---
_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: '1079'
abstract:
- lang: eng
text: We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory
for atoms and molecules. We prove the nonexistence of minimizers for the energy
functional when the number of electrons is large and the total nuclear charge
is small. This nonexistence result also applies to external potentials decaying
faster than the Coulomb potential. In the case of arbitrary nuclear charges, we
obtain the nonexistence of stable minimizers and radial minimizers.
article_number: '6'
article_processing_charge: No
author:
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Hanne
full_name: Van Den Bosch, Hanne
last_name: Van Den Bosch
citation:
ama: Nam P, Van Den Bosch H. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory
with small nuclear charges. Mathematical Physics, Analysis and Geometry.
2017;20(2). doi:10.1007/s11040-017-9238-0
apa: Nam, P., & Van Den Bosch, H. (2017). Nonexistence in Thomas Fermi-Dirac-von
Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis
and Geometry. Springer. https://doi.org/10.1007/s11040-017-9238-0
chicago: Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von
Weizsäcker Theory with Small Nuclear Charges.” Mathematical Physics, Analysis
and Geometry. Springer, 2017. https://doi.org/10.1007/s11040-017-9238-0.
ieee: P. Nam and H. Van Den Bosch, “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker
theory with small nuclear charges,” Mathematical Physics, Analysis and Geometry,
vol. 20, no. 2. Springer, 2017.
ista: Nam P, Van Den Bosch H. 2017. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker
theory with small nuclear charges. Mathematical Physics, Analysis and Geometry.
20(2), 6.
mla: Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von
Weizsäcker Theory with Small Nuclear Charges.” Mathematical Physics, Analysis
and Geometry, vol. 20, no. 2, 6, Springer, 2017, doi:10.1007/s11040-017-9238-0.
short: P. Nam, H. Van Den Bosch, Mathematical Physics, Analysis and Geometry 20
(2017).
date_created: 2018-12-11T11:50:02Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2023-09-20T11:53:35Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s11040-017-9238-0
external_id:
isi:
- '000401270000004'
intvolume: ' 20'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1603.07368
month: '06'
oa: 1
oa_version: Submitted Version
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
issn:
- '13850172'
publication_status: published
publisher: Springer
publist_id: '6300'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear
charges
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 20
year: '2017'
...
---
_id: '739'
abstract:
- lang: eng
text: We study the norm approximation to the Schrödinger dynamics of N bosons in
with an interaction potential of the form . Assuming that in the initial state
the particles outside of the condensate form a quasi-free state with finite kinetic
energy, we show that in the large N limit, the fluctuations around the condensate
can be effectively described using Bogoliubov approximation for all . The range
of β is expected to be optimal for this large class of initial states.
article_processing_charge: No
author:
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
citation:
ama: Nam P, Napiórkowski MM. A note on the validity of Bogoliubov correction to
mean field dynamics. Journal de Mathématiques Pures et Appliquées. 2017;108(5):662-688.
doi:10.1016/j.matpur.2017.05.013
apa: Nam, P., & Napiórkowski, M. M. (2017). A note on the validity of Bogoliubov
correction to mean field dynamics. Journal de Mathématiques Pures et Appliquées.
Elsevier. https://doi.org/10.1016/j.matpur.2017.05.013
chicago: Nam, Phan, and Marcin M Napiórkowski. “A Note on the Validity of Bogoliubov
Correction to Mean Field Dynamics.” Journal de Mathématiques Pures et Appliquées.
Elsevier, 2017. https://doi.org/10.1016/j.matpur.2017.05.013.
ieee: P. Nam and M. M. Napiórkowski, “A note on the validity of Bogoliubov correction
to mean field dynamics,” Journal de Mathématiques Pures et Appliquées,
vol. 108, no. 5. Elsevier, pp. 662–688, 2017.
ista: Nam P, Napiórkowski MM. 2017. A note on the validity of Bogoliubov correction
to mean field dynamics. Journal de Mathématiques Pures et Appliquées. 108(5),
662–688.
mla: Nam, Phan, and Marcin M. Napiórkowski. “A Note on the Validity of Bogoliubov
Correction to Mean Field Dynamics.” Journal de Mathématiques Pures et Appliquées,
vol. 108, no. 5, Elsevier, 2017, pp. 662–88, doi:10.1016/j.matpur.2017.05.013.
short: P. Nam, M.M. Napiórkowski, Journal de Mathématiques Pures et Appliquées 108
(2017) 662–688.
date_created: 2018-12-11T11:48:15Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-09-27T12:52:07Z
day: '01'
department:
- _id: RoSe
doi: 10.1016/j.matpur.2017.05.013
external_id:
isi:
- '000414113600003'
intvolume: ' 108'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1604.05240
month: '11'
oa: 1
oa_version: Submitted Version
page: 662 - 688
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Journal de Mathématiques Pures et Appliquées
publication_identifier:
issn:
- '00217824'
publication_status: published
publisher: Elsevier
publist_id: '6928'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A note on the validity of Bogoliubov correction to mean field dynamics
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 108
year: '2017'
...
---
_id: '484'
abstract:
- lang: eng
text: We consider the dynamics of a large quantum system of N identical bosons in
3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed
0 = β < 1/3 and large N, we obtain a norm approximation to the many-body evolution
in the Nparticle Hilbert space. The leading order behaviour of the dynamics is
determined by Hartree theory while the second order is given by Bogoliubov theory.
author:
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
citation:
ama: Nam P, Napiórkowski MM. Bogoliubov correction to the mean-field dynamics of
interacting bosons. Advances in Theoretical and Mathematical Physics. 2017;21(3):683-738.
doi:10.4310/ATMP.2017.v21.n3.a4
apa: Nam, P., & Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field
dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a4
chicago: Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field
Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics.
International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a4.
ieee: P. Nam and M. M. Napiórkowski, “Bogoliubov correction to the mean-field dynamics
of interacting bosons,” Advances in Theoretical and Mathematical Physics,
vol. 21, no. 3. International Press, pp. 683–738, 2017.
ista: Nam P, Napiórkowski MM. 2017. Bogoliubov correction to the mean-field dynamics
of interacting bosons. Advances in Theoretical and Mathematical Physics. 21(3),
683–738.
mla: Nam, Phan, and Marcin M. Napiórkowski. “Bogoliubov Correction to the Mean-Field
Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics,
vol. 21, no. 3, International Press, 2017, pp. 683–738, doi:10.4310/ATMP.2017.v21.n3.a4.
short: P. Nam, M.M. Napiórkowski, Advances in Theoretical and Mathematical Physics
21 (2017) 683–738.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:00:58Z
day: '01'
department:
- _id: RoSe
doi: 10.4310/ATMP.2017.v21.n3.a4
ec_funded: 1
intvolume: ' 21'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1509.04631
month: '01'
oa: 1
oa_version: Submitted Version
page: 683 - 738
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- '10950761'
publication_status: published
publisher: International Press
publist_id: '7336'
quality_controlled: '1'
scopus_import: 1
status: public
title: Bogoliubov correction to the mean-field dynamics of interacting bosons
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2017'
...
---
_id: '632'
abstract:
- lang: eng
text: 'We consider a 2D quantum system of N bosons in a trapping potential |x|s,
interacting via a pair potential of the form N2β−1 w(Nβ x). We show that for all
0 < β < (s + 1)/(s + 2), the leading order behavior of ground states of
the many-body system is described in the large N limit by the corresponding cubic
nonlinear Schrödinger energy functional. Our result covers the focusing case (w
< 0) where even the stability of the many-body system is not obvious. This
answers an open question mentioned by X. Chen and J. Holmer for harmonic traps
(s = 2). Together with the BBGKY hierarchy approach used by these authors, our
result implies the convergence of the many-body quantum dynamics to the focusing
NLS equation with harmonic trap for all 0 < β < 3/4. '
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Nicolas
full_name: Rougerie, Nicolas
last_name: Rougerie
citation:
ama: Lewin M, Nam P, Rougerie N. A note on 2D focusing many boson systems. Proceedings
of the American Mathematical Society. 2017;145(6):2441-2454. doi:10.1090/proc/13468
apa: Lewin, M., Nam, P., & Rougerie, N. (2017). A note on 2D focusing many boson
systems. Proceedings of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/proc/13468
chicago: Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “A Note on 2D Focusing
Many Boson Systems.” Proceedings of the American Mathematical Society.
American Mathematical Society, 2017. https://doi.org/10.1090/proc/13468.
ieee: M. Lewin, P. Nam, and N. Rougerie, “A note on 2D focusing many boson systems,”
Proceedings of the American Mathematical Society, vol. 145, no. 6. American
Mathematical Society, pp. 2441–2454, 2017.
ista: Lewin M, Nam P, Rougerie N. 2017. A note on 2D focusing many boson systems.
Proceedings of the American Mathematical Society. 145(6), 2441–2454.
mla: Lewin, Mathieu, et al. “A Note on 2D Focusing Many Boson Systems.” Proceedings
of the American Mathematical Society, vol. 145, no. 6, American Mathematical
Society, 2017, pp. 2441–54, doi:10.1090/proc/13468.
short: M. Lewin, P. Nam, N. Rougerie, Proceedings of the American Mathematical Society
145 (2017) 2441–2454.
date_created: 2018-12-11T11:47:36Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:07:03Z
day: '01'
department:
- _id: RoSe
doi: 10.1090/proc/13468
ec_funded: 1
intvolume: ' 145'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1509.09045
month: '01'
oa: 1
oa_version: Submitted Version
page: 2441 - 2454
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '7160'
quality_controlled: '1'
scopus_import: 1
status: public
title: A note on 2D focusing many boson systems
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 145
year: '2017'
...
---
_id: '1143'
abstract:
- lang: eng
text: We study the ground state of a dilute Bose gas in a scaling limit where the
Gross-Pitaevskii functional emerges. This is a repulsive nonlinear Schrödinger
functional whose quartic term is proportional to the scattering length of the
interparticle interaction potential. We propose a new derivation of this limit
problem, with a method that bypasses some of the technical difficulties that previous
derivations had to face. The new method is based on a combination of Dyson\'s
lemma, the quantum de Finetti theorem and a second moment estimate for ground
states of the effective Dyson Hamiltonian. It applies equally well to the case
where magnetic fields or rotation are present.
author:
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Nicolas
full_name: Rougerie, Nicolas
last_name: Rougerie
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Nam P, Rougerie N, Seiringer R. Ground states of large bosonic systems: The
gross Pitaevskii limit revisited. Analysis and PDE. 2016;9(2):459-485.
doi:10.2140/apde.2016.9.459'
apa: 'Nam, P., Rougerie, N., & Seiringer, R. (2016). Ground states of large
bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE.
Mathematical Sciences Publishers. https://doi.org/10.2140/apde.2016.9.459'
chicago: 'Nam, Phan, Nicolas Rougerie, and Robert Seiringer. “Ground States of Large
Bosonic Systems: The Gross Pitaevskii Limit Revisited.” Analysis and PDE.
Mathematical Sciences Publishers, 2016. https://doi.org/10.2140/apde.2016.9.459.'
ieee: 'P. Nam, N. Rougerie, and R. Seiringer, “Ground states of large bosonic systems:
The gross Pitaevskii limit revisited,” Analysis and PDE, vol. 9, no. 2.
Mathematical Sciences Publishers, pp. 459–485, 2016.'
ista: 'Nam P, Rougerie N, Seiringer R. 2016. Ground states of large bosonic systems:
The gross Pitaevskii limit revisited. Analysis and PDE. 9(2), 459–485.'
mla: 'Nam, Phan, et al. “Ground States of Large Bosonic Systems: The Gross Pitaevskii
Limit Revisited.” Analysis and PDE, vol. 9, no. 2, Mathematical Sciences
Publishers, 2016, pp. 459–85, doi:10.2140/apde.2016.9.459.'
short: P. Nam, N. Rougerie, R. Seiringer, Analysis and PDE 9 (2016) 459–485.
date_created: 2018-12-11T11:50:23Z
date_published: 2016-03-24T00:00:00Z
date_updated: 2021-01-12T06:48:36Z
day: '24'
department:
- _id: RoSe
doi: 10.2140/apde.2016.9.459
ec_funded: 1
intvolume: ' 9'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1503.07061
month: '03'
oa: 1
oa_version: Preprint
page: 459 - 485
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Analysis and PDE
publication_status: published
publisher: Mathematical Sciences Publishers
publist_id: '6215'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'Ground states of large bosonic systems: The gross Pitaevskii limit revisited'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 9
year: '2016'
...
---
_id: '1622'
abstract:
- lang: eng
text: We prove analogues of the Lieb–Thirring and Hardy–Lieb–Thirring inequalities
for many-body quantum systems with fractional kinetic operators and homogeneous
interaction potentials, where no anti-symmetry on the wave functions is assumed.
These many-body inequalities imply interesting one-body interpolation inequalities,
and we show that the corresponding one- and many-body inequalities are actually
equivalent in certain cases.
acknowledgement: "We thank Jan Philip Solovej, Robert Seiringer and Vladimir Maz’ya
for helpful discussions, as well as Rupert Frank\r\nand the anonymous referee for
useful comments. Part of this work has been carried out during a visit at the Institut
Mittag-Leffler (Stockholm). D.L. acknowledges financial support by the grant KAW
2010.0063 from the Knut and Alice Wallenberg Foundation and the Swedish Research
Council grant no. 2013-4734. P.T.N. is supported by the People Programme (Marie
Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013)
under REA grant agreement no. 291734. F.P. acknowledges support from the ERC project
no. 321029 “The\r\nmathematics of the structure of matter”."
author:
- first_name: Douglas
full_name: Lundholm, Douglas
last_name: Lundholm
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Fabian
full_name: Portmann, Fabian
last_name: Portmann
citation:
ama: Lundholm D, Nam P, Portmann F. Fractional Hardy–Lieb–Thirring and related Inequalities
for interacting systems. Archive for Rational Mechanics and Analysis. 2016;219(3):1343-1382.
doi:10.1007/s00205-015-0923-5
apa: Lundholm, D., Nam, P., & Portmann, F. (2016). Fractional Hardy–Lieb–Thirring
and related Inequalities for interacting systems. Archive for Rational Mechanics
and Analysis. Springer. https://doi.org/10.1007/s00205-015-0923-5
chicago: Lundholm, Douglas, Phan Nam, and Fabian Portmann. “Fractional Hardy–Lieb–Thirring
and Related Inequalities for Interacting Systems.” Archive for Rational Mechanics
and Analysis. Springer, 2016. https://doi.org/10.1007/s00205-015-0923-5.
ieee: D. Lundholm, P. Nam, and F. Portmann, “Fractional Hardy–Lieb–Thirring and
related Inequalities for interacting systems,” Archive for Rational Mechanics
and Analysis, vol. 219, no. 3. Springer, pp. 1343–1382, 2016.
ista: Lundholm D, Nam P, Portmann F. 2016. Fractional Hardy–Lieb–Thirring and related
Inequalities for interacting systems. Archive for Rational Mechanics and Analysis.
219(3), 1343–1382.
mla: Lundholm, Douglas, et al. “Fractional Hardy–Lieb–Thirring and Related Inequalities
for Interacting Systems.” Archive for Rational Mechanics and Analysis,
vol. 219, no. 3, Springer, 2016, pp. 1343–82, doi:10.1007/s00205-015-0923-5.
short: D. Lundholm, P. Nam, F. Portmann, Archive for Rational Mechanics and Analysis
219 (2016) 1343–1382.
date_created: 2018-12-11T11:53:05Z
date_published: 2016-03-01T00:00:00Z
date_updated: 2021-01-12T06:52:04Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00205-015-0923-5
ec_funded: 1
intvolume: ' 219'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1501.04570
month: '03'
oa: 1
oa_version: Submitted Version
page: 1343 - 1382
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Archive for Rational Mechanics and Analysis
publication_status: published
publisher: Springer
publist_id: '5542'
quality_controlled: '1'
scopus_import: 1
status: public
title: Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 219
year: '2016'
...
---
_id: '1491'
abstract:
- lang: eng
text: We study the ground state of a trapped Bose gas, starting from the full many-body
Schrödinger Hamiltonian, and derive the non-linear Schrödinger energy functional
in the limit of a large particle number, when the interaction potential converges
slowly to a Dirac delta function. Our method is based on quantitative estimates
on the discrepancy between the full many-body energy and its mean-field approximation
using Hartree states. These are proved using finite dimensional localization and
a quantitative version of the quantum de Finetti theorem. Our approach covers
the case of attractive interactions in the regime of stability. In particular,
our main new result is a derivation of the 2D attractive non-linear Schrödinger
ground state.
acknowledgement: The authors acknowledge financial support from the European Research
Council (FP7/2007-2013 Grant Agreement MNIQS 258023) and the ANR (Mathostaq project,
ANR-13-JS01-0005-01). The second and third authors have benefited from the hospitality
of the Institute for Mathematical Science of the National University of Singapore.
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Nicolas
full_name: Rougerie, Nicolas
last_name: Rougerie
citation:
ama: Lewin M, Nam P, Rougerie N. The mean-field approximation and the non-linear
Schrödinger functional for trapped Bose gases. Transactions of the American
Mathematical Society. 2016;368(9):6131-6157. doi:10.1090/tran/6537
apa: Lewin, M., Nam, P., & Rougerie, N. (2016). The mean-field approximation
and the non-linear Schrödinger functional for trapped Bose gases. Transactions
of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/6537
chicago: Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “The Mean-Field Approximation
and the Non-Linear Schrödinger Functional for Trapped Bose Gases.” Transactions
of the American Mathematical Society. American Mathematical Society, 2016.
https://doi.org/10.1090/tran/6537.
ieee: M. Lewin, P. Nam, and N. Rougerie, “The mean-field approximation and the non-linear
Schrödinger functional for trapped Bose gases,” Transactions of the American
Mathematical Society, vol. 368, no. 9. American Mathematical Society, pp.
6131–6157, 2016.
ista: Lewin M, Nam P, Rougerie N. 2016. The mean-field approximation and the non-linear
Schrödinger functional for trapped Bose gases. Transactions of the American Mathematical
Society. 368(9), 6131–6157.
mla: Lewin, Mathieu, et al. “The Mean-Field Approximation and the Non-Linear Schrödinger
Functional for Trapped Bose Gases.” Transactions of the American Mathematical
Society, vol. 368, no. 9, American Mathematical Society, 2016, pp. 6131–57,
doi:10.1090/tran/6537.
short: M. Lewin, P. Nam, N. Rougerie, Transactions of the American Mathematical
Society 368 (2016) 6131–6157.
date_created: 2018-12-11T11:52:20Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2021-01-12T06:51:07Z
day: '01'
department:
- _id: RoSe
doi: 10.1090/tran/6537
intvolume: ' 368'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1405.3220
month: '01'
oa: 1
oa_version: Submitted Version
page: 6131 - 6157
publication: Transactions of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '5692'
quality_controlled: '1'
scopus_import: 1
status: public
title: The mean-field approximation and the non-linear Schrödinger functional for
trapped Bose gases
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 368
year: '2016'
...
---
_id: '1545'
abstract:
- lang: eng
text: We provide general conditions for which bosonic quadratic Hamiltonians on
Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover
the case when quantum systems have infinite degrees of freedom and the associated
one-body kinetic and paring operators are unbounded. Our sufficient conditions
are optimal in the sense that they become necessary when the relevant one-body
operators commute.
acknowledgement: We thank Jan Dereziński for several inspiring discussions and useful
remarks. We thank the referee for helpful comments. J.P.S. thanks the Erwin Schrödinger
Institute for the hospitality during the thematic programme “Quantum many-body systems,
random matrices, and disorder”. We gratefully acknowledge the financial supports
by the European Union's Seventh Framework Programme under the ERC Advanced Grant
ERC-2012-AdG 321029 (J.P.S.) and the REA grant agreement No. 291734 (P.T.N.), as
well as the support of the National Science Center (NCN) grant No. 2012/07/N/ST1/03185
and the Austrian Science Fund (FWF) project No. P 27533-N27 (M.N.).
author:
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Marcin M
full_name: Napiórkowski, Marcin M
id: 4197AD04-F248-11E8-B48F-1D18A9856A87
last_name: Napiórkowski
- first_name: Jan
full_name: Solovej, Jan
last_name: Solovej
citation:
ama: Nam P, Napiórkowski MM, Solovej J. Diagonalization of bosonic quadratic Hamiltonians
by Bogoliubov transformations. Journal of Functional Analysis. 2016;270(11):4340-4368.
doi:10.1016/j.jfa.2015.12.007
apa: Nam, P., Napiórkowski, M. M., & Solovej, J. (2016). Diagonalization of
bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional
Analysis. Academic Press. https://doi.org/10.1016/j.jfa.2015.12.007
chicago: Nam, Phan, Marcin M Napiórkowski, and Jan Solovej. “Diagonalization of
Bosonic Quadratic Hamiltonians by Bogoliubov Transformations.” Journal of Functional
Analysis. Academic Press, 2016. https://doi.org/10.1016/j.jfa.2015.12.007.
ieee: P. Nam, M. M. Napiórkowski, and J. Solovej, “Diagonalization of bosonic quadratic
Hamiltonians by Bogoliubov transformations,” Journal of Functional Analysis,
vol. 270, no. 11. Academic Press, pp. 4340–4368, 2016.
ista: Nam P, Napiórkowski MM, Solovej J. 2016. Diagonalization of bosonic quadratic
Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. 270(11),
4340–4368.
mla: Nam, Phan, et al. “Diagonalization of Bosonic Quadratic Hamiltonians by Bogoliubov
Transformations.” Journal of Functional Analysis, vol. 270, no. 11, Academic
Press, 2016, pp. 4340–68, doi:10.1016/j.jfa.2015.12.007.
short: P. Nam, M.M. Napiórkowski, J. Solovej, Journal of Functional Analysis 270
(2016) 4340–4368.
date_created: 2018-12-11T11:52:38Z
date_published: 2016-06-01T00:00:00Z
date_updated: 2021-01-12T06:51:30Z
day: '01'
department:
- _id: RoSe
doi: 10.1016/j.jfa.2015.12.007
ec_funded: 1
intvolume: ' 270'
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1508.07321
month: '06'
oa: 1
oa_version: Submitted Version
page: 4340 - 4368
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Journal of Functional Analysis
publication_status: published
publisher: Academic Press
publist_id: '5626'
quality_controlled: '1'
scopus_import: 1
status: public
title: Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 270
year: '2016'
...
---
_id: '1267'
abstract:
- lang: eng
text: We give a simplified proof of the nonexistence of large nuclei in the liquid
drop model and provide an explicit bound. Our bound is within a factor of 2.3
of the conjectured value and seems to be the first quantitative result.
acknowledgement: "Open access funding provided by Institute of Science and Technology
Austria.\r\n"
author:
- first_name: Rupert
full_name: Frank, Rupert
last_name: Frank
- first_name: Rowan
full_name: Killip, Rowan
last_name: Killip
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
citation:
ama: Frank R, Killip R, Nam P. Nonexistence of large nuclei in the liquid drop model.
Letters in Mathematical Physics. 2016;106(8):1033-1036. doi:10.1007/s11005-016-0860-8
apa: Frank, R., Killip, R., & Nam, P. (2016). Nonexistence of large nuclei in
the liquid drop model. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-016-0860-8
chicago: Frank, Rupert, Rowan Killip, and Phan Nam. “Nonexistence of Large Nuclei
in the Liquid Drop Model.” Letters in Mathematical Physics. Springer, 2016.
https://doi.org/10.1007/s11005-016-0860-8.
ieee: R. Frank, R. Killip, and P. Nam, “Nonexistence of large nuclei in the liquid
drop model,” Letters in Mathematical Physics, vol. 106, no. 8. Springer,
pp. 1033–1036, 2016.
ista: Frank R, Killip R, Nam P. 2016. Nonexistence of large nuclei in the liquid
drop model. Letters in Mathematical Physics. 106(8), 1033–1036.
mla: Frank, Rupert, et al. “Nonexistence of Large Nuclei in the Liquid Drop Model.”
Letters in Mathematical Physics, vol. 106, no. 8, Springer, 2016, pp. 1033–36,
doi:10.1007/s11005-016-0860-8.
short: R. Frank, R. Killip, P. Nam, Letters in Mathematical Physics 106 (2016) 1033–1036.
date_created: 2018-12-11T11:51:02Z
date_published: 2016-08-01T00:00:00Z
date_updated: 2021-01-12T06:49:30Z
day: '01'
ddc:
- '510'
- '539'
department:
- _id: RoSe
doi: 10.1007/s11005-016-0860-8
file:
- access_level: open_access
checksum: d740a6a226e0f5f864f40e3e269d3cc0
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:11:09Z
date_updated: 2020-07-14T12:44:42Z
file_id: '4863'
file_name: IST-2016-698-v1+1_s11005-016-0860-8.pdf
file_size: 349464
relation: main_file
file_date_updated: 2020-07-14T12:44:42Z
has_accepted_license: '1'
intvolume: ' 106'
issue: '8'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 1033 - 1036
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
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '6054'
pubrep_id: '698'
quality_controlled: '1'
scopus_import: 1
status: public
title: Nonexistence of large nuclei in the liquid drop model
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: 106
year: '2016'
...
---
_id: '2085'
abstract:
- lang: eng
text: 'We study the spectrum of a large system of N identical bosons interacting
via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov''s
theory predicts that the spectrum of the N-particle Hamiltonian can be approximated
by that of an effective quadratic Hamiltonian acting on Fock space, which describes
the fluctuations around a condensed state. Recently, Bogoliubov''s theory has
been justified rigorously in the case that the low-energy eigenvectors of the
N-particle Hamiltonian display complete condensation in the unique minimizer of
the corresponding Hartree functional. In this paper, we shall justify Bogoliubov''s
theory for the high-energy part of the spectrum of the N-particle Hamiltonian
corresponding to (non-linear) excited states of the Hartree functional. Moreover,
we shall extend the existing results on the excitation spectrum to the case of
non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the
latter covers the case of rotating Bose gases, when the rotation speed is large
enough to break the symmetry and to produce multiple quantized vortices in the
Hartree minimizer. '
author:
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Nam P, Seiringer R. Collective excitations of Bose gases in the mean-field
regime. Archive for Rational Mechanics and Analysis. 2015;215(2):381-417.
doi:10.1007/s00205-014-0781-6
apa: Nam, P., & Seiringer, R. (2015). Collective excitations of Bose gases in
the mean-field regime. Archive for Rational Mechanics and Analysis. Springer.
https://doi.org/10.1007/s00205-014-0781-6
chicago: Nam, Phan, and Robert Seiringer. “Collective Excitations of Bose Gases
in the Mean-Field Regime.” Archive for Rational Mechanics and Analysis.
Springer, 2015. https://doi.org/10.1007/s00205-014-0781-6.
ieee: P. Nam and R. Seiringer, “Collective excitations of Bose gases in the mean-field
regime,” Archive for Rational Mechanics and Analysis, vol. 215, no. 2.
Springer, pp. 381–417, 2015.
ista: Nam P, Seiringer R. 2015. Collective excitations of Bose gases in the mean-field
regime. Archive for Rational Mechanics and Analysis. 215(2), 381–417.
mla: Nam, Phan, and Robert Seiringer. “Collective Excitations of Bose Gases in the
Mean-Field Regime.” Archive for Rational Mechanics and Analysis, vol. 215,
no. 2, Springer, 2015, pp. 381–417, doi:10.1007/s00205-014-0781-6.
short: P. Nam, R. Seiringer, Archive for Rational Mechanics and Analysis 215 (2015)
381–417.
date_created: 2018-12-11T11:55:37Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2021-01-12T06:55:13Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00205-014-0781-6
intvolume: ' 215'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1402.1153
month: '02'
oa: 1
oa_version: Preprint
page: 381 - 417
publication: Archive for Rational Mechanics and Analysis
publication_status: published
publisher: Springer
publist_id: '4951'
quality_controlled: '1'
scopus_import: 1
status: public
title: Collective excitations of Bose gases in the mean-field regime
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 215
year: '2015'
...
---
_id: '473'
abstract:
- lang: eng
text: We prove that nonlinear Gibbs measures can be obtained from the corresponding
many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where
the temperature T diverges and the interaction strength behaves as 1/T. We proceed
by characterizing the interacting Gibbs state as minimizing a functional counting
the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional
analogue of phase-space semiclassical analysis, using fine properties of the quantum
relative entropy, the link between quantum de Finetti measures and upper/lower
symbols in a coherent state basis, as well as Berezin-Lieb type inequalities.
Our results cover the measure built on the defocusing nonlinear Schrödinger functional
on a finite interval, as well as smoother interactions in dimensions d 2.
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Nam
full_name: Phan Thanh, Nam
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Phan Thanh
- first_name: Nicolas
full_name: Rougerie, Nicolas
last_name: Rougerie
citation:
ama: Lewin M, Nam P, Rougerie N. Derivation of nonlinear gibbs measures from many-body
quantum mechanics. Journal de l’Ecole Polytechnique - Mathematiques. 2015;2:65-115.
doi:10.5802/jep.18
apa: Lewin, M., Nam, P., & Rougerie, N. (2015). Derivation of nonlinear gibbs
measures from many-body quantum mechanics. Journal de l’Ecole Polytechnique
- Mathematiques. Ecole Polytechnique. https://doi.org/10.5802/jep.18
chicago: Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “Derivation of Nonlinear
Gibbs Measures from Many-Body Quantum Mechanics.” Journal de l’Ecole Polytechnique
- Mathematiques. Ecole Polytechnique, 2015. https://doi.org/10.5802/jep.18.
ieee: M. Lewin, P. Nam, and N. Rougerie, “Derivation of nonlinear gibbs measures
from many-body quantum mechanics,” Journal de l’Ecole Polytechnique - Mathematiques,
vol. 2. Ecole Polytechnique, pp. 65–115, 2015.
ista: Lewin M, Nam P, Rougerie N. 2015. Derivation of nonlinear gibbs measures from
many-body quantum mechanics. Journal de l’Ecole Polytechnique - Mathematiques.
2, 65–115.
mla: Lewin, Mathieu, et al. “Derivation of Nonlinear Gibbs Measures from Many-Body
Quantum Mechanics.” Journal de l’Ecole Polytechnique - Mathematiques, vol.
2, Ecole Polytechnique, 2015, pp. 65–115, doi:10.5802/jep.18.
short: M. Lewin, P. Nam, N. Rougerie, Journal de l’Ecole Polytechnique - Mathematiques
2 (2015) 65–115.
date_created: 2018-12-11T11:46:40Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2021-01-12T08:00:52Z
day: '01'
ddc:
- '539'
department:
- _id: RoSe
doi: 10.5802/jep.18
ec_funded: 1
file:
- access_level: open_access
checksum: a40eb4016717ddc9927154798a4c164a
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:53Z
date_updated: 2020-07-14T12:46:35Z
file_id: '4974'
file_name: IST-2018-951-v1+1_2015_Thanh-Nam_Derivation_of.pdf
file_size: 1084254
relation: main_file
file_date_updated: 2020-07-14T12:46:35Z
has_accepted_license: '1'
intvolume: ' 2'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 65 - 115
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Journal de l'Ecole Polytechnique - Mathematiques
publication_status: published
publisher: Ecole Polytechnique
publist_id: '7344'
pubrep_id: '951'
quality_controlled: '1'
scopus_import: 1
status: public
title: Derivation of nonlinear gibbs measures from many-body quantum mechanics
tmp:
image: /image/cc_by_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
short: CC BY-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2015'
...