensions
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: 372
year: '2019'
...
---
_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: '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: 2025-04-14T07:26:59Z
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:
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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: '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.
corr_author: '1'
date_created: 2018-12-11T11:46:34Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2024-10-09T20:58:43Z
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: '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.).
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
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: 2025-07-10T11:52:52Z
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:
- 0010-3616
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: 2025-04-14T07:26:59Z
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: 2025-04-15T08:26:15Z
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: '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. 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, 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, 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, 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: 2025-04-15T08:26:14Z
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
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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.
corr_author: '1'
date_created: 2018-12-11T11:46:15Z
date_published: 2018-05-01T00:00:00Z
date_updated: 2025-04-14T07:26:53Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00023-018-0665-7
ec_funded: 1
external_id:
isi:
- '000429799900008'
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creator: system
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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
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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: '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: 2025-04-14T07:26:59Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.5802/jep.64
ec_funded: 1
external_id:
arxiv:
- '1705.10676'
file:
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creator: dernst
date_created: 2018-12-17T16:38:18Z
date_updated: 2020-07-14T12:45:16Z
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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
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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'
...