---
_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).
date_created: 2023-12-31T23:01:02Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-02T08:51:28Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1063/5.0172199
external_id:
arxiv:
- '2307.11062'
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'
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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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 64
year: '2023'
...
---
_id: '14854'
abstract:
- lang: eng
text: "\r\nAbstract\r\nWe 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
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.
date_created: 2024-01-22T08:24:23Z
date_published: 2023-12-15T00:00:00Z
date_updated: 2024-01-23T12:55:12Z
day: '15'
department:
- _id: RoSe
doi: 10.2140/paa.2023.5.973
intvolume: ' 5'
issue: '4'
keyword:
- General Medicine
language:
- iso: eng
month: '12'
oa_version: None
page: 973-1008
publication: Pure and Applied Analysis
publication_identifier:
issn:
- 2578-5885
- 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '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: '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.
date_created: 2023-07-02T22:00:43Z
date_published: 2023-06-13T00:00:00Z
date_updated: 2023-11-02T12:30:50Z
day: '13'
ddc:
- '500'
department:
- _id: RoSe
doi: 10.1017/fms.2023.45
ec_funded: 1
external_id:
arxiv:
- '2203.02454'
isi:
- '001005008800001'
file:
- access_level: open_access
checksum: f672eb7dd015c472c9a04f1b9bf9df7d
content_type: application/pdf
creator: alisjak
date_created: 2023-07-03T10:36:25Z
date_updated: 2023-07-03T10:36:25Z
file_id: '13186'
file_name: 2023_ForumofMathematics.Sigma_Mitrouskas.pdf
file_size: 943192
relation: main_file
success: 1
file_date_updated: 2023-07-03T10:36:25Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 1-52
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Forum of Mathematics
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
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)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2023'
...
---
_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).
date_created: 2023-08-22T14:09:47Z
date_published: 2023-07-26T00:00:00Z
date_updated: 2023-12-13T12:16:19Z
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: '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: '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.
date_created: 2024-01-28T23:01:43Z
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doi: 10.2140/paa.2021.3.653
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name: Analysis of quantum many-body systems
publication: Pure and Applied Analysis
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title: Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly
coupled polaron
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---
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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."
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author:
- first_name: Nikolai K
full_name: Leopold, Nikolai K
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last_name: Leopold
orcid: 0000-0002-0495-6822
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
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last_name: Mitrouskas
- first_name: Robert
full_name: Seiringer, Robert
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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: 2023-08-07T14:12:27Z
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ddc:
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- _id: RoSe
doi: 10.1007/s00205-021-01616-9
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title: Derivation of the Landau–Pekar equations in a many-body mean-field limit
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---
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abstract:
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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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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).
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title: A note on the Fröhlich dynamics in the strong coupling limit
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