---
OA_place: publisher
_id: '14374'
abstract:
- lang: eng
text: "Superconductivity has many important applications ranging from levitating
trains over qubits to MRI scanners. The phenomenon is successfully modeled by
Bardeen-Cooper-Schrieffer (BCS) theory. From a mathematical perspective, BCS theory
has been studied extensively for systems without boundary. However, little is
known in the presence of boundaries. With the help of numerical methods physicists
observed that the critical temperature may increase in the presence of a boundary.
The goal of this thesis is to understand the influence of boundaries on the critical
temperature in BCS theory and to give a first rigorous justification of these
observations. On the way, we also study two-body Schrödinger operators on domains
with boundaries and prove additional results for superconductors without boundary.\r\n\r\nBCS
theory is based on a non-linear functional, where the minimizer indicates whether
the system is superconducting or in the normal, non-superconducting state. By
considering the Hessian of the BCS functional at the normal state, one can analyze
whether the normal state is possibly a minimum of the BCS functional and estimate
the critical temperature. The Hessian turns out to be a linear operator resembling
a Schrödinger operator for two interacting particles, but with more complicated
kinetic energy. As a first step, we study the two-body Schrödinger operator in
the presence of boundaries.\r\nFor Neumann boundary conditions, we prove that
the addition of a boundary can create new eigenvalues, which correspond to the
two particles forming a bound state close to the boundary.\r\n\r\nSecond, we need
to understand superconductivity in the translation invariant setting. While in
three dimensions this has been extensively studied, there is no mathematical literature
for the one and two dimensional cases. In dimensions one and two, we compute the
weak coupling asymptotics of the critical temperature and the energy gap in the
translation invariant setting. We also prove that their ratio is independent of
the microscopic details of the model in the weak coupling limit; this property
is referred to as universality.\r\n\r\nIn the third part, we study the critical
temperature of superconductors in the presence of boundaries. We start by considering
the one-dimensional case of a half-line with contact interaction. Then, we generalize
the results to generic interactions and half-spaces in one, two and three dimensions.
Finally, we compare the critical temperature of a quarter space in two dimensions
to the critical temperatures of a half-space and of the full space."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Barbara
full_name: Roos, Barbara
id: 5DA90512-D80F-11E9-8994-2E2EE6697425
last_name: Roos
orcid: 0000-0002-9071-5880
citation:
ama: Roos B. Boundary superconductivity in BCS theory. 2023. doi:10.15479/at:ista:14374
apa: Roos, B. (2023). Boundary superconductivity in BCS theory. Institute
of Science and Technology Austria. https://doi.org/10.15479/at:ista:14374
chicago: Roos, Barbara. “Boundary Superconductivity in BCS Theory.” Institute of
Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14374.
ieee: B. Roos, “Boundary superconductivity in BCS theory,” Institute of Science
and Technology Austria, 2023.
ista: Roos B. 2023. Boundary superconductivity in BCS theory. Institute of Science
and Technology Austria.
mla: Roos, Barbara. Boundary Superconductivity in BCS Theory. Institute of
Science and Technology Austria, 2023, doi:10.15479/at:ista:14374.
short: B. Roos, Boundary Superconductivity in BCS Theory, Institute of Science and
Technology Austria, 2023.
corr_author: '1'
date_created: 2023-09-28T14:23:04Z
date_published: 2023-09-30T00:00:00Z
date_updated: 2026-04-07T13:27:39Z
day: '30'
ddc:
- '515'
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: RoSe
doi: 10.15479/at:ista:14374
ec_funded: 1
file:
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creator: broos
date_created: 2023-10-06T11:35:56Z
date_updated: 2023-10-06T11:35:56Z
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file_size: 4691734
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has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '09'
oa: 1
oa_version: Published Version
page: '206'
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b
grant_number: I06427
name: Mathematical Challenges in BCS Theory of Superconductivity
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10850'
relation: part_of_dissertation
status: public
- id: '13207'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
title: Boundary superconductivity in BCS theory
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2023'
...
---
_id: '14441'
abstract:
- lang: eng
text: We study the Fröhlich polaron model in R3, and establish the subleading term
in the strong coupling asymptotics of its ground state energy, corresponding to
the quantum corrections to the classical energy determined by the Pekar approximation.
acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation
programme under the ERC grant agreement No 694227 is acknowledged. Open access funding
provided by Institute of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
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: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Brooks M, Seiringer R. The Fröhlich Polaron at strong coupling: Part I - The
quantum correction to the classical energy. Communications in Mathematical
Physics. 2023;404:287-337. doi:10.1007/s00220-023-04841-3'
apa: 'Brooks, M., & Seiringer, R. (2023). The Fröhlich Polaron at strong coupling:
Part I - The quantum correction to the classical energy. Communications in
Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04841-3'
chicago: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong
Coupling: Part I - The Quantum Correction to the Classical Energy.” Communications
in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04841-3.'
ieee: 'M. Brooks and R. Seiringer, “The Fröhlich Polaron at strong coupling: Part
I - The quantum correction to the classical energy,” Communications in Mathematical
Physics, vol. 404. Springer Nature, pp. 287–337, 2023.'
ista: 'Brooks M, Seiringer R. 2023. The Fröhlich Polaron at strong coupling: Part
I - The quantum correction to the classical energy. Communications in Mathematical
Physics. 404, 287–337.'
mla: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling:
Part I - The Quantum Correction to the Classical Energy.” Communications in
Mathematical Physics, vol. 404, Springer Nature, 2023, pp. 287–337, doi:10.1007/s00220-023-04841-3.'
short: M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023)
287–337.
corr_author: '1'
date_created: 2023-10-22T22:01:13Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2025-09-09T13:12:02Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00220-023-04841-3
ec_funded: 1
external_id:
arxiv:
- '2207.03156'
isi:
- '001096217400007'
file:
- access_level: open_access
checksum: 1ae49b39247cb6b40ff75997381581b8
content_type: application/pdf
creator: dernst
date_created: 2023-10-31T12:21:39Z
date_updated: 2023-10-31T12:21:39Z
file_id: '14477'
file_name: 2023_CommMathPhysics_Brooks.pdf
file_size: 832375
relation: main_file
success: 1
file_date_updated: 2023-10-31T12:21:39Z
fulldoi: https://doi.org/10.1007/s00220-023-04841-3
has_accepted_license: '1'
intvolume: ' 404'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '11'
oa: 1
oa_version: Published Version
page: 287-337
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The Fröhlich Polaron at strong coupling: Part I - The quantum correction to
the classical energy'
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: 404
year: '2023'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: diamond
_id: '14662'
abstract:
- lang: eng
text: We consider a class of polaron models, including the Fröhlich model, at zero
total momentum, and show that at sufficiently weak coupling there are no excited
eigenvalues below the essential spectrum.
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Seiringer R. Absence of excited eigenvalues for Fröhlich type polaron models
at weak coupling. Journal of Spectral Theory. 2023;13(3):1045-1055. doi:10.4171/JST/469
apa: Seiringer, R. (2023). Absence of excited eigenvalues for Fröhlich type polaron
models at weak coupling. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/JST/469
chicago: Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron
Models at Weak Coupling.” Journal of Spectral Theory. EMS Press, 2023.
https://doi.org/10.4171/JST/469.
ieee: R. Seiringer, “Absence of excited eigenvalues for Fröhlich type polaron models
at weak coupling,” Journal of Spectral Theory, vol. 13, no. 3. EMS Press,
pp. 1045–1055, 2023.
ista: Seiringer R. 2023. Absence of excited eigenvalues for Fröhlich type polaron
models at weak coupling. Journal of Spectral Theory. 13(3), 1045–1055.
mla: Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron
Models at Weak Coupling.” Journal of Spectral Theory, vol. 13, no. 3, EMS
Press, 2023, pp. 1045–55, doi:10.4171/JST/469.
short: R. Seiringer, Journal of Spectral Theory 13 (2023) 1045–1055.
corr_author: '1'
date_created: 2023-12-10T23:00:59Z
date_published: 2023-11-25T00:00:00Z
date_updated: 2025-09-09T13:40:33Z
day: '25'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.4171/JST/469
external_id:
arxiv:
- '2210.17123'
isi:
- '001127467700008'
file:
- access_level: open_access
checksum: 9ce96ca87d56ea9a70d2eb9a32839f8d
content_type: application/pdf
creator: dernst
date_created: 2023-12-11T12:03:12Z
date_updated: 2023-12-11T12:03:12Z
file_id: '14677'
file_name: 2023_JST_Seiringer.pdf
file_size: 201513
relation: main_file
success: 1
file_date_updated: 2023-12-11T12:03:12Z
fulldoi: https://doi.org/10.4171/JST/469
has_accepted_license: '1'
intvolume: ' 13'
isi: 1
issue: '3'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 1045-1055
publication: Journal of Spectral Theory
publication_identifier:
eissn:
- 1664-0403
issn:
- 1664-039X
publication_status: published
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling
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: 13
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
fulldoi: https://doi.org/10.1063/5.0172199
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'
...
---
OA_place: repository
OA_type: green
_id: '14854'
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'
fulldoi: https://doi.org/10.2140/paa.2023.5.973
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: '14992'
abstract:
- lang: eng
text: In this chapter we first review the Levy–Lieb functional, which gives the
lowest kinetic and interaction energy that can be reached with all possible quantum
states having a given density. We discuss two possible convex generalizations
of this functional, corresponding to using mixed canonical and grand-canonical
states, respectively. We present some recent works about the local density approximation,
in which the functionals get replaced by purely local functionals constructed
using the uniform electron gas energy per unit volume. We then review the known
upper and lower bounds on the Levy–Lieb functionals. We start with the kinetic
energy alone, then turn to the classical interaction alone, before we are able
to put everything together. A later section is devoted to the Hohenberg–Kohn theorem
and the role of many-body unique continuation in its proof.
alternative_title:
- Mathematics and Molecular Modeling
article_processing_charge: No
arxiv: 1
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Elliott H.
full_name: Lieb, Elliott H.
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Lewin M, Lieb EH, Seiringer R. Universal Functionals in Density Functional
Theory. In: Cances E, Friesecke G, eds. Density Functional Theory. 1st
ed. MAMOMO. Springer; 2023:115-182. doi:10.1007/978-3-031-22340-2_3'
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2023). Universal Functionals in
Density Functional Theory. In E. Cances & G. Friesecke (Eds.), Density
Functional Theory (1st ed., pp. 115–182). Springer. https://doi.org/10.1007/978-3-031-22340-2_3
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Universal Functionals
in Density Functional Theory.” In Density Functional Theory, edited by
Eric Cances and Gero Friesecke, 1st ed., 115–82. MAMOMO. Springer, 2023. https://doi.org/10.1007/978-3-031-22340-2_3.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Universal Functionals in Density
Functional Theory,” in Density Functional Theory, 1st ed., E. Cances and
G. Friesecke, Eds. Springer, 2023, pp. 115–182.
ista: 'Lewin M, Lieb EH, Seiringer R. 2023.Universal Functionals in Density Functional
Theory. In: Density Functional Theory. Mathematics and Molecular Modeling, , 115–182.'
mla: Lewin, Mathieu, et al. “Universal Functionals in Density Functional Theory.”
Density Functional Theory, edited by Eric Cances and Gero Friesecke, 1st
ed., Springer, 2023, pp. 115–82, doi:10.1007/978-3-031-22340-2_3.
short: M. Lewin, E.H. Lieb, R. Seiringer, in:, E. Cances, G. Friesecke (Eds.), Density
Functional Theory, 1st ed., Springer, 2023, pp. 115–182.
date_created: 2024-02-14T14:44:33Z
date_published: 2023-07-19T00:00:00Z
date_updated: 2024-02-20T08:33:06Z
day: '19'
department:
- _id: RoSe
doi: 10.1007/978-3-031-22340-2_3
edition: '1'
editor:
- first_name: Eric
full_name: Cances, Eric
last_name: Cances
- first_name: Gero
full_name: Friesecke, Gero
last_name: Friesecke
external_id:
arxiv:
- '1912.10424'
fulldoi: https://doi.org/10.1007/978-3-031-22340-2_3
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1912.10424
month: '07'
oa: 1
oa_version: Preprint
page: 115-182
publication: Density Functional Theory
publication_identifier:
eisbn:
- '9783031223402'
isbn:
- '9783031223396'
issn:
- 3005-0286
publication_status: published
publisher: Springer
quality_controlled: '1'
series_title: MAMOMO
status: public
title: Universal Functionals in Density Functional Theory
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '17074'
abstract:
- lang: eng
text: We verify Bogoliubov's approximation for translation invariant Bose gases
in the mean field regime, i.e. we prove that the ground state energy EN is given
by EN=NeH+infσ(H)+oN→∞(1), where N is the number of particles, eH is the minimal
Hartree energy and H is the Bogoliubov Hamiltonian. As an intermediate result
we show the existence of approximate ground states ΨN, i.e. states satisfying
⟨HN⟩ΨN=EN+oN→∞(1), exhibiting complete Bose--Einstein condensation with respect
to one of the Hartree minimizers.
acknowledgement: "We are grateful to Rupert Frank for helpful discussions at an early
stage of this project.\r\nFunding from the European Union’s Horizon 2020 research
and innovation programme\r\nunder the ERC grant agreement No 694227 is acknowledged."
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: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Brooks M, Seiringer R. Validity of Bogoliubov’s approximation fortranslation-invariant
Bose gases. Probability and Mathematical Physics. 2023;3(4):939-1000. doi:10.2140/pmp.2022.3.939
apa: Brooks, M., & Seiringer, R. (2023). Validity of Bogoliubov’s approximation
fortranslation-invariant Bose gases. Probability and Mathematical Physics.
Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2022.3.939
chicago: Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation
Fortranslation-Invariant Bose Gases.” Probability and Mathematical Physics.
Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/pmp.2022.3.939.
ieee: M. Brooks and R. Seiringer, “Validity of Bogoliubov’s approximation fortranslation-invariant
Bose gases,” Probability and Mathematical Physics, vol. 3, no. 4. Mathematical
Sciences Publishers, pp. 939–1000, 2023.
ista: Brooks M, Seiringer R. 2023. Validity of Bogoliubov’s approximation fortranslation-invariant
Bose gases. Probability and Mathematical Physics. 3(4), 939–1000.
mla: Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation
Fortranslation-Invariant Bose Gases.” Probability and Mathematical Physics,
vol. 3, no. 4, Mathematical Sciences Publishers, 2023, pp. 939–1000, doi:10.2140/pmp.2022.3.939.
short: M. Brooks, R. Seiringer, Probability and Mathematical Physics 3 (2023) 939–1000.
corr_author: '1'
date_created: 2024-05-29T06:12:54Z
date_published: 2023-02-21T00:00:00Z
date_updated: 2025-04-14T07:26:59Z
day: '21'
department:
- _id: RoSe
doi: 10.2140/pmp.2022.3.939
ec_funded: 1
external_id:
arxiv:
- '2111.13864'
fulldoi: https://doi.org/10.2140/pmp.2022.3.939
intvolume: ' 3'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2111.13864
month: '02'
oa: 1
oa_version: Preprint
page: 939-1000
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
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: Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2023'
...
---
_id: '10850'
abstract:
- lang: eng
text: "We study two interacting quantum particles forming a bound state in d-dimensional
free\r\nspace, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with
Neumann boundary\r\nconditions. First, we prove that the ground state energy strictly
decreases upon going from k\r\nto k+1. This shows that the particles stick to
the corner where all boundary planes intersect.\r\nSecond, we show that for all
k the resulting Hamiltonian, after removing the free part of the\r\nkinetic energy,
has only finitely many eigenvalues below the essential spectrum. This paper\r\ngeneralizes
the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444,\r\n2020)
to dimensions d > 1."
acknowledgement: We thank Rupert Frank for contributing Appendix B. Funding from the
European Union's Horizon 2020 research and innovation programme under the ERC grant
agreement No. 694227 is gratefully acknowledged.
article_number: '109455'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Barbara
full_name: Roos, Barbara
id: 5DA90512-D80F-11E9-8994-2E2EE6697425
last_name: Roos
orcid: 0000-0002-9071-5880
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Roos B, Seiringer R. Two-particle bound states at interfaces and corners. Journal
of Functional Analysis. 2022;282(12). doi:10.1016/j.jfa.2022.109455
apa: Roos, B., & Seiringer, R. (2022). Two-particle bound states at interfaces
and corners. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109455
chicago: Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces
and Corners.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109455.
ieee: B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,”
Journal of Functional Analysis, vol. 282, no. 12. Elsevier, 2022.
ista: Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners.
Journal of Functional Analysis. 282(12), 109455.
mla: Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces
and Corners.” Journal of Functional Analysis, vol. 282, no. 12, 109455,
Elsevier, 2022, doi:10.1016/j.jfa.2022.109455.
short: B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022).
corr_author: '1'
date_created: 2022-03-16T08:41:53Z
date_published: 2022-06-15T00:00:00Z
date_updated: 2026-04-07T13:27:39Z
day: '15'
ddc:
- '510'
department:
- _id: GradSch
- _id: RoSe
doi: 10.1016/j.jfa.2022.109455
ec_funded: 1
external_id:
arxiv:
- '2105.04874'
isi:
- '000795160200009'
file:
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checksum: 63efcefaa1f2717244ef5407bd564426
content_type: application/pdf
creator: dernst
date_created: 2022-08-02T10:37:55Z
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file_size: 631391
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file_date_updated: 2022-08-02T10:37:55Z
fulldoi: https://doi.org/10.1016/j.jfa.2022.109455
has_accepted_license: '1'
intvolume: ' 282'
isi: 1
issue: '12'
keyword:
- Analysis
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '14374'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Two-particle bound states at interfaces and corners
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 282
year: '2022'
...
---
OA_place: publisher
_id: '11473'
abstract:
- lang: eng
text: "The polaron model is a basic model of quantum field theory describing a single
particle\r\ninteracting with a bosonic field. It arises in many physical contexts.
We are mostly concerned\r\nwith models applicable in the context of an impurity
atom in a Bose-Einstein condensate as\r\nwell as the problem of electrons moving
in polar crystals.\r\nThe model has a simple structure in which the interaction
of the particle with the field is given\r\nby a term linear in the field’s creation
and annihilation operators. In this work, we investigate\r\nthe properties of
this model by providing rigorous estimates on various energies relevant to the\r\nproblem.
The estimates are obtained, for the most part, by suitable operator techniques
which\r\nconstitute the principal mathematical substance of the thesis.\r\nThe
first application of these techniques is to derive the polaron model rigorously
from first\r\nprinciples, i.e., from a full microscopic quantum-mechanical many-body
problem involving an\r\nimpurity in an otherwise homogeneous system. We accomplish
this for the N + 1 Bose gas\r\nin the mean-field regime by showing that a suitable
polaron-type Hamiltonian arises at weak\r\ninteractions as a low-energy effective
theory for this problem.\r\nIn the second part, we investigate rigorously the
ground state of the model at fixed momentum\r\nand for large values of the coupling
constant. Qualitatively, the system is expected to display\r\na transition from
the quasi-particle behavior at small momenta, where the dispersion relation\r\nis
parabolic and the particle moves through the medium dragging along a cloud of
phonons, to\r\nthe radiative behavior at larger momenta where the polaron decelerates
and emits free phonons.\r\nAt the same time, in the strong coupling regime, the
bosonic field is expected to behave purely\r\nclassically. Accordingly, the effective
mass of the polaron at strong coupling is conjectured to\r\nbe asymptotically
equal to the one obtained from the semiclassical counterpart of the problem,\r\nfirst
studied by Landau and Pekar in the 1940s. For polaron models with regularized
form\r\nfactors and phonon dispersion relations of superfluid type, i.e., bounded
below by a linear\r\nfunction of the wavenumbers for all phonon momenta as in
the interacting Bose gas, we prove\r\nthat for a large window of momenta below
the radiation threshold, the energy-momentum\r\nrelation at strong coupling is
indeed essentially a parabola with semi-latus rectum equal to the\r\nLandau–Pekar
effective mass, as expected.\r\nFor the Fröhlich polaron describing electrons
in polar crystals where the dispersion relation is\r\nof the optical type and
the form factor is formally UV–singular due to the nature of the point\r\ncharge-dipole
interaction, we are able to give the corresponding upper bound. In contrast to\r\nthe
regular case, this requires the inclusion of the quantum fluctuations of the phonon
field,\r\nwhich makes the problem considerably more difficult.\r\nThe results
are supplemented by studies on the absolute ground-state energy at strong coupling,\r\na
proof of the divergence of the effective mass with the coupling constant for a
wide class of\r\npolaron models, as well as the discussion of the apparent UV
singularity of the Fröhlich model\r\nand the application of the techniques used
for its removal for the energy estimates.\r\n"
acknowledged_ssus:
- _id: SSU
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Krzysztof
full_name: Mysliwy, Krzysztof
id: 316457FC-F248-11E8-B48F-1D18A9856A87
last_name: Mysliwy
citation:
ama: 'Mysliwy K. Polarons in Bose gases and polar crystals: Some rigorous energy
estimates. 2022. doi:10.15479/at:ista:11473'
apa: 'Mysliwy, K. (2022). Polarons in Bose gases and polar crystals: Some rigorous
energy estimates. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:11473'
chicago: 'Mysliwy, Krzysztof. “Polarons in Bose Gases and Polar Crystals: Some Rigorous
Energy Estimates.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:11473.'
ieee: 'K. Mysliwy, “Polarons in Bose gases and polar crystals: Some rigorous energy
estimates,” Institute of Science and Technology Austria, 2022.'
ista: 'Mysliwy K. 2022. Polarons in Bose gases and polar crystals: Some rigorous
energy estimates. Institute of Science and Technology Austria.'
mla: 'Mysliwy, Krzysztof. Polarons in Bose Gases and Polar Crystals: Some Rigorous
Energy Estimates. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:11473.'
short: 'K. Mysliwy, Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy
Estimates, Institute of Science and Technology Austria, 2022.'
corr_author: '1'
date_created: 2022-06-30T12:15:03Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2026-04-07T14:14:52Z
day: '01'
ddc:
- '515'
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: RoSe
doi: 10.15479/at:ista:11473
ec_funded: 1
file:
- access_level: open_access
checksum: 7970714a20a6052f75fb27a6c3e9976e
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creator: kmysliwy
date_created: 2022-07-05T08:12:56Z
date_updated: 2022-07-05T08:12:56Z
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creator: kmysliwy
date_created: 2022-07-05T08:15:52Z
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file_name: thes_source.zip
file_size: 5831060
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has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '138'
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10564'
relation: part_of_dissertation
status: public
- id: '8705'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
title: 'Polarons in Bose gases and polar crystals: Some rigorous energy estimates'
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2022'
...
---
_id: '11783'
abstract:
- lang: eng
text: We consider a gas of N bosons with interactions in the mean-field scaling
regime. We review the proof of an asymptotic expansion of its low-energy spectrum,
eigenstates, and dynamics, which provides corrections to Bogoliubov theory to
all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer,
and Soffer. In addition, we derive a full asymptotic expansion of the ground state
one-body reduced density matrix.
acknowledgement: "The author thanks Nataˇsa Pavlovic, Sören Petrat, Peter Pickl, Robert
Seiringer, and Avy Soffer for the collaboration on Refs. 1, 2 and 21. Funding from
the European Union’s Horizon 2020 Research and Innovation Programme under Marie
Skℓodowska-Curie Grant Agreement\r\nNo. 754411 is gratefully acknowledged."
article_number: '061102'
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
citation:
ama: Bossmann L. Low-energy spectrum and dynamics of the weakly interacting Bose
gas. Journal of Mathematical Physics. 2022;63(6). doi:10.1063/5.0089983
apa: Bossmann, L. (2022). Low-energy spectrum and dynamics of the weakly interacting
Bose gas. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0089983
chicago: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting
Bose Gas.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0089983.
ieee: L. Bossmann, “Low-energy spectrum and dynamics of the weakly interacting Bose
gas,” Journal of Mathematical Physics, vol. 63, no. 6. AIP Publishing,
2022.
ista: Bossmann L. 2022. Low-energy spectrum and dynamics of the weakly interacting
Bose gas. Journal of Mathematical Physics. 63(6), 061102.
mla: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting
Bose Gas.” Journal of Mathematical Physics, vol. 63, no. 6, 061102, AIP
Publishing, 2022, doi:10.1063/5.0089983.
short: L. Bossmann, Journal of Mathematical Physics 63 (2022).
corr_author: '1'
date_created: 2022-08-11T06:37:52Z
date_published: 2022-06-10T00:00:00Z
date_updated: 2025-04-14T07:43:58Z
day: '10'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1063/5.0089983
ec_funded: 1
external_id:
arxiv:
- '2203.00730'
isi:
- '000809648100002'
file:
- access_level: open_access
checksum: d0d32c338c1896680174be88c70968fa
content_type: application/pdf
creator: dernst
date_created: 2022-08-11T07:03:02Z
date_updated: 2022-08-11T07:03:02Z
file_id: '11784'
file_name: 2022_JourMathPhysics_Bossmann.pdf
file_size: 5957888
relation: main_file
success: 1
file_date_updated: 2022-08-11T07:03:02Z
fulldoi: https://doi.org/10.1063/5.0089983
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intvolume: ' 63'
isi: 1
issue: '6'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Low-energy spectrum and dynamics of 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2022'
...
---
_id: '11917'
abstract:
- lang: eng
text: We study the many-body dynamics of an initially factorized bosonic wave function
in the mean-field regime. We prove large deviation estimates for the fluctuations
around the condensate. We derive an upper bound extending a recent result to more
general interactions. Furthermore, we derive a new lower bound which agrees with
the upper bound in leading order.
acknowledgement: "The authors thank Gérard Ben Arous for pointing out the question
of a lower bound. Funding from the European Union’s Horizon 2020 research and innovation
programme under the ERC Grant Agreement No. 694227 (R.S.) and under the Marie Skłodowska-Curie
Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.\r\nOpen access funding
provided by IST Austria."
article_number: '9'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- 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: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Rademacher SAE, Seiringer R. Large deviation estimates for weakly interacting
bosons. Journal of Statistical Physics. 2022;188. doi:10.1007/s10955-022-02940-4
apa: Rademacher, S. A. E., & Seiringer, R. (2022). Large deviation estimates
for weakly interacting bosons. Journal of Statistical Physics. Springer
Nature. https://doi.org/10.1007/s10955-022-02940-4
chicago: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation
Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics.
Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02940-4.
ieee: S. A. E. Rademacher and R. Seiringer, “Large deviation estimates for weakly
interacting bosons,” Journal of Statistical Physics, vol. 188. Springer
Nature, 2022.
ista: Rademacher SAE, Seiringer R. 2022. Large deviation estimates for weakly interacting
bosons. Journal of Statistical Physics. 188, 9.
mla: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates
for Weakly Interacting Bosons.” Journal of Statistical Physics, vol. 188,
9, Springer Nature, 2022, doi:10.1007/s10955-022-02940-4.
short: S.A.E. Rademacher, R. Seiringer, Journal of Statistical Physics 188 (2022).
corr_author: '1'
date_created: 2022-08-18T07:23:26Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2025-04-14T07:26:59Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s10955-022-02940-4
ec_funded: 1
external_id:
isi:
- '000805175000001'
file:
- access_level: open_access
checksum: 44418cb44f07fa21ed3907f85abf7f39
content_type: application/pdf
creator: dernst
date_created: 2022-08-18T08:09:00Z
date_updated: 2022-08-18T08:09:00Z
file_id: '11922'
file_name: 2022_JournalStatisticalPhysics_Rademacher.pdf
file_size: 483481
relation: main_file
success: 1
file_date_updated: 2022-08-18T08:09:00Z
fulldoi: https://doi.org/10.1007/s10955-022-02940-4
has_accepted_license: '1'
intvolume: ' 188'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Large deviation estimates for weakly interacting bosons
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 188
year: '2022'
...
---
_id: '12083'
abstract:
- lang: eng
text: We consider the many-body time evolution of weakly interacting bosons in the
mean field regime for initial coherent states. We show that bounded k-particle
operators, corresponding to dependent random variables, satisfy both a law of
large numbers and a central limit theorem.
acknowledgement: S.R. would like to thank Robert Seiringer and Benedikt Stufler for
helpful discussions. Funding from the European Union’s Horizon 2020 Research and
Innovation Program under the ERC grant (Grant Agreement No. 694227) and under the
Marie Skłodowska-Curie grant (Agreement No. 754411) is acknowledged.
article_number: '081902'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- 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
citation:
ama: Rademacher SAE. Dependent random variables in quantum dynamics. Journal
of Mathematical Physics. 2022;63(8). doi:10.1063/5.0086712
apa: Rademacher, S. A. E. (2022). Dependent random variables in quantum dynamics.
Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0086712
chicago: Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum
Dynamics.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0086712.
ieee: S. A. E. Rademacher, “Dependent random variables in quantum dynamics,” Journal
of Mathematical Physics, vol. 63, no. 8. AIP Publishing, 2022.
ista: Rademacher SAE. 2022. Dependent random variables in quantum dynamics. Journal
of Mathematical Physics. 63(8), 081902.
mla: Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.”
Journal of Mathematical Physics, vol. 63, no. 8, 081902, AIP Publishing,
2022, doi:10.1063/5.0086712.
short: S.A.E. Rademacher, Journal of Mathematical Physics 63 (2022).
corr_author: '1'
date_created: 2022-09-11T22:01:56Z
date_published: 2022-08-25T00:00:00Z
date_updated: 2025-04-14T07:26:59Z
day: '25'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1063/5.0086712
ec_funded: 1
external_id:
arxiv:
- '2112.04817'
isi:
- '000844402500001'
file:
- access_level: open_access
checksum: e6fb0cf3f0327739c5e69a2cfc4020eb
content_type: application/pdf
creator: dernst
date_created: 2022-09-12T07:35:34Z
date_updated: 2022-09-12T07:35:34Z
file_id: '12089'
file_name: 2022_JourMathPhysics_Rademacher.pdf
file_size: 4552261
relation: main_file
success: 1
file_date_updated: 2022-09-12T07:35:34Z
fulldoi: https://doi.org/10.1063/5.0086712
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '8'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Mathematical Physics
publication_identifier:
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dependent random variables in quantum dynamics
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2022'
...
---
_id: '12246'
abstract:
- lang: eng
text: The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of
a classical system of N identical charges only in terms of their one-particle
density. We prove here a new estimate on the best constant in this inequality.
Numerical evaluation provides the value 1.58, which is a significant improvement
to the previously known value 1.64. The best constant has recently been shown
to be larger than 1.44. In a second part, we prove that the constant can be reduced
to 1.25 when the inequality is restricted to Hartree–Fock states. This is the
first proof that the exchange term is always much lower than the full indirect
Coulomb energy.
acknowledgement: We would like to thank David Gontier for useful advice on the numerical
simulations. This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation program (Grant
Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful
for the hospitality of the Institut Henri Poincaré in Paris, where part of this
work was done.
article_number: '92'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Elliott H.
full_name: Lieb, Elliott H.
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Lewin M, Lieb EH, Seiringer R. Improved Lieb–Oxford bound on the indirect and
exchange energies. Letters in Mathematical Physics. 2022;112(5). doi:10.1007/s11005-022-01584-5
apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2022). Improved Lieb–Oxford bound
on the indirect and exchange energies. Letters in Mathematical Physics.
Springer Nature. https://doi.org/10.1007/s11005-022-01584-5
chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford
Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics.
Springer Nature, 2022. https://doi.org/10.1007/s11005-022-01584-5.
ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the
indirect and exchange energies,” Letters in Mathematical Physics, vol.
112, no. 5. Springer Nature, 2022.
ista: Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect
and exchange energies. Letters in Mathematical Physics. 112(5), 92.
mla: Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange
Energies.” Letters in Mathematical Physics, vol. 112, no. 5, 92, Springer
Nature, 2022, doi:10.1007/s11005-022-01584-5.
short: M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022).
date_created: 2023-01-16T09:53:54Z
date_published: 2022-09-15T00:00:00Z
date_updated: 2025-04-14T07:26:59Z
day: '15'
department:
- _id: RoSe
doi: 10.1007/s11005-022-01584-5
ec_funded: 1
external_id:
arxiv:
- '2203.12473'
isi:
- '000854762600001'
fulldoi: https://doi.org/10.1007/s11005-022-01584-5
intvolume: ' 112'
isi: 1
issue: '5'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2203.12473
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Letters in Mathematical Physics
publication_identifier:
eissn:
- 1573-0530
issn:
- 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Improved Lieb–Oxford bound on the indirect and exchange energies
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 112
year: '2022'
...
---
_id: '12276'
abstract:
- lang: eng
text: Ongoing development of quantum simulators allows for a progressively finer
degree of control of quantum many-body systems. This motivates the development
of efficient approaches to facilitate the control of such systems and enable the
preparation of nontrivial quantum states. Here we formulate an approach to control
quantum systems based on matrix product states (MPSs). We compare counterdiabatic
and leakage minimization approaches to the so-called local steering problem that
consists in finding the best value of the control parameters for generating a
unitary evolution of the specific MPS in a given direction. In order to benchmark
the different approaches, we apply them to the generalization of the PXP model
known to exhibit coherent quantum dynamics due to quantum many-body scars. We
find that the leakage-based approach generally outperforms the counterdiabatic
framework and use it to construct a Floquet model with quantum scars. We perform
the first steps towards global trajectory optimization and demonstrate entanglement
steering capabilities in the generalized PXP model. Finally, we apply our leakage
minimization approach to construct quantum scars in the periodically driven nonintegrable
Ising model.
acknowledgement: We thank A. A. Michailidis for insightful discussions. M.L. and M.S.
acknowledge support from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 850899).
D.A. is supported by the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (Grant Agreement No. 864597) and
by the Swiss National Science Foundation. The infinite TEBD simulations were performed
using the ITensor library [67].
article_number: '030343'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marko
full_name: Ljubotina, Marko
id: F75EE9BE-5C90-11EA-905D-16643DDC885E
last_name: Ljubotina
orcid: 0000-0003-0038-7068
- first_name: Barbara
full_name: Roos, Barbara
id: 5DA90512-D80F-11E9-8994-2E2EE6697425
last_name: Roos
orcid: 0000-0002-9071-5880
- first_name: Dmitry A.
full_name: Abanin, Dmitry A.
last_name: Abanin
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
citation:
ama: Ljubotina M, Roos B, Abanin DA, Serbyn M. Optimal steering of matrix product
states and quantum many-body scars. PRX Quantum. 2022;3(3). doi:10.1103/prxquantum.3.030343
apa: Ljubotina, M., Roos, B., Abanin, D. A., & Serbyn, M. (2022). Optimal steering
of matrix product states and quantum many-body scars. PRX Quantum. American
Physical Society. https://doi.org/10.1103/prxquantum.3.030343
chicago: Ljubotina, Marko, Barbara Roos, Dmitry A. Abanin, and Maksym Serbyn. “Optimal
Steering of Matrix Product States and Quantum Many-Body Scars.” PRX Quantum.
American Physical Society, 2022. https://doi.org/10.1103/prxquantum.3.030343.
ieee: M. Ljubotina, B. Roos, D. A. Abanin, and M. Serbyn, “Optimal steering of matrix
product states and quantum many-body scars,” PRX Quantum, vol. 3, no. 3.
American Physical Society, 2022.
ista: Ljubotina M, Roos B, Abanin DA, Serbyn M. 2022. Optimal steering of matrix
product states and quantum many-body scars. PRX Quantum. 3(3), 030343.
mla: Ljubotina, Marko, et al. “Optimal Steering of Matrix Product States and Quantum
Many-Body Scars.” PRX Quantum, vol. 3, no. 3, 030343, American Physical
Society, 2022, doi:10.1103/prxquantum.3.030343.
short: M. Ljubotina, B. Roos, D.A. Abanin, M. Serbyn, PRX Quantum 3 (2022).
corr_author: '1'
date_created: 2023-01-16T10:01:56Z
date_published: 2022-09-23T00:00:00Z
date_updated: 2025-04-14T07:52:07Z
day: '23'
ddc:
- '530'
department:
- _id: MaSe
- _id: RoSe
doi: 10.1103/prxquantum.3.030343
ec_funded: 1
external_id:
arxiv:
- '2204.02899'
file:
- access_level: open_access
checksum: ef8f0a1b5a019b3958009162de0fa4c3
content_type: application/pdf
creator: dernst
date_created: 2023-01-30T11:02:50Z
date_updated: 2023-01-30T11:02:50Z
file_id: '12457'
file_name: 2022_PRXQuantum_Ljubotina.pdf
file_size: 7661905
relation: main_file
success: 1
file_date_updated: 2023-01-30T11:02:50Z
fulldoi: https://doi.org/10.1103/prxquantum.3.030343
has_accepted_license: '1'
intvolume: ' 3'
issue: '3'
keyword:
- General Medicine
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
call_identifier: H2020
grant_number: '850899'
name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication: PRX Quantum
publication_identifier:
eissn:
- 2691-3399
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal steering of matrix product states and quantum many-body scars
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: 3
year: '2022'
...
---
OA_place: publisher
_id: '12390'
abstract:
- lang: eng
text: "The scope of this thesis is to study quantum systems exhibiting a continuous
symmetry that\r\nis broken on the level of the corresponding effective theory.
In particular we are going to\r\ninvestigate translation-invariant Bose gases
in the mean field limit, effectively described by\r\nthe Hartree functional, and
the Fröhlich Polaron in the regime of strong coupling, effectively\r\ndescribed
by the Pekar functional. The latter is a model describing the interaction between
a\r\ncharged particle and the optical modes of a polar crystal. Regarding the
former, we assume in\r\naddition that the particles in the gas are unconfined,
and typically we will consider particles\r\nthat are subject to an attractive
interaction. In both cases the ground state energy of the\r\nHamiltonian is not
a proper eigenvalue due to the underlying translation-invariance, while on\r\nthe
contrary there exists a whole invariant orbit of minimizers for the corresponding
effective\r\nfunctionals. Both, the absence of proper eigenstates and the broken
symmetry of the effective\r\ntheory, make the study significantly more involved
and it is the content of this thesis to\r\ndevelop a frameworks which allows for
a systematic way to circumvent these issues.\r\nIt is a well-established result
that the ground state energy of Bose gases in the mean field limit,\r\nas well
as the ground state energy of the Fröhlich Polaron in the regime of strong coupling,
is\r\nto leading order given by the minimal energy of the corresponding effective
theory. As part\r\nof this thesis we identify the sub-leading term in the expansion
of the ground state energy,\r\nwhich can be interpreted as the quantum correction
to the classical energy, since the effective\r\ntheories under consideration can
be seen as classical counterparts.\r\nWe are further going to establish an asymptotic
expression for the energy-momentum relation\r\nof the Fröhlich Polaron in the
strong coupling limit. In the regime of suitably small momenta,\r\nthis asymptotic
expression agrees with the energy-momentum relation of a free particle having\r\nan
effectively increased mass, and we find that this effectively increased mass agrees
with the\r\nconjectured value in the physics literature.\r\nIn addition we will
discuss two unrelated papers written by the author during his stay at ISTA\r\nin
the appendix. The first one concerns the realization of anyons, which are quasi-particles\r\nacquiring
a non-trivial phase under the exchange of two particles, as molecular impurities.\r\nThe
second one provides a classification of those vector fields defined on a given
manifold\r\nthat can be written as the gradient of a given functional with respect
to a suitable metric,\r\nprovided that some mild smoothness assumptions hold.
This classification is subsequently\r\nused to identify those quantum Markov semigroups
that can be written as a gradient flow of\r\nthe relative entropy.\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Morris
full_name: Brooks, Morris
id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
last_name: Brooks
orcid: 0000-0002-6249-0928
citation:
ama: Brooks M. Translation-invariant quantum systems with effectively broken symmetry.
2022. doi:10.15479/at:ista:12390
apa: Brooks, M. (2022). Translation-invariant quantum systems with effectively
broken symmetry. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:12390
chicago: Brooks, Morris. “Translation-Invariant Quantum Systems with Effectively
Broken Symmetry.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:12390.
ieee: M. Brooks, “Translation-invariant quantum systems with effectively broken
symmetry,” Institute of Science and Technology Austria, 2022.
ista: Brooks M. 2022. Translation-invariant quantum systems with effectively broken
symmetry. Institute of Science and Technology Austria.
mla: Brooks, Morris. Translation-Invariant Quantum Systems with Effectively Broken
Symmetry. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:12390.
short: M. Brooks, Translation-Invariant Quantum Systems with Effectively Broken
Symmetry, Institute of Science and Technology Austria, 2022.
corr_author: '1'
date_created: 2023-01-26T10:00:42Z
date_published: 2022-12-15T00:00:00Z
date_updated: 2026-04-16T08:20:52Z
day: '15'
ddc:
- '500'
degree_awarded: PhD
department:
- _id: GradSch
- _id: RoSe
doi: 10.15479/at:ista:12390
ec_funded: 1
file:
- access_level: open_access
checksum: b31460e937f33b557abb40ebef02b567
content_type: application/pdf
creator: cchlebak
date_created: 2023-01-26T10:02:34Z
date_updated: 2023-01-26T10:02:34Z
file_id: '12391'
file_name: Brooks_Thesis.pdf
file_size: 3095225
relation: main_file
success: 1
- access_level: closed
checksum: 9751869fa5e7981588ad4228f4fd4bd6
content_type: application/octet-stream
creator: cchlebak
date_created: 2023-01-26T10:02:42Z
date_updated: 2023-01-26T10:02:42Z
file_id: '12392'
file_name: Brooks_Thesis.tex
file_size: 809842
relation: source_file
file_date_updated: 2023-01-26T10:02:42Z
fulldoi: https://doi.org/10.15479/at:ista:12390
has_accepted_license: '1'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: '196'
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '9005'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
title: Translation-invariant quantum systems with effectively broken symmetry
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2022'
...
---
_id: '10537'
abstract:
- lang: eng
text: We consider the quantum many-body evolution of a homogeneous Fermi gas in
three dimensions in the coupled semiclassical and mean-field scaling regime. We
study a class of initial data describing collective particle–hole pair excitations
on the Fermi ball. Using a rigorous version of approximate bosonization, we prove
that the many-body evolution can be approximated in Fock space norm by a quasi-free
bosonic evolution of the collective particle–hole excitations.
acknowledgement: NB was supported by Gruppo Nazionale per la Fisica Matematica (GNFM).
RS was supported by the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation program (Grant Agreement No. 694227). PTN was
supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)
under Germany’s Excellence Strategy (EXC-2111-390814868). MP was supported by the
European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation program (ERC StG MaMBoQ, Grant Agreement No. 802901). BS was supported
by the NCCR SwissMAP, the Swiss National Science Foundation through the Grant “Dynamical
and energetic properties of Bose-Einstein condensates,” and the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation program
through the ERC-AdG CLaQS (Grant Agreement No. 834782).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Niels P
full_name: Benedikter, Niels P
id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
last_name: Benedikter
orcid: 0000-0002-1071-6091
- first_name: Phan Thành
full_name: Nam, Phan Thành
last_name: Nam
- first_name: Marcello
full_name: Porta, Marcello
last_name: Porta
- 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: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Bosonization of fermionic
many-body dynamics. Annales Henri Poincaré. 2022;23(5):1725-1764. doi:10.1007/s00023-021-01136-y
apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R.
(2022). Bosonization of fermionic many-body dynamics. Annales Henri Poincaré.
Springer Nature. https://doi.org/10.1007/s00023-021-01136-y
chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
and Robert Seiringer. “Bosonization of Fermionic Many-Body Dynamics.” Annales
Henri Poincaré. Springer Nature, 2022. https://doi.org/10.1007/s00023-021-01136-y.
ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Bosonization
of fermionic many-body dynamics,” Annales Henri Poincaré, vol. 23, no.
5. Springer Nature, pp. 1725–1764, 2022.
ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2022. Bosonization
of fermionic many-body dynamics. Annales Henri Poincaré. 23(5), 1725–1764.
mla: Benedikter, Niels P., et al. “Bosonization of Fermionic Many-Body Dynamics.”
Annales Henri Poincaré, vol. 23, no. 5, Springer Nature, 2022, pp. 1725–64,
doi:10.1007/s00023-021-01136-y.
short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Annales Henri
Poincaré 23 (2022) 1725–1764.
date_created: 2021-12-12T23:01:28Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2025-04-14T07:26:53Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00023-021-01136-y
ec_funded: 1
external_id:
arxiv:
- '2103.08224'
isi:
- '000725405700001'
fulldoi: https://doi.org/10.1007/s00023-021-01136-y
intvolume: ' 23'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.08224
month: '05'
oa: 1
oa_version: Preprint
page: 1725-1764
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Annales Henri Poincaré
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bosonization of fermionic many-body dynamics
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 23
year: '2022'
...
---
_id: '10564'
abstract:
- lang: eng
text: We study a class of polaron-type Hamiltonians with sufficiently regular form
factor in the interaction term. We investigate the strong-coupling limit of the
model, and prove suitable bounds on the ground state energy as a function of the
total momentum of the system. These bounds agree with the semiclassical approximation
to leading order. The latter corresponds here to the situation when the particle
undergoes harmonic motion in a potential well whose frequency is determined by
the corresponding Pekar functional. We show that for all such models the effective
mass diverges in the strong coupling limit, in all spatial dimensions. Moreover,
for the case when the phonon dispersion relation grows at least linearly with
momentum, the bounds result in an asymptotic formula for the effective mass quotient,
a quantity generalizing the usual notion of the effective mass. This asymptotic
form agrees with the semiclassical Landau–Pekar formula and can be regarded as
the first rigorous confirmation, in a slightly weaker sense than usually considered,
of the validity of the semiclassical formula for the effective mass.
acknowledgement: Financial support through 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.)
is gratefully acknowledged. Open access funding provided by Institute of Science
and Technology (IST Austria).
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- 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: Mysliwy K, Seiringer R. Polaron models with regular interactions at strong
coupling. Journal of Statistical Physics. 2022;186(1). doi:10.1007/s10955-021-02851-w
apa: Mysliwy, K., & Seiringer, R. (2022). Polaron models with regular interactions
at strong coupling. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-021-02851-w
chicago: Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular
Interactions at Strong Coupling.” Journal of Statistical Physics. Springer
Nature, 2022. https://doi.org/10.1007/s10955-021-02851-w.
ieee: K. Mysliwy and R. Seiringer, “Polaron models with regular interactions at
strong coupling,” Journal of Statistical Physics, vol. 186, no. 1. Springer
Nature, 2022.
ista: Mysliwy K, Seiringer R. 2022. Polaron models with regular interactions at
strong coupling. Journal of Statistical Physics. 186(1), 5.
mla: Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions
at Strong Coupling.” Journal of Statistical Physics, vol. 186, no. 1, 5,
Springer Nature, 2022, doi:10.1007/s10955-021-02851-w.
short: K. Mysliwy, R. Seiringer, Journal of Statistical Physics 186 (2022).
corr_author: '1'
date_created: 2021-12-19T23:01:32Z
date_published: 2022-01-01T00:00:00Z
date_updated: 2026-04-07T14:14:51Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s10955-021-02851-w
ec_funded: 1
external_id:
arxiv:
- '2106.09328'
isi:
- '000726275600001'
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language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
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name: International IST Doctoral Program
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name: IST Austria Open Access Fund
publication: Journal of Statistical Physics
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issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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title: Polaron models with regular interactions at strong coupling
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 186
year: '2022'
...
---
_id: '10755'
abstract:
- lang: eng
text: We provide a definition of the effective mass for the classical polaron described
by the Landau–Pekar (LP) equations. It is based on a novel variational principle,
minimizing the energy functional over states with given (initial) velocity. The
resulting formula for the polaron's effective mass agrees with the prediction
by LP (1948 J. Exp. Theor. Phys. 18 419–423).
acknowledgement: "We thank Herbert Spohn for helpful comments. Funding from the European
Union’s Horizon\r\n2020 research and innovation programme under the ERC Grant Agreement
No. 694227\r\n(DF and RS) and under the Marie Skłodowska-Curie Grant Agreement No.
754411 (SR) is\r\ngratefully acknowledged."
article_number: '015201'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
- 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: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for
the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical.
2022;55(1). doi:10.1088/1751-8121/ac3947'
apa: 'Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2022). The effective
mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical
and Theoretical. IOP Publishing. https://doi.org/10.1088/1751-8121/ac3947'
chicago: 'Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer.
“The Effective Mass Problem for the Landau-Pekar Equations.” Journal of Physics
A: Mathematical and Theoretical. IOP Publishing, 2022. https://doi.org/10.1088/1751-8121/ac3947.'
ieee: 'D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass
problem for the Landau-Pekar equations,” Journal of Physics A: Mathematical
and Theoretical, vol. 55, no. 1. IOP Publishing, 2022.'
ista: 'Feliciangeli D, Rademacher SAE, Seiringer R. 2022. The effective mass problem
for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical.
55(1), 015201.'
mla: 'Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar
Equations.” Journal of Physics A: Mathematical and Theoretical, vol. 55,
no. 1, 015201, IOP Publishing, 2022, doi:10.1088/1751-8121/ac3947.'
short: 'D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Journal of Physics A:
Mathematical and Theoretical 55 (2022).'
corr_author: '1'
date_created: 2022-02-13T23:01:35Z
date_published: 2022-01-19T00:00:00Z
date_updated: 2025-04-15T06:54:54Z
day: '19'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1088/1751-8121/ac3947
ec_funded: 1
external_id:
arxiv:
- '2107.03720'
file:
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file_name: 2022_JournalPhysicsA_Feliciangeli.pdf
file_size: 1132380
relation: main_file
success: 1
file_date_updated: 2022-02-14T08:20:19Z
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intvolume: ' 55'
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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'
related_material:
record:
- id: '9791'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The effective mass problem for the Landau-Pekar equations
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2022'
...
---
_id: '11732'
abstract:
- lang: eng
text: We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic
formula, which strongly depends on the strength of the interaction potential V
on the Fermi surface. In combination with the recent result by one of us (Math.
Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities,
we prove the universality of the ratio of the energy gap and the critical temperature.
acknowledgement: "We are grateful to Robert Seiringer for helpful discussions and
many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges
partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open
access funding provided by Institute of Science and Technology (IST Austria)"
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
citation:
ama: Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of
Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9
apa: Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density.
Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9
chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap
at High Density.” Journal of Statistical Physics. Springer Nature, 2022.
https://doi.org/10.1007/s10955-022-02965-9.
ieee: S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal
of Statistical Physics, vol. 189. Springer Nature, 2022.
ista: Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal
of Statistical Physics. 189, 5.
mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at
High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature,
2022, doi:10.1007/s10955-022-02965-9.
short: S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).
corr_author: '1'
date_created: 2022-08-05T11:36:56Z
date_published: 2022-07-29T00:00:00Z
date_updated: 2026-10-02T11:43:00Z
day: '29'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
- _id: RoSe
doi: 10.1007/s10955-022-02965-9
ec_funded: 1
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- '000833007200002'
file:
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date_created: 2022-08-08T07:36:34Z
date_updated: 2022-08-08T07:36:34Z
file_id: '11746'
file_name: 2022_JourStatisticalPhysics_Henheik.pdf
file_size: 419563
relation: main_file
success: 1
file_date_updated: 2022-08-08T07:36:34Z
fulldoi: https://doi.org/10.1007/s10955-022-02965-9
has_accepted_license: '1'
intvolume: ' 189'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '19540'
relation: dissertation_contains
status: public
- id: '18135'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: The BCS energy gap at high density
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 189
year: '2022'
...
---
_id: '10852'
abstract:
- lang: eng
text: ' We review old and new results on the Fröhlich polaron model. The discussion
includes the validity of the (classical) Pekar approximation in the strong coupling
limit, quantum corrections to this limit, as well as the divergence of the effective
polaron mass.'
acknowledgement: This work was supported by the European Research Council (ERC) under
the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo.
694227).
article_number: '2060012'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Seiringer R. The polaron at strong coupling. Reviews in Mathematical Physics.
2021;33(01). doi:10.1142/s0129055x20600120
apa: Seiringer, R. (2021). The polaron at strong coupling. Reviews in Mathematical
Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600120
chicago: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical
Physics. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600120.
ieee: R. Seiringer, “The polaron at strong coupling,” Reviews in Mathematical
Physics, vol. 33, no. 01. World Scientific Publishing, 2021.
ista: Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical
Physics. 33(01), 2060012.
mla: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical
Physics, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600120.
short: R. Seiringer, Reviews in Mathematical Physics 33 (2021).
corr_author: '1'
date_created: 2022-03-18T08:11:34Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2025-04-14T07:26:58Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600120
ec_funded: 1
external_id:
arxiv:
- '1912.12509'
isi:
- '000613313200013'
fulldoi: https://doi.org/10.1142/s0129055x20600120
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isi: 1
issue: '01'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
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oa: 1
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project:
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call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Reviews in Mathematical Physics
publication_identifier:
eissn:
- 1793-6659
issn:
- 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The polaron at strong coupling
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...