---
DOAJ_listed: '1'
OA_place: repository
OA_type: green
_id: '20045'
abstract:
- lang: eng
text: We consider the time evolution of the renormalized Nelson model, which describes
N bosons linearly coupled to a quantized scalar field, in the mean-field limit
of many particles N≫1 with coupling constant proportional to N^−1/2. First, we
show that initial states exhibiting Bose–Einstein condensation for the particles
and approximating a coherent state for the quantum field retain their structure
under the many-body time evolution. Concretely, the dynamics of the reduced densities
are approximated by solutions of two coupled PDEs, the Schrödinger–Klein–Gordon
equations. Second, we construct a renormalized Bogoliubov evolution that describes
the quantum fluctuations around the Schrödinger–Klein–Gordon equations. This evolution
is used to extend the approximation of the evolved many-body state to the full
norm topology. In summary, we provide a comprehensive analysis of the Nelson model
that reveals the role of renormalization in the mean-field Bogoliubov theory.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marco
full_name: Falconi, Marco
last_name: Falconi
- first_name: Jonas
full_name: Lampart, Jonas
last_name: Lampart
- first_name: Nikolai
full_name: Leopold, Nikolai
last_name: Leopold
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
citation:
ama: Falconi M, Lampart J, Leopold N, Mitrouskas DJ. Renormalized Bogoliubov theory
for the Nelson model. Annales de l’Institut Henri Poincaré C. 2025. doi:10.4171/aihpc/154
apa: Falconi, M., Lampart, J., Leopold, N., & Mitrouskas, D. J. (2025). Renormalized
Bogoliubov theory for the Nelson model. Annales de l’Institut Henri Poincaré
C. EMS Press. https://doi.org/10.4171/aihpc/154
chicago: Falconi, Marco, Jonas Lampart, Nikolai Leopold, and David Johannes Mitrouskas.
“Renormalized Bogoliubov Theory for the Nelson Model.” Annales de l’Institut
Henri Poincaré C. EMS Press, 2025. https://doi.org/10.4171/aihpc/154.
ieee: M. Falconi, J. Lampart, N. Leopold, and D. J. Mitrouskas, “Renormalized Bogoliubov
theory for the Nelson model,” Annales de l’Institut Henri Poincaré C. EMS
Press, 2025.
ista: Falconi M, Lampart J, Leopold N, Mitrouskas DJ. 2025. Renormalized Bogoliubov
theory for the Nelson model. Annales de l’Institut Henri Poincaré C.
mla: Falconi, Marco, et al. “Renormalized Bogoliubov Theory for the Nelson Model.”
Annales de l’Institut Henri Poincaré C, EMS Press, 2025, doi:10.4171/aihpc/154.
short: M. Falconi, J. Lampart, N. Leopold, D.J. Mitrouskas, Annales de l’Institut
Henri Poincaré C (2025).
date_created: 2025-07-21T07:59:16Z
date_published: 2025-05-06T00:00:00Z
date_updated: 2025-12-30T07:31:09Z
day: '06'
department:
- _id: RoSe
doi: 10.4171/aihpc/154
external_id:
arxiv:
- '2305.06722'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2305.06722
month: '05'
oa: 1
oa_version: Preprint
publication: Annales de l'Institut Henri Poincaré C
publication_identifier:
eissn:
- 1873-1430
issn:
- 0294-1449
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
status: public
title: Renormalized Bogoliubov theory for the Nelson model
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '20495'
abstract:
- lang: eng
text: We consider a tracer particle coupled to a Bose scalar field and study the
regime where the field’s propagation speed approaches infinity. For initial states
devoid of field excitations, we introduce an effective approximation of the time-evolved
wave function and prove its validity in Hilbert space norm. In this approximation,
the field remains in the vacuum state, while the tracer particle propagates with
a modified dispersion relation. Physically, the new dispersion relation can be
understood as the effect of radiative corrections due to interactions with virtual
bosons. Mathematically, it is defined as the solution of a self-consistent nonlinear
equation, whose form depends on the relevant time scale.
acknowledgement: E.C. is deeply grateful to Robert Seiringer for his hospitality at
ISTA, without which this project would not have been possible. E.C. is thankful
to Thomas Chen for valuable comments and for pointing out useful references. E.C
gratefully acknowledges support from the Provost’s Graduate Excellence Fellowship
at The University of Texas at Austin and from the NSF grant DMS-2009549, and the
NSF grant DMS-2009800 through T. Chen. This material is based upon work supported
by the National Science Foundation under Grant No. DMS-1928930, while E.C was in
residence at the Simons Laufer Mathematical Sciences Institute in Berkeley, California,
during the Fall 2025 semester.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Esteban
full_name: Cárdenas, Esteban
last_name: Cárdenas
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
citation:
ama: Cárdenas E, Mitrouskas DJ. Radiative corrections to the dynamics of a tracer
particle coupled to a Bose ccalar field. Annales Henri Poincare. 2025.
doi:10.1007/s00023-025-01626-3
apa: Cárdenas, E., & Mitrouskas, D. J. (2025). Radiative corrections to the
dynamics of a tracer particle coupled to a Bose ccalar field. Annales Henri
Poincare. Springer Nature. https://doi.org/10.1007/s00023-025-01626-3
chicago: Cárdenas, Esteban, and David Johannes Mitrouskas. “Radiative Corrections
to the Dynamics of a Tracer Particle Coupled to a Bose Ccalar Field.” Annales
Henri Poincare. Springer Nature, 2025. https://doi.org/10.1007/s00023-025-01626-3.
ieee: E. Cárdenas and D. J. Mitrouskas, “Radiative corrections to the dynamics of
a tracer particle coupled to a Bose ccalar field,” Annales Henri Poincare.
Springer Nature, 2025.
ista: Cárdenas E, Mitrouskas DJ. 2025. Radiative corrections to the dynamics of
a tracer particle coupled to a Bose ccalar field. Annales Henri Poincare.
mla: Cárdenas, Esteban, and David Johannes Mitrouskas. “Radiative Corrections to
the Dynamics of a Tracer Particle Coupled to a Bose Ccalar Field.” Annales
Henri Poincare, Springer Nature, 2025, doi:10.1007/s00023-025-01626-3.
short: E. Cárdenas, D.J. Mitrouskas, Annales Henri Poincare (2025).
date_created: 2025-10-19T22:01:32Z
date_published: 2025-10-03T00:00:00Z
date_updated: 2025-12-01T12:56:12Z
day: '03'
department:
- _id: RoSe
doi: 10.1007/s00023-025-01626-3
external_id:
arxiv:
- '2405.05251'
isi:
- '001586237500001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2405.05251
month: '10'
oa: 1
oa_version: Preprint
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Radiative corrections to the dynamics of a tracer particle coupled to a Bose
ccalar field
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '19372'
abstract:
- lang: eng
text: We consider the confined Fröhlich polaron and establish an asymptotic series
for the low-energy eigenvalues in negative powers of the coupling constant. The
coefficients of the series are derived through a two-fold perturbation approach,
involving expansions around the electron Pekar minimizer and the excitations of
the quantum field.
acknowledgement: M.B. gratefully acknowledges funding from the ERC Advanced Grant
ERC-AdG CLaQS, grant agreement n. 83478.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Morris
full_name: Brooks, Morris
id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
last_name: Brooks
orcid: 0000-0002-6249-0928
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
citation:
ama: Brooks M, Mitrouskas DJ. Asymptotic series for low-energy excitations of the
Fröhlich polaron at strong coupling. Probability and Mathematical Physics.
2025;6(1):281-325. doi:10.2140/pmp.2025.6.281
apa: Brooks, M., & Mitrouskas, D. J. (2025). Asymptotic series for low-energy
excitations of the Fröhlich polaron at strong coupling. Probability and Mathematical
Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2025.6.281
chicago: Brooks, Morris, and David Johannes Mitrouskas. “ Asymptotic Series for
Low-Energy Excitations of the Fröhlich Polaron at Strong Coupling.” Probability
and Mathematical Physics. Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/pmp.2025.6.281.
ieee: M. Brooks and D. J. Mitrouskas, “ Asymptotic series for low-energy excitations
of the Fröhlich polaron at strong coupling,” Probability and Mathematical Physics,
vol. 6, no. 1. Mathematical Sciences Publishers, pp. 281–325, 2025.
ista: Brooks M, Mitrouskas DJ. 2025. Asymptotic series for low-energy excitations
of the Fröhlich polaron at strong coupling. Probability and Mathematical Physics.
6(1), 281–325.
mla: Brooks, Morris, and David Johannes Mitrouskas. “ Asymptotic Series for Low-Energy
Excitations of the Fröhlich Polaron at Strong Coupling.” Probability and Mathematical
Physics, vol. 6, no. 1, Mathematical Sciences Publishers, 2025, pp. 281–325,
doi:10.2140/pmp.2025.6.281.
short: M. Brooks, D.J. Mitrouskas, Probability and Mathematical Physics 6 (2025)
281–325.
corr_author: '1'
date_created: 2025-03-09T23:01:28Z
date_published: 2025-02-23T00:00:00Z
date_updated: 2025-03-10T07:19:02Z
day: '23'
department:
- _id: RoSe
doi: 10.2140/pmp.2025.6.281
external_id:
arxiv:
- '2306.16373'
intvolume: ' 6'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2306.16373
month: '02'
oa: 1
oa_version: Preprint
page: 281-325
publication: Probability and Mathematical Physics
publication_identifier:
eissn:
- 2690-1005
issn:
- 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' Asymptotic series for low-energy excitations of the Fröhlich polaron at strong
coupling'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 6
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19660'
abstract:
- lang: eng
text: We analyze the ground state energy of N fermions in a two-dimensional box
interacting with an impurity particle via two-body point interactions. We show
that for weak coupling, the ground state energy is asymptotically described by
the polaron energy, as proposed by F. Chevy in the physics literature. The polaron
energy is the solution of a nonlinear equation involving the Green’s function
of the free Fermi gas and the binding energy of the two-body point interaction.
We provide quantitative error estimates that are uniform in the thermodynamic
limit.
acknowledgement: The author would like to thank Ulrich Linden for introducing him
to the Fermi polaron and for his valuable contributions in the early stages of this
project. Additionally, the author is grateful to Krzysztof Myśliwy for helpful comments.
Open access funding provided by Institute of Science and Technology (IST Austria).
article_number: '30'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
citation:
ama: Mitrouskas DJ. The weakly coupled two-dimensional Fermi polaron. Archive
for Rational Mechanics and Analysis. 2025;249(3). doi:10.1007/s00205-025-02098-9
apa: Mitrouskas, D. J. (2025). The weakly coupled two-dimensional Fermi polaron.
Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-025-02098-9
chicago: Mitrouskas, David Johannes. “The Weakly Coupled Two-Dimensional Fermi Polaron.”
Archive for Rational Mechanics and Analysis. Springer Nature, 2025. https://doi.org/10.1007/s00205-025-02098-9.
ieee: D. J. Mitrouskas, “The weakly coupled two-dimensional Fermi polaron,” Archive
for Rational Mechanics and Analysis, vol. 249, no. 3. Springer Nature, 2025.
ista: Mitrouskas DJ. 2025. The weakly coupled two-dimensional Fermi polaron. Archive
for Rational Mechanics and Analysis. 249(3), 30.
mla: Mitrouskas, David Johannes. “The Weakly Coupled Two-Dimensional Fermi Polaron.”
Archive for Rational Mechanics and Analysis, vol. 249, no. 3, 30, Springer
Nature, 2025, doi:10.1007/s00205-025-02098-9.
short: D.J. Mitrouskas, Archive for Rational Mechanics and Analysis 249 (2025).
corr_author: '1'
date_created: 2025-05-11T22:02:37Z
date_published: 2025-06-01T00:00:00Z
date_updated: 2025-09-30T12:25:19Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00205-025-02098-9
external_id:
isi:
- '001482770500001'
file:
- access_level: open_access
checksum: 3606ebd34d59d03f8c66a3a1794c3e4f
content_type: application/pdf
creator: dernst
date_created: 2025-05-12T07:27:28Z
date_updated: 2025-05-12T07:27:28Z
file_id: '19676'
file_name: 2025_ArchiveRatioMechanics_Mitrouskas.pdf
file_size: 886318
relation: main_file
success: 1
file_date_updated: 2025-05-12T07:27:28Z
has_accepted_license: '1'
intvolume: ' 249'
isi: 1
issue: '3'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
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 weakly coupled two-dimensional Fermi polaron
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 249
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19661'
abstract:
- lang: eng
text: The Nelson model describes non-relativistic particles coupled to a relativistic
Bose scalar field. In this article, we study the renormalized version of the Nelson
model with massless bosons in Davies' weak coupling limit. Our main result states
that the two-body Coulomb potential emerges as an effective pair interaction between
the particles, which arises from the exchange of virtual excitations of the quantum
field.
acknowledgement: "D M thanks Nataˇsa Pavlovi´c for the invitation to the University
of Texas at Austin and for the\r\nhospitality offered by the department, where part
of this work was performed. E C gratefully\r\nacknowledges support from NSF under
Grant Nos DMS-2009549 and DMS-2052789 through\r\nNataˇsa Pavlovi´"
article_number: '175201'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Esteban
full_name: Cárdenas, Esteban
last_name: Cárdenas
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
citation:
ama: 'Cárdenas E, Mitrouskas DJ. The renormalized Nelson model in the weak coupling
limit. Journal of Physics A: Mathematical and Theoretical. 2025;58(17).
doi:10.1088/1751-8121/adcdd9'
apa: 'Cárdenas, E., & Mitrouskas, D. J. (2025). The renormalized Nelson model
in the weak coupling limit. Journal of Physics A: Mathematical and Theoretical.
IOP Publishing. https://doi.org/10.1088/1751-8121/adcdd9'
chicago: 'Cárdenas, Esteban, and David Johannes Mitrouskas. “The Renormalized Nelson
Model in the Weak Coupling Limit.” Journal of Physics A: Mathematical and Theoretical.
IOP Publishing, 2025. https://doi.org/10.1088/1751-8121/adcdd9.'
ieee: 'E. Cárdenas and D. J. Mitrouskas, “The renormalized Nelson model in the weak
coupling limit,” Journal of Physics A: Mathematical and Theoretical, vol.
58, no. 17. IOP Publishing, 2025.'
ista: 'Cárdenas E, Mitrouskas DJ. 2025. The renormalized Nelson model in the weak
coupling limit. Journal of Physics A: Mathematical and Theoretical. 58(17), 175201.'
mla: 'Cárdenas, Esteban, and David Johannes Mitrouskas. “The Renormalized Nelson
Model in the Weak Coupling Limit.” Journal of Physics A: Mathematical and Theoretical,
vol. 58, no. 17, 175201, IOP Publishing, 2025, doi:10.1088/1751-8121/adcdd9.'
short: 'E. Cárdenas, D.J. Mitrouskas, Journal of Physics A: Mathematical and Theoretical
58 (2025).'
corr_author: '1'
date_created: 2025-05-11T22:02:37Z
date_published: 2025-04-28T00:00:00Z
date_updated: 2025-09-30T12:24:45Z
day: '28'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1088/1751-8121/adcdd9
external_id:
arxiv:
- '2412.01670'
isi:
- '001474094200001'
file:
- access_level: open_access
checksum: a181e1c2d8df08eb683a355e81c5e85a
content_type: application/pdf
creator: dernst
date_created: 2025-05-12T07:13:07Z
date_updated: 2025-05-12T07:13:07Z
file_id: '19675'
file_name: 2025_JourPhysicsA_Cardenas.pdf
file_size: 551190
relation: main_file
success: 1
file_date_updated: 2025-05-12T07:13:07Z
has_accepted_license: '1'
intvolume: ' 58'
isi: 1
issue: '17'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
eissn:
- 1751-8121
issn:
- 1751-8113
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The renormalized Nelson model in the weak coupling limit
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 58
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '21270'
abstract:
- lang: eng
text: "The one-dimensional Fröhlich model describing the motion of a single electron
interacting with optical phonons is a paradigmatic model of quantum many-body
physics. We predict the existence of an arbitrarily large number of bound excited
states in the strong-coupling limit and calculate their excitation energies. Numerical
simulations of a discretized model demonstrate the complete amelioration of the
projector Monte Carlo sign problem by walker annihilation in an infinite Hilbert
space. They reveal the threshold for the occurrence of the first bound excited
states at a value of \U0001D6FC≈1.73 for the dimensionless coupling constant.
This puts the threshold into the regime of intermediate interaction strength.
We find a significant spectral weight and increased phonon number of the bound
excited state at threshold."
acknowledgement: We are grateful to Dmytro Kolisnyk for his help in working out the
spectrum of the Hessian. This work was supported by the Marsden Fund of New Zealand
(Contract No. MAU2007) from government funding administered by the Royal Society
Te Apārangi and by a summer scholarship from Te Whai Ao – Dodd-Walls Centre for
Photonic and Quantum Technologies and the Physics Department, University of Auckland.
We acknowledge support by the New Zealand eScience Infrastructure (NeSI) high-performance
computing facilities in the form of a merit project allocation.
article_number: '184312'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: J.
full_name: Taylor, J.
last_name: Taylor
- first_name: M.
full_name: Čufar, M.
last_name: Čufar
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: E.
full_name: Pahl, E.
last_name: Pahl
- first_name: J.
full_name: Brand, J.
last_name: Brand
citation:
ama: Taylor J, Čufar M, Mitrouskas DJ, Seiringer R, Pahl E, Brand J. Bound excited
states of Fröhlich polarons in one dimension. Physical Review B. 2025;112(18).
doi:10.1103/s9p9-jflq
apa: Taylor, J., Čufar, M., Mitrouskas, D. J., Seiringer, R., Pahl, E., & Brand,
J. (2025). Bound excited states of Fröhlich polarons in one dimension. Physical
Review B. American Physical Society. https://doi.org/10.1103/s9p9-jflq
chicago: Taylor, J., M. Čufar, David Johannes Mitrouskas, Robert Seiringer, E. Pahl,
and J. Brand. “Bound Excited States of Fröhlich Polarons in One Dimension.” Physical
Review B. American Physical Society, 2025. https://doi.org/10.1103/s9p9-jflq.
ieee: J. Taylor, M. Čufar, D. J. Mitrouskas, R. Seiringer, E. Pahl, and J. Brand,
“Bound excited states of Fröhlich polarons in one dimension,” Physical Review
B, vol. 112, no. 18. American Physical Society, 2025.
ista: Taylor J, Čufar M, Mitrouskas DJ, Seiringer R, Pahl E, Brand J. 2025. Bound
excited states of Fröhlich polarons in one dimension. Physical Review B. 112(18),
184312.
mla: Taylor, J., et al. “Bound Excited States of Fröhlich Polarons in One Dimension.”
Physical Review B, vol. 112, no. 18, 184312, American Physical Society,
2025, doi:10.1103/s9p9-jflq.
short: J. Taylor, M. Čufar, D.J. Mitrouskas, R. Seiringer, E. Pahl, J. Brand, Physical
Review B 112 (2025).
date_created: 2026-02-17T07:56:20Z
date_published: 2025-11-18T00:00:00Z
date_updated: 2026-02-18T08:23:59Z
day: '18'
department:
- _id: RoSe
doi: 10.1103/s9p9-jflq
external_id:
arxiv:
- '2506.02440 '
intvolume: ' 112'
issue: '18'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 'https://doi.org/10.48550/arXiv.2506.02440 '
month: '11'
oa: 1
oa_version: Preprint
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: Bound excited states of Fröhlich polarons in one dimension
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 112
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '18948'
abstract:
- lang: eng
text: We consider a gas of N bosons with interactions in the mean-field scaling
regime. We review a recent proof of the asymptotic expansion of its spectrum and
eigenstates and two applications of this result, namely the derivation of an Edgeworth
expansion for fluctuations of one-body operators and the computation of the binding
energy of an inhomogeneous Bose gas to any order. Finally, we collect related
results for the dynamics of the weakly interacting Bose gas and for the regularized
Nelson model.
acknowledgement: It is our pleasure to thank Marco Falconi, Nataša Pavlović, Peter
Pickl, Robert Seiringer and Avy Soffer for the collaboration on the works [11, 13,
14, 21, 33, 39]. L.B. was supported by the German Research Foundation within the
Munich Center of Quantum Science and Technology (EXC 2111). N.L. acknowledges support
from the Swiss National Science Foundation through the NCCR SwissMap and funding
from the European Union’s Horizon 2020 research and innovation programme under the
Marie Skłodowska-Curie grant agreement No 101024712. S.P. acknowledges funding by
the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - project
number 512258249.
alternative_title:
- Fundamental Theories of Physics
article_processing_charge: No
arxiv: 1
author:
- first_name: Lea
full_name: Bossmann, Lea
id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
last_name: Bossmann
orcid: 0000-0002-6854-1343
- first_name: Nikolai
full_name: Leopold, Nikolai
last_name: Leopold
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Sören
full_name: Petrat, Sören
last_name: Petrat
citation:
ama: 'Bossmann L, Leopold N, Mitrouskas DJ, Petrat S. Asymptotic Analysis of the Weakly
Interacting Bose Gas: A Collection of Recent Results and Applications. In: Bassi
A, Goldstein S, Tumulka R, Zanghi N, eds. Physics and the Nature of Reality.
Vol 215. FTPH. Cham: Springer Nature; 2024:307-321. doi:10.1007/978-3-031-45434-9_22'
apa: 'Bossmann, L., Leopold, N., Mitrouskas, D. J., & Petrat, S. (2024). Asymptotic
Analysis of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications.
In A. Bassi, S. Goldstein, R. Tumulka, & N. Zanghi (Eds.), Physics and
the Nature of Reality (Vol. 215, pp. 307–321). Cham: Springer Nature. https://doi.org/10.1007/978-3-031-45434-9_22'
chicago: 'Bossmann, Lea, Nikolai Leopold, David Johannes Mitrouskas, and Sören Petrat.
“Asymptotic Analysis of the Weakly Interacting Bose Gas: A Collection of Recent
Results and Applications.” In Physics and the Nature of Reality, edited
by Angelo Bassi, Sheldon Goldstein, Roderich Tumulka, and Nino Zanghi, 215:307–21.
FTPH. Cham: Springer Nature, 2024. https://doi.org/10.1007/978-3-031-45434-9_22.'
ieee: 'L. Bossmann, N. Leopold, D. J. Mitrouskas, and S. Petrat, “Asymptotic Analysis
of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications,”
in Physics and the Nature of Reality, vol. 215, A. Bassi, S. Goldstein,
R. Tumulka, and N. Zanghi, Eds. Cham: Springer Nature, 2024, pp. 307–321.'
ista: 'Bossmann L, Leopold N, Mitrouskas DJ, Petrat S. 2024.Asymptotic Analysis
of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications.
In: Physics and the Nature of Reality. Fundamental Theories of Physics, vol. 215,
307–321.'
mla: 'Bossmann, Lea, et al. “Asymptotic Analysis of the Weakly Interacting Bose
Gas: A Collection of Recent Results and Applications.” Physics and the Nature
of Reality, edited by Angelo Bassi et al., vol. 215, Springer Nature, 2024,
pp. 307–21, doi:10.1007/978-3-031-45434-9_22.'
short: L. Bossmann, N. Leopold, D.J. Mitrouskas, S. Petrat, in:, A. Bassi, S. Goldstein,
R. Tumulka, N. Zanghi (Eds.), Physics and the Nature of Reality, Springer Nature,
Cham, 2024, pp. 307–321.
date_created: 2025-01-29T10:30:08Z
date_published: 2024-02-04T00:00:00Z
date_updated: 2025-01-29T10:35:10Z
day: '04'
department:
- _id: RoSe
doi: 10.1007/978-3-031-45434-9_22
editor:
- first_name: Angelo
full_name: Bassi, Angelo
last_name: Bassi
- first_name: Sheldon
full_name: Goldstein, Sheldon
last_name: Goldstein
- first_name: Roderich
full_name: Tumulka, Roderich
last_name: Tumulka
- first_name: Nino
full_name: Zanghi, Nino
last_name: Zanghi
external_id:
arxiv:
- '2304.12910'
intvolume: ' 215'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2304.12910
month: '02'
oa: 1
oa_version: Preprint
page: 307-321
place: Cham
publication: Physics and the Nature of Reality
publication_identifier:
eisbn:
- '9783031454349'
eissn:
- 2365-6425
isbn:
- '9783031454332'
issn:
- 0168-1222
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: FTPH
status: public
title: 'Asymptotic Analysis of the Weakly Interacting Bose Gas: A Collection of Recent
Results and Applications'
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 215
year: '2024'
...
---
_id: '15318'
abstract:
- lang: eng
text: We consider a gas of N weakly interacting bosons in the ground state. Such
gases exhibit Bose–Einstein condensation. The binding energy is defined as the
energy it takes to remove one particle from the gas. In this article, we prove
an asymptotic expansion for the binding energy, and compute the first orders explicitly
for the homogeneous gas. Our result addresses in particular a conjecture by Nam
(Lett Math Phys 108(1):141–159, 2018), and provides an asymptotic expansion of
the ionization energy of bosonic atoms.
acknowledgement: "It is a pleasure to thank Phan Thành Nam for helpful discussions
on bosonic atoms. L.B. was supported by the German Research Foundation within the
Munich Center of Quantum Science and Technology (EXC 2111). N.L. gratefully acknowledges
support from the Swiss National Science Foundation through the NCCR SwissMap and
funding from the European Union’s Horizon 2020 research and innovation programme
under the Marie Skłodowska-Curie Grant agreement No 101024712. S.P. acknowledges
funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project
number 512258249.\r\nOpen Access funding enabled and organized by Projekt DEAL."
article_number: '48'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
full_name: Bossmann, Lea
id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
last_name: Bossmann
orcid: 0000-0002-6854-1343
- 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: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- 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: Bossmann L, Leopold NK, Mitrouskas DJ, Petrat SP. A note on the binding energy
for Bosons in the mean-field limit. Journal of Statistical Physics. 2024;191(4).
doi:10.1007/s10955-024-03260-5
apa: Bossmann, L., Leopold, N. K., Mitrouskas, D. J., & Petrat, S. P. (2024).
A note on the binding energy for Bosons in the mean-field limit. Journal of
Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-024-03260-5
chicago: Bossmann, Lea, Nikolai K Leopold, David Johannes Mitrouskas, and Sören
P Petrat. “A Note on the Binding Energy for Bosons in the Mean-Field Limit.” Journal
of Statistical Physics. Springer Nature, 2024. https://doi.org/10.1007/s10955-024-03260-5.
ieee: L. Bossmann, N. K. Leopold, D. J. Mitrouskas, and S. P. Petrat, “A note on
the binding energy for Bosons in the mean-field limit,” Journal of Statistical
Physics, vol. 191, no. 4. Springer Nature, 2024.
ista: Bossmann L, Leopold NK, Mitrouskas DJ, Petrat SP. 2024. A note on the binding
energy for Bosons in the mean-field limit. Journal of Statistical Physics. 191(4),
48.
mla: Bossmann, Lea, et al. “A Note on the Binding Energy for Bosons in the Mean-Field
Limit.” Journal of Statistical Physics, vol. 191, no. 4, 48, Springer Nature,
2024, doi:10.1007/s10955-024-03260-5.
short: L. Bossmann, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Journal of Statistical
Physics 191 (2024).
date_created: 2024-04-14T22:01:02Z
date_published: 2024-04-06T00:00:00Z
date_updated: 2025-09-04T13:36:49Z
day: '06'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s10955-024-03260-5
external_id:
arxiv:
- '2307.13115'
isi:
- '001197663100002'
file:
- access_level: open_access
checksum: 839242a9ec1c01158112de25f196e60d
content_type: application/pdf
creator: dernst
date_created: 2024-04-16T11:09:37Z
date_updated: 2024-04-16T11:09:37Z
file_id: '15325'
file_name: 2024_JourStatPhysics_Bossmann.pdf
file_size: 398665
relation: main_file
success: 1
file_date_updated: 2024-04-16T11:09:37Z
has_accepted_license: '1'
intvolume: ' 191'
isi: 1
issue: '4'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A note on the binding energy for Bosons in the mean-field limit
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 191
year: '2024'
...
---
_id: '14192'
abstract:
- lang: eng
text: For the Fröhlich model of the large polaron, we prove that the ground state
energy as a function of the total momentum has a unique global minimum at momentum
zero. This implies the non-existence of a ground state of the translation invariant
Fröhlich Hamiltonian and thus excludes the possibility of a localization transition
at finite coupling.
acknowledgement: D.M. and K.M. thank Robert Seiringer for helpful discussions. Open
access funding provided by Institute of Science and Technology (IST Austria). Financial
support from the Agence Nationale de la Recherche (ANR) through the projects ANR-17-CE40-0016,
ANR-17-CE40-0007-01, ANR-17-EURE-0002 (J.L.) and from the European Union’s Horizon
2020 research and innovation programme under the Maria Skłodowska-Curie grant agreement
No. 665386 (K.M.) is gratefully acknowledged.
article_number: '17'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jonas
full_name: Lampart, Jonas
last_name: Lampart
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Krzysztof
full_name: Mysliwy, Krzysztof
id: 316457FC-F248-11E8-B48F-1D18A9856A87
last_name: Mysliwy
citation:
ama: Lampart J, Mitrouskas DJ, Mysliwy K. On the global minimum of the energy–momentum
relation for the polaron. Mathematical Physics, Analysis and Geometry.
2023;26(3). doi:10.1007/s11040-023-09460-x
apa: Lampart, J., Mitrouskas, D. J., & Mysliwy, K. (2023). On the global minimum
of the energy–momentum relation for the polaron. Mathematical Physics, Analysis
and Geometry. Springer Nature. https://doi.org/10.1007/s11040-023-09460-x
chicago: Lampart, Jonas, David Johannes Mitrouskas, and Krzysztof Mysliwy. “On the
Global Minimum of the Energy–Momentum Relation for the Polaron.” Mathematical
Physics, Analysis and Geometry. Springer Nature, 2023. https://doi.org/10.1007/s11040-023-09460-x.
ieee: J. Lampart, D. J. Mitrouskas, and K. Mysliwy, “On the global minimum of the
energy–momentum relation for the polaron,” Mathematical Physics, Analysis and
Geometry, vol. 26, no. 3. Springer Nature, 2023.
ista: Lampart J, Mitrouskas DJ, Mysliwy K. 2023. On the global minimum of the energy–momentum
relation for the polaron. Mathematical Physics, Analysis and Geometry. 26(3),
17.
mla: Lampart, Jonas, et al. “On the Global Minimum of the Energy–Momentum Relation
for the Polaron.” Mathematical Physics, Analysis and Geometry, vol. 26,
no. 3, 17, Springer Nature, 2023, doi:10.1007/s11040-023-09460-x.
short: J. Lampart, D.J. Mitrouskas, K. Mysliwy, Mathematical Physics, Analysis and
Geometry 26 (2023).
corr_author: '1'
date_created: 2023-08-22T14:09:47Z
date_published: 2023-07-26T00:00:00Z
date_updated: 2024-10-09T21:06:41Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11040-023-09460-x
external_id:
arxiv:
- '2206.14708'
isi:
- '001032992600001'
file:
- access_level: open_access
checksum: f0941cc66cb3ed06a12ca4b7e356cfd6
content_type: application/pdf
creator: dernst
date_created: 2023-08-23T10:59:15Z
date_updated: 2023-08-23T10:59:15Z
file_id: '14225'
file_name: 2023_MathPhysics_Lampart.pdf
file_size: 317026
relation: main_file
success: 1
file_date_updated: 2023-08-23T10:59:15Z
has_accepted_license: '1'
intvolume: ' 26'
isi: 1
issue: '3'
keyword:
- Geometry and Topology
- Mathematical Physics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
eissn:
- 1572-9656
issn:
- 1385-0172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the global minimum of the energy–momentum relation for the polaron
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: 26
year: '2023'
...
---
_id: '14715'
abstract:
- lang: eng
text: We consider N trapped bosons in the mean-field limit with coupling constant
λN = 1/(N − 1). The ground state of such systems exhibits Bose–Einstein condensation.
We prove that the probability of finding ℓ particles outside the condensate wave
function decays exponentially in ℓ.
acknowledgement: We thank Lea Boßmann, Phan Thành Nam and Simone Rademacher for helpful
remarks. P.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) - Grant No. SFB/TRR 352 “Mathematics of Many-Body Quantum
Systems and Their Collective Phenomena.”
article_number: '121901'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Peter
full_name: Pickl, Peter
last_name: Pickl
citation:
ama: Mitrouskas DJ, Pickl P. Exponential decay of the number of excitations in the
weakly interacting Bose gas. Journal of Mathematical Physics. 2023;64(12).
doi:10.1063/5.0172199
apa: Mitrouskas, D. J., & Pickl, P. (2023). Exponential decay of the number
of excitations in the weakly interacting Bose gas. Journal of Mathematical
Physics. AIP Publishing. https://doi.org/10.1063/5.0172199
chicago: Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the
Number of Excitations in the Weakly Interacting Bose Gas.” Journal of Mathematical
Physics. AIP Publishing, 2023. https://doi.org/10.1063/5.0172199.
ieee: D. J. Mitrouskas and P. Pickl, “Exponential decay of the number of excitations
in the weakly interacting Bose gas,” Journal of Mathematical Physics, vol.
64, no. 12. AIP Publishing, 2023.
ista: Mitrouskas DJ, Pickl P. 2023. Exponential decay of the number of excitations
in the weakly interacting Bose gas. Journal of Mathematical Physics. 64(12), 121901.
mla: Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the Number
of Excitations in the Weakly Interacting Bose Gas.” Journal of Mathematical
Physics, vol. 64, no. 12, 121901, AIP Publishing, 2023, doi:10.1063/5.0172199.
short: D.J. Mitrouskas, P. Pickl, Journal of Mathematical Physics 64 (2023).
corr_author: '1'
date_created: 2023-12-31T23:01:02Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2025-09-09T14:05:28Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1063/5.0172199
external_id:
arxiv:
- '2307.11062'
isi:
- '001127432200002'
file:
- access_level: open_access
checksum: 66572f718a36465576cf0d6b3f7e01fc
content_type: application/pdf
creator: dernst
date_created: 2024-01-02T08:45:07Z
date_updated: 2024-01-02T08:45:07Z
file_id: '14722'
file_name: 2023_JourMathPhysics_Mitrouskas.pdf
file_size: 4346922
relation: main_file
success: 1
file_date_updated: 2024-01-02T08:45:07Z
has_accepted_license: '1'
intvolume: ' 64'
isi: 1
issue: '12'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Exponential decay of the number of excitations in the weakly interacting Bose
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 64
year: '2023'
...
---
_id: '12430'
abstract:
- lang: eng
text: We study the time evolution of the Nelson model in a mean-field limit in which
N nonrelativistic bosons weakly couple (with respect to the particle number) to
a positive or zero mass quantized scalar field. Our main result is the derivation
of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove
the convergence of the approximate wave function to the many-body wave function
in norm, with a convergence rate proportional to the number of corrections taken
into account in the approximation. We prove an analogous result for the unitary
propagator. As an application, we derive a simple system of partial differential
equations describing the time evolution of the first- and second-order approximations
to the one-particle reduced density matrices of the particles and the quantum
field, respectively.
article_number: '2350006'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marco
full_name: Falconi, Marco
last_name: Falconi
- 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: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- 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: Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. Bogoliubov dynamics and higher-order
corrections for the regularized Nelson model. Reviews in Mathematical Physics.
2023;35(4). doi:10.1142/S0129055X2350006X
apa: Falconi, M., Leopold, N. K., Mitrouskas, D. J., & Petrat, S. P. (2023).
Bogoliubov dynamics and higher-order corrections for the regularized Nelson model.
Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X2350006X
chicago: Falconi, Marco, Nikolai K Leopold, David Johannes Mitrouskas, and Sören
P Petrat. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized
Nelson Model.” Reviews in Mathematical Physics. World Scientific Publishing,
2023. https://doi.org/10.1142/S0129055X2350006X.
ieee: M. Falconi, N. K. Leopold, D. J. Mitrouskas, and S. P. Petrat, “Bogoliubov
dynamics and higher-order corrections for the regularized Nelson model,” Reviews
in Mathematical Physics, vol. 35, no. 4. World Scientific Publishing, 2023.
ista: Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. 2023. Bogoliubov dynamics
and higher-order corrections for the regularized Nelson model. Reviews in Mathematical
Physics. 35(4), 2350006.
mla: Falconi, Marco, et al. “Bogoliubov Dynamics and Higher-Order Corrections for
the Regularized Nelson Model.” Reviews in Mathematical Physics, vol. 35,
no. 4, 2350006, World Scientific Publishing, 2023, doi:10.1142/S0129055X2350006X.
short: M. Falconi, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Reviews in Mathematical
Physics 35 (2023).
date_created: 2023-01-29T23:00:59Z
date_published: 2023-01-09T00:00:00Z
date_updated: 2023-08-16T11:47:27Z
day: '09'
department:
- _id: RoSe
doi: 10.1142/S0129055X2350006X
external_id:
arxiv:
- '2110.00458'
isi:
- '000909760300001'
intvolume: ' 35'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2110.00458'
month: '01'
oa: 1
oa_version: Preprint
publication: Reviews in Mathematical Physics
publication_identifier:
issn:
- 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bogoliubov dynamics and higher-order corrections for the regularized Nelson
model
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2023'
...
---
_id: '13178'
abstract:
- lang: eng
text: We consider the large polaron described by the Fröhlich Hamiltonian and study
its energy-momentum relation defined as the lowest possible energy as a function
of the total momentum. Using a suitable family of trial states, we derive an optimal
parabolic upper bound for the energy-momentum relation in the limit of strong
coupling. The upper bound consists of a momentum independent term that agrees
with the predicted two-term expansion for the ground state energy of the strongly
coupled polaron at rest and a term that is quadratic in the momentum with coefficient
given by the inverse of twice the classical effective mass introduced by Landau
and Pekar.
acknowledgement: This research was supported by the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme grant
agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie grant agreement No. 665386
(K.M.).
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Krzysztof
full_name: Mysliwy, Krzysztof
id: 316457FC-F248-11E8-B48F-1D18A9856A87
last_name: Mysliwy
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Mitrouskas DJ, Mysliwy K, Seiringer R. Optimal parabolic upper bound for the
energy-momentum relation of a strongly coupled polaron. Forum of Mathematics.
2023;11:1-52. doi:10.1017/fms.2023.45
apa: Mitrouskas, D. J., Mysliwy, K., & Seiringer, R. (2023). Optimal parabolic
upper bound for the energy-momentum relation of a strongly coupled polaron. Forum
of Mathematics. Cambridge University Press. https://doi.org/10.1017/fms.2023.45
chicago: Mitrouskas, David Johannes, Krzysztof Mysliwy, and Robert Seiringer. “Optimal
Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.”
Forum of Mathematics. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.45.
ieee: D. J. Mitrouskas, K. Mysliwy, and R. Seiringer, “Optimal parabolic upper bound
for the energy-momentum relation of a strongly coupled polaron,” Forum of Mathematics,
vol. 11. Cambridge University Press, pp. 1–52, 2023.
ista: Mitrouskas DJ, Mysliwy K, Seiringer R. 2023. Optimal parabolic upper bound
for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics.
11, 1–52.
mla: Mitrouskas, David Johannes, et al. “Optimal Parabolic Upper Bound for the Energy-Momentum
Relation of a Strongly Coupled Polaron.” Forum of Mathematics, vol. 11,
Cambridge University Press, 2023, pp. 1–52, doi:10.1017/fms.2023.45.
short: D.J. Mitrouskas, K. Mysliwy, R. Seiringer, Forum of Mathematics 11 (2023)
1–52.
corr_author: '1'
date_created: 2023-07-02T22:00:43Z
date_published: 2023-06-13T00:00:00Z
date_updated: 2025-04-14T07:26:58Z
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- '500'
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doi: 10.1017/fms.2023.45
ec_funded: 1
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publication: Forum of Mathematics
publication_identifier:
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publisher: Cambridge University Press
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title: Optimal parabolic upper bound for the energy-momentum relation of a strongly
coupled polaron
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)
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type: journal_article
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---
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abstract:
- lang: eng
text: We study the spectrum of the Fröhlich Hamiltonian for the polaron at fixed
total momentum. We prove the existence of excited eigenvalues between the ground
state energy and the essential spectrum at strong coupling. In fact, our main
result shows that the number of excited energy bands diverges in the strong coupling
limit. To prove this we derive upper bounds for the min-max values of the corresponding
fiber Hamiltonians and compare them with the bottom of the essential spectrum,
a lower bound on which was recently obtained by Brooks and Seiringer (Comm. Math.
Phys. 404:1 (2023), 287–337). The upper bounds are given in terms of the ground
state energy band shifted by momentum-independent excitation energies determined
by an effective Hamiltonian of Bogoliubov type.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Mitrouskas DJ, Seiringer R. Ubiquity of bound states for the strongly coupled
polaron. Pure and Applied Analysis. 2023;5(4):973-1008. doi:10.2140/paa.2023.5.973
apa: Mitrouskas, D. J., & Seiringer, R. (2023). Ubiquity of bound states for
the strongly coupled polaron. Pure and Applied Analysis. Mathematical Sciences
Publishers. https://doi.org/10.2140/paa.2023.5.973
chicago: Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States
for the Strongly Coupled Polaron.” Pure and Applied Analysis. Mathematical
Sciences Publishers, 2023. https://doi.org/10.2140/paa.2023.5.973.
ieee: D. J. Mitrouskas and R. Seiringer, “Ubiquity of bound states for the strongly
coupled polaron,” Pure and Applied Analysis, vol. 5, no. 4. Mathematical
Sciences Publishers, pp. 973–1008, 2023.
ista: Mitrouskas DJ, Seiringer R. 2023. Ubiquity of bound states for the strongly
coupled polaron. Pure and Applied Analysis. 5(4), 973–1008.
mla: Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States
for the Strongly Coupled Polaron.” Pure and Applied Analysis, vol. 5, no.
4, Mathematical Sciences Publishers, 2023, pp. 973–1008, doi:10.2140/paa.2023.5.973.
short: D.J. Mitrouskas, R. Seiringer, Pure and Applied Analysis 5 (2023) 973–1008.
corr_author: '1'
date_created: 2024-01-22T08:24:23Z
date_published: 2023-12-15T00:00:00Z
date_updated: 2025-04-23T14:21:39Z
day: '15'
department:
- _id: RoSe
doi: 10.2140/paa.2023.5.973
external_id:
arxiv:
- '2211.03606'
intvolume: ' 5'
issue: '4'
keyword:
- General Medicine
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2211.03606
month: '12'
oa: 1
oa_version: Preprint
page: 973-1008
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: Ubiquity of bound states for the strongly coupled polaron
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2023'
...
---
_id: '14889'
abstract:
- lang: eng
text: We consider the Fröhlich Hamiltonian with large coupling constant α. For initial
data of Pekar product form with coherent phonon field and with the electron minimizing
the corresponding energy, we provide a norm approximation of the evolution, valid
up to times of order α2. The approximation is given in terms of a Pekar product
state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics
taking quantum fluctuations into account. This allows us to show that the Landau-Pekar
equations approximately describe the evolution of the electron- and one-phonon
reduced density matrices under the Fröhlich dynamics up to times of order α2.
acknowledgement: "Financial support by the European Union’s Horizon 2020 research
and innovation programme\r\nunder the Marie Skłodowska-Curie grant agreement No.
754411 (S.R.) and the European\r\nResearch Council under grant agreement No. 694227
(N.L. and R.S.), as well as by the SNSF\r\nEccellenza project PCEFP2 181153 (N.L.),
the NCCR SwissMAP (N.L. and B.S.) and by the\r\nDeutsche Forschungsgemeinschaft
(DFG) through the Research Training Group 1838: Spectral\r\nTheory and Dynamics
of Quantum Systems (D.M.) is gratefully acknowledged. B.S. gratefully\r\nacknowledges
financial support from the Swiss National Science Foundation through the Grant\r\n“Dynamical
and energetic properties of Bose-Einstein condensates” and from the European\r\nResearch
Council through the ERC-AdG CLaQS (grant agreement No 834782). D.M. thanks\r\nMarcel
Griesemer for helpful discussions."
article_processing_charge: No
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: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. Landau–Pekar
equations and quantum fluctuations for the dynamics of a strongly coupled polaron.
Pure and Applied Analysis. 2021;3(4):653-676. doi:10.2140/paa.2021.3.653
apa: Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., &
Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the
dynamics of a strongly coupled polaron. Pure and Applied Analysis. Mathematical
Sciences Publishers. https://doi.org/10.2140/paa.2021.3.653
chicago: Leopold, Nikolai K, David Johannes Mitrouskas, Simone Anna Elvira Rademacher,
Benjamin Schlein, and Robert Seiringer. “Landau–Pekar Equations and Quantum Fluctuations
for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis.
Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/paa.2021.3.653.
ieee: N. K. Leopold, D. J. Mitrouskas, S. A. E. Rademacher, B. Schlein, and R. Seiringer,
“Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly
coupled polaron,” Pure and Applied Analysis, vol. 3, no. 4. Mathematical
Sciences Publishers, pp. 653–676, 2021.
ista: Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. 2021. Landau–Pekar
equations and quantum fluctuations for the dynamics of a strongly coupled polaron.
Pure and Applied Analysis. 3(4), 653–676.
mla: Leopold, Nikolai K., et al. “Landau–Pekar Equations and Quantum Fluctuations
for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis,
vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:10.2140/paa.2021.3.653.
short: N.K. Leopold, D.J. Mitrouskas, S.A.E. Rademacher, B. Schlein, R. Seiringer,
Pure and Applied Analysis 3 (2021) 653–676.
corr_author: '1'
date_created: 2024-01-28T23:01:43Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2021.3.653
ec_funded: 1
external_id:
arxiv:
- '2005.02098'
intvolume: ' 3'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2005.02098
month: '10'
oa: 1
oa_version: Preprint
page: 653-676
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
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: Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly
coupled polaron
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2021'
...
---
_id: '9246'
abstract:
- lang: eng
text: We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic
particles weakly couple to the quantized phonon field. For large particle numbers
and a suitably small coupling, we show that the dynamics of the system is approximately
described by the Landau–Pekar equations. These describe a Bose–Einstein condensate
interacting with a classical polarization field, whose dynamics is effected by
the condensate, i.e., the back-reaction of the phonons that are created by the
particles during the time evolution is of leading order.
acknowledgement: "Financial support by the European Research Council (ERC) under the\r\nEuropean
Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo 694227;
N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the\r\nDeutsche
Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral\r\nTheory
and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.\r\ngratefully
acknowledges support from the NCCRSwissMAP and would like to thank Simone\r\nRademacher
and Benjamin Schlein for interesting discussions about the time-evolution of\r\nthe
polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for\r\nextensive
discussions about the Fröhlich polaron."
article_processing_charge: No
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: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Leopold NK, Mitrouskas DJ, Seiringer R. Derivation of the Landau–Pekar equations
in a many-body mean-field limit. Archive for Rational Mechanics and Analysis.
2021;240:383-417. doi:10.1007/s00205-021-01616-9
apa: Leopold, N. K., Mitrouskas, D. J., & Seiringer, R. (2021). Derivation of
the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational
Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01616-9
chicago: Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation
of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” Archive for
Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01616-9.
ieee: N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar
equations in a many-body mean-field limit,” Archive for Rational Mechanics
and Analysis, vol. 240. Springer Nature, pp. 383–417, 2021.
ista: Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar
equations in a many-body mean-field limit. Archive for Rational Mechanics and
Analysis. 240, 383–417.
mla: Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a
Many-Body Mean-Field Limit.” Archive for Rational Mechanics and Analysis,
vol. 240, Springer Nature, 2021, pp. 383–417, doi:10.1007/s00205-021-01616-9.
short: N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics
and Analysis 240 (2021) 383–417.
date_created: 2021-03-14T23:01:34Z
date_published: 2021-02-26T00:00:00Z
date_updated: 2025-06-12T06:35:22Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-021-01616-9
ec_funded: 1
external_id:
arxiv:
- '2001.03993'
isi:
- '000622226200001'
pmid:
- '33785964'
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checksum: 23449e44dc5132501a5c86e70638800f
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creator: dernst
date_created: 2021-03-22T08:31:29Z
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oa_version: Published Version
page: 383-417
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project:
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call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body 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'
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title: Derivation of the Landau–Pekar equations in a many-body mean-field limit
tmp:
image: /images/cc_by.png
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---
_id: '9333'
abstract:
- lang: eng
text: We revise a previous result about the Fröhlich dynamics in the strong coupling
limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter
it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα,
where φ0 is the electron ground state of the Pekar energy functional and ξα the
associated coherent state of the phonons, can be approximated by a global phase
for times small compared to α2. In the present note we prove that a similar approximation
holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons
that is generated by an operator proportional to α−2 and quadratic in creation
and annihilation operators. Our result implies that the electron ground state
remains close to its initial state for times of order α2, while the phonon fluctuations
around the coherent state ξα can be described by a time-dependent Bogoliubov transformation.
acknowledgement: 'I thank Marcel Griesemer for many interesting discussions about
the Fröhlich polaron and also for valuable comments on this manuscript. Helpful
discussions with Nikolai Leopold and Robert Seiringer are also gratefully acknowledged.
This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG) through
the Research Training Group 1838: Spectral Theory and Dynamics of Quantum Systems.
Open Access funding enabled and organized by Projekt DEAL.'
article_number: '45'
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article_type: original
author:
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
citation:
ama: Mitrouskas DJ. A note on the Fröhlich dynamics in the strong coupling limit.
Letters in Mathematical Physics. 2021;111. doi:10.1007/s11005-021-01380-7
apa: Mitrouskas, D. J. (2021). A note on the Fröhlich dynamics in the strong coupling
limit. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01380-7
chicago: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong
Coupling Limit.” Letters in Mathematical Physics. Springer Nature, 2021.
https://doi.org/10.1007/s11005-021-01380-7.
ieee: D. J. Mitrouskas, “A note on the Fröhlich dynamics in the strong coupling
limit,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021.
ista: Mitrouskas DJ. 2021. A note on the Fröhlich dynamics in the strong coupling
limit. Letters in Mathematical Physics. 111, 45.
mla: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong
Coupling Limit.” Letters in Mathematical Physics, vol. 111, 45, Springer
Nature, 2021, doi:10.1007/s11005-021-01380-7.
short: D.J. Mitrouskas, Letters in Mathematical Physics 111 (2021).
date_created: 2021-04-18T22:01:41Z
date_published: 2021-04-05T00:00:00Z
date_updated: 2026-04-02T13:58:00Z
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issn:
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publisher: Springer Nature
quality_controlled: '1'
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title: A note on the Fröhlich dynamics in the strong coupling limit
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...