---
_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
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: 2023-08-29T07:19:13Z
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: '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.
date_created: 2019-11-25T08:08:02Z
date_published: 2019-11-08T00:00:00Z
date_updated: 2023-09-06T10:47:43Z
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
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 372
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
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'
...
---
_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
author:
- first_name: Thomas
full_name: Moser, Thomas
id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87
last_name: Moser
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Moser T, Seiringer R. Energy contribution of a point-interacting impurity in
a Fermi gas. Annales Henri Poincare. 2019;20(4):1325–1365. doi:10.1007/s00023-018-00757-0
apa: Moser, T., & Seiringer, R. (2019). Energy contribution of a point-interacting
impurity in a Fermi gas. Annales Henri Poincare. Springer. https://doi.org/10.1007/s00023-018-00757-0
chicago: Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting
Impurity in a Fermi Gas.” Annales Henri Poincare. Springer, 2019. https://doi.org/10.1007/s00023-018-00757-0.
ieee: T. Moser and R. Seiringer, “Energy contribution of a point-interacting impurity
in a Fermi gas,” Annales Henri Poincare, vol. 20, no. 4. Springer, pp.
1325–1365, 2019.
ista: Moser T, Seiringer R. 2019. Energy contribution of a point-interacting impurity
in a Fermi gas. Annales Henri Poincare. 20(4), 1325–1365.
mla: Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting
Impurity in a Fermi Gas.” Annales Henri Poincare, vol. 20, no. 4, Springer,
2019, pp. 1325–1365, doi:10.1007/s00023-018-00757-0.
short: T. Moser, R. Seiringer, Annales Henri Poincare 20 (2019) 1325–1365.
date_created: 2019-01-20T22:59:17Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2023-09-07T12:37:42Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00023-018-00757-0
ec_funded: 1
external_id:
arxiv:
- '1807.00739'
isi:
- '000462444300008'
file:
- access_level: open_access
checksum: 255e42f957a8e2b10aad2499c750a8d6
content_type: application/pdf
creator: dernst
date_created: 2019-01-28T15:27:17Z
date_updated: 2020-07-14T12:47:12Z
file_id: '5894'
file_name: 2019_Annales_Moser.pdf
file_size: 859846
relation: main_file
file_date_updated: 2020-07-14T12:47:12Z
has_accepted_license: '1'
intvolume: ' 20'
isi: 1
issue: '4'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 1325–1365
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P27533_N27
name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Annales Henri Poincare
publication_identifier:
issn:
- '14240637'
publication_status: published
publisher: Springer
quality_controlled: '1'
related_material:
record:
- id: '52'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Energy contribution of a point-interacting impurity in a Fermi gas
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 20
year: '2019'
...
---
_id: '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_processing_charge: No
author:
- first_name: Andreas
full_name: Deuchert, Andreas
id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
last_name: Deuchert
orcid: 0000-0003-3146-6746
- 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:191003372.
apa: Deuchert, A., Mayer, S., & Seiringer, R. (n.d.). The free energy of the
two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372. ArXiv.
chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy
of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv:1910.03372.
ArXiv, n.d.
ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional
dilute Bose gas. I. Lower bound,” arXiv:1910.03372. 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, ArXiv.
short: A. Deuchert, S. Mayer, R. Seiringer, ArXiv:1910.03372 (n.d.).
date_created: 2020-02-26T08:46:40Z
date_published: 2019-10-08T00:00:00Z
date_updated: 2023-09-07T13:12:41Z
day: '08'
department:
- _id: RoSe
ec_funded: 1
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:1910.03372
publication_status: draft
publisher: ArXiv
related_material:
record:
- id: '7790'
relation: later_version
status: public
- id: '7514'
relation: dissertation_contains
status: public
scopus_import: 1
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'
...