---
_id: '10600'
abstract:
- lang: eng
text: We show that recent results on adiabatic theory for interacting gapped many-body
systems on finite lattices remain valid in the thermodynamic limit. More precisely,
we prove a generalized super-adiabatic theorem for the automorphism group describing
the infinite volume dynamics on the quasi-local algebra of observables. The key
assumption is the existence of a sequence of gapped finite volume Hamiltonians,
which generates the same infinite volume dynamics in the thermodynamic limit.
Our adiabatic theorem also holds for certain perturbations of gapped ground states
that close the spectral gap (so it is also an adiabatic theorem for resonances
and, in this sense, “generalized”), and it provides an adiabatic approximation
to all orders in the adiabatic parameter (a property often called “super-adiabatic”).
In addition to the existing results for finite lattices, we also perform a resummation
of the adiabatic expansion and allow for observables that are not strictly local.
Finally, as an application, we prove the validity of linear and higher order response
theory for our class of perturbations for infinite systems. While we consider
the result and its proof as new and interesting in itself, we also lay the foundation
for the proof of an adiabatic theorem for systems with a gap only in the bulk,
which will be presented in a follow-up article.
acknowledgement: J.H. acknowledges partial financial support from ERC Advanced Grant
“RMTBeyond” No. 101020331.
article_number: '011901'
article_processing_charge: No
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: Stefan
full_name: Teufel, Stefan
last_name: Teufel
citation:
ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems
with a uniform gap. *Journal of Mathematical Physics*. 2022;63(1). doi:10.1063/5.0051632'
apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic
limit: Systems with a uniform gap. *Journal of Mathematical Physics*. AIP
Publishing. https://doi.org/10.1063/5.0051632'
chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Uniform Gap.” *Journal of Mathematical Physics*. AIP
Publishing, 2022. https://doi.org/10.1063/5.0051632.'
ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit:
Systems with a uniform gap,” *Journal of Mathematical Physics*, vol. 63,
no. 1. AIP Publishing, 2022.'
ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit:
Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.'
mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Uniform Gap.” *Journal of Mathematical Physics*, vol.
63, no. 1, 011901, AIP Publishing, 2022, doi:10.1063/5.0051632.'
short: S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).
date_created: 2022-01-03T12:19:48Z
date_published: 2022-01-03T00:00:00Z
date_updated: 2022-04-04T06:19:24Z
day: '03'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1063/5.0051632
ec_funded: 1
external_id:
arxiv:
- '2012.15238'
intvolume: ' 63'
issue: '1'
keyword:
- mathematical physics
- statistical and nonlinear physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2012.15238
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
status: public
title: 'Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 63
year: '2022'
...
---
_id: '10623'
abstract:
- lang: eng
text: We investigate the BCS critical temperature Tc in the high-density limit and
derive an asymptotic formula, which strongly depends on the behavior of the interaction
potential V on the Fermi-surface. Our results include a rigorous confirmation
for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev
Lett 122:157001, 2019) and identify precise conditions under which superconducting
domes arise in BCS theory.
acknowledgement: I am very grateful to Robert Seiringer for his guidance during this
project and for many valuable comments on an earlier version of the manuscript.
Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions
and comments, pointing out the reference [22] and for his involvement in a closely
related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable
comments on an earlier version of the manuscript and Andreas Deuchert for interesting
discussions.
article_number: '3'
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
citation:
ama: Henheik SJ. The BCS critical temperature at high density. *Mathematical
Physics, Analysis and Geometry*. 2022;25(1). doi:10.1007/s11040-021-09415-0
apa: Henheik, S. J. (2022). The BCS critical temperature at high density. *Mathematical
Physics, Analysis and Geometry*. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0
chicago: Henheik, Sven Joscha. “ The BCS Critical Temperature at High Density.”
*Mathematical Physics, Analysis and Geometry*. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0.
ieee: S. J. Henheik, “ The BCS critical temperature at high density,” *Mathematical
Physics, Analysis and Geometry*, vol. 25, no. 1. Springer Nature, 2022.
ista: Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical
Physics, Analysis and Geometry. 25(1), 3.
mla: Henheik, Sven Joscha. “ The BCS Critical Temperature at High Density.” *Mathematical
Physics, Analysis and Geometry*, vol. 25, no. 1, 3, Springer Nature, 2022,
doi:10.1007/s11040-021-09415-0.
short: S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).
date_created: 2022-01-13T15:40:53Z
date_published: 2022-01-11T00:00:00Z
date_updated: 2022-04-05T14:08:23Z
day: '11'
ddc:
- '514'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11040-021-09415-0
ec_funded: 1
external_id:
arxiv:
- '2106.02015'
file:
- access_level: open_access
checksum: d44f8123a52592a75b2c3b8ee2cd2435
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-14T07:27:45Z
date_updated: 2022-01-14T07:27:45Z
file_id: '10624'
file_name: 2022_MathPhyAnalGeo_Henheik.pdf
file_size: 505804
relation: main_file
success: 1
file_date_updated: 2022-01-14T07:27:45Z
has_accepted_license: '1'
intvolume: ' 25'
issue: '1'
keyword:
- geometry and topology
- mathematical physics
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '01'
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
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
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: ' The BCS critical temperature 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: 4A997E50-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2022'
...
---
_id: '10642'
abstract:
- lang: eng
text: Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized
but otherwise arbitrary perturbations of weakly interacting quantum spin systems
with uniformly gapped on-site terms change the ground state of such a system only
locally, even if they close the spectral gap. We call this a strong version of
the local perturbations perturb locally (LPPL) principle which is known to hold
for much more general gapped systems, but only for perturbations that do not close
the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle
to Hamiltonians that have the appropriate structure of gapped on-site terms and
weak interactions only locally in some region of space. While our results are
technically corollaries to a theorem of Yarotsky, we expect that the paradigm
of systems with a locally gapped ground state that is completely insensitive to
the form of the Hamiltonian elsewhere extends to other situations and has important
physical consequences.
acknowledgement: J. H. acknowledges partial financial support by the ERC Advanced
Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for
very helpful comments and discussions and Jürg Fröhlich for references to the literature.
Open Access funding enabled and organized by Projekt DEAL.
article_number: '9'
article_processing_charge: Yes
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: Stefan
full_name: Teufel, Stefan
last_name: Teufel
- first_name: Tom
full_name: Wessel, Tom
last_name: Wessel
citation:
ama: Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally
gapped and weakly interacting quantum spin systems. *Letters in Mathematical
Physics*. 2022;112(1). doi:10.1007/s11005-021-01494-y
apa: Henheik, S. J., Teufel, S., & Wessel, T. (2022). Local stability of ground
states in locally gapped and weakly interacting quantum spin systems. *Letters
in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s11005-021-01494-y
chicago: Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of
Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.”
*Letters in Mathematical Physics*. Springer Nature, 2022. https://doi.org/10.1007/s11005-021-01494-y.
ieee: S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states
in locally gapped and weakly interacting quantum spin systems,” *Letters in
Mathematical Physics*, vol. 112, no. 1. Springer Nature, 2022.
ista: Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in
locally gapped and weakly interacting quantum spin systems. Letters in Mathematical
Physics. 112(1), 9.
mla: Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped
and Weakly Interacting Quantum Spin Systems.” *Letters in Mathematical Physics*,
vol. 112, no. 1, 9, Springer Nature, 2022, doi:10.1007/s11005-021-01494-y.
short: S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).
date_created: 2022-01-18T16:18:25Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2022-01-24T07:55:43Z
day: '18'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11005-021-01494-y
ec_funded: 1
external_id:
arxiv:
- '2106.13780'
file:
- access_level: open_access
checksum: 7e8e69b76e892c305071a4736131fe18
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-19T09:41:14Z
date_updated: 2022-01-19T09:41:14Z
file_id: '10647'
file_name: 2022_LettersMathPhys_Henheik.pdf
file_size: 357547
relation: main_file
success: 1
file_date_updated: 2022-01-19T09:41:14Z
has_accepted_license: '1'
intvolume: ' 112'
issue: '1'
keyword:
- mathematical physics
- statistical and nonlinear physics
language:
- iso: eng
month: '01'
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: Letters in Mathematical Physics
publication_identifier:
eissn:
- 1573-0530
issn:
- 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Local stability of ground states in locally gapped and weakly interacting quantum
spin systems
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: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 112
year: '2022'
...
---
_id: '10643'
abstract:
- lang: eng
text: "We prove a generalised super-adiabatic theorem for extended fermionic systems
assuming a spectral gap only in the bulk. More precisely, we assume that the infinite
system has a unique ground state and that the corresponding Gelfand–Naimark–Segal
Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that
a similar adiabatic theorem also holds in the bulk of finite systems up to errors
that vanish faster than any inverse power of the system size, although the corresponding
finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"
acknowledgement: J.H. acknowledges partial financial support by the ERC Advanced Grant
‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft
and the Open Access Publishing Fund of the University of Tübingen is gratefully
acknowledged.
article_number: e4
article_processing_charge: Yes
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: Stefan
full_name: Teufel, Stefan
last_name: Teufel
citation:
ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems
with a gap in the bulk. *Forum of Mathematics, Sigma*. 2022;10. doi:10.1017/fms.2021.80'
apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic
limit: Systems with a gap in the bulk. *Forum of Mathematics, Sigma*. Cambridge
University Press. https://doi.org/10.1017/fms.2021.80'
chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Gap in the Bulk.” *Forum of Mathematics, Sigma*. Cambridge
University Press, 2022. https://doi.org/10.1017/fms.2021.80.'
ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit:
Systems with a gap in the bulk,” *Forum of Mathematics, Sigma*, vol. 10.
Cambridge University Press, 2022.'
ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit:
Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.'
mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Gap in the Bulk.” *Forum of Mathematics, Sigma*, vol.
10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.'
short: S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).
date_created: 2022-01-18T16:18:51Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2022-01-19T09:31:10Z
day: '18'
ddc:
- '510'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1017/fms.2021.80
ec_funded: 1
external_id:
arxiv:
- '2012.15239'
file:
- access_level: open_access
checksum: 87592a755adcef22ea590a99dc728dd3
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-19T09:27:43Z
date_updated: 2022-01-19T09:27:43Z
file_id: '10646'
file_name: 2022_ForumMathSigma_Henheik.pdf
file_size: 705323
relation: main_file
success: 1
file_date_updated: 2022-01-19T09:27:43Z
has_accepted_license: '1'
intvolume: ' 10'
keyword:
- computational mathematics
- discrete mathematics and combinatorics
- geometry and topology
- mathematical physics
- statistics and probability
- algebra and number theory
- theoretical computer science
- analysis
language:
- iso: eng
month: '01'
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: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
status: public
title: 'Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk'
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 10
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
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).
date_created: 2022-03-18T08:11:34Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2022-03-18T08:19:49Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600120
ec_funded: 1
external_id:
arxiv:
- '1912.12509'
intvolume: ' 33'
issue: '01'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1912.12509
month: '02'
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: Reviews in Mathematical Physics
publication_identifier:
issn:
- 0129-055X
- 1793-6659
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2021'
...
---
_id: '9121'
abstract:
- lang: eng
text: "We show that the energy gap for the BCS gap equation is\r\nΞ=μ(8e−2+o(1))exp(π2μ−−√a)\r\nin
the low density limit μ→0. Together with the similar result for the critical temperature
by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in
the low density limit, the ratio of the energy gap and critical temperature is
a universal constant independent of the interaction potential V. The results hold
for a class of potentials with negative scattering length a and no bound states."
acknowledgement: "Most of this work was done as part of the author’s master’s thesis.
The author would like to thank Jan Philip Solovej for his supervision of this process.\r\nOpen
Access funding provided by Institute of Science and Technology (IST Austria)"
article_number: '20'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- 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: Lauritsen AB. The BCS energy gap at low density. *Letters in Mathematical
Physics*. 2021;111. doi:10.1007/s11005-021-01358-5
apa: Lauritsen, A. B. (2021). The BCS energy gap at low density. *Letters in Mathematical
Physics*. Springer Nature. https://doi.org/10.1007/s11005-021-01358-5
chicago: Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” *Letters
in Mathematical Physics*. Springer Nature, 2021. https://doi.org/10.1007/s11005-021-01358-5.
ieee: A. B. Lauritsen, “The BCS energy gap at low density,” *Letters in Mathematical
Physics*, vol. 111. Springer Nature, 2021.
ista: Lauritsen AB. 2021. The BCS energy gap at low density. Letters in Mathematical
Physics. 111, 20.
mla: Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” *Letters
in Mathematical Physics*, vol. 111, 20, Springer Nature, 2021, doi:10.1007/s11005-021-01358-5.
short: A.B. Lauritsen, Letters in Mathematical Physics 111 (2021).
date_created: 2021-02-15T09:27:14Z
date_published: 2021-02-12T00:00:00Z
date_updated: 2021-02-15T09:32:40Z
day: '12'
ddc:
- '510'
department:
- _id: GradSch
doi: 10.1007/s11005-021-01358-5
file:
- access_level: open_access
checksum: eaf1b3ff5026f120f0929a5c417dc842
content_type: application/pdf
creator: dernst
date_created: 2021-02-15T09:31:07Z
date_updated: 2021-02-15T09:31:07Z
file_id: '9122'
file_name: 2021_LettersMathPhysics_Lauritsen.pdf
file_size: 329332
relation: main_file
success: 1
file_date_updated: 2021-02-15T09:31:07Z
has_accepted_license: '1'
intvolume: ' 111'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_identifier:
issn:
- 0377-9017
- 1573-0530
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: The BCS energy gap at low 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 111
year: '2021'
...
---
_id: '9285'
abstract:
- lang: eng
text: We first review the problem of a rigorous justification of Kubo’s formula
for transport coefficients in gapped extended Hamiltonian quantum systems at zero
temperature. In particular, the theoretical understanding of the quantum Hall
effect rests on the validity of Kubo’s formula for such systems, a connection
that we review briefly as well. We then highlight an approach to linear response
theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding
adiabatic theorem for such systems that was recently proposed and worked out by
one of us in [51] for interacting fermionic systems on finite lattices. In the
second part of our paper, we show how to lift the results of [51] to infinite
systems by taking a thermodynamic limit.
article_number: '2060004'
article_processing_charge: No
article_type: original
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
- first_name: Stefan
full_name: Teufel, Stefan
last_name: Teufel
citation:
ama: 'Henheik SJ, Teufel S. Justifying Kubo’s formula for gapped systems at zero
temperature: A brief review and some new results. *Reviews in Mathematical Physics*.
2021;33(01). doi:10.1142/s0129055x20600041'
apa: 'Henheik, S. J., & Teufel, S. (2021). Justifying Kubo’s formula for gapped
systems at zero temperature: A brief review and some new results. *Reviews in
Mathematical Physics*. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600041'
chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for
Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” *Reviews
in Mathematical Physics*. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600041.'
ieee: 'S. J. Henheik and S. Teufel, “Justifying Kubo’s formula for gapped systems
at zero temperature: A brief review and some new results,” *Reviews in Mathematical
Physics*, vol. 33, no. 01. World Scientific Publishing, 2021.'
ista: 'Henheik SJ, Teufel S. 2021. Justifying Kubo’s formula for gapped systems
at zero temperature: A brief review and some new results. Reviews in Mathematical
Physics. 33(01), 2060004.'
mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped
Systems at Zero Temperature: A Brief Review and Some New Results.” *Reviews
in Mathematical Physics*, vol. 33, no. 01, 2060004, World Scientific Publishing,
2021, doi:10.1142/s0129055x20600041.'
short: S.J. Henheik, S. Teufel, Reviews in Mathematical Physics 33 (2021).
date_created: 2021-03-26T11:29:46Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2021-03-29T07:50:18Z
day: '01'
ddc:
- '500'
doi: 10.1142/s0129055x20600041
extern: '1'
external_id:
arxiv:
- '2002.08669'
has_accepted_license: '1'
intvolume: ' 33'
issue: '01'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2002.08669
month: '02'
oa: 1
oa_version: Preprint
publication: Reviews in Mathematical Physics
publication_identifier:
issn:
- 0129-055X
- 1793-6659
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Justifying Kubo’s formula for gapped systems at zero temperature: A brief
review and some new results'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2021'
...
---
_id: '9891'
abstract:
- lang: eng
text: 'Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127
(2019)], we present a modified “floating crystal” trial state for jellium (also
known as the classical homogeneous electron gas) with density equal to a characteristic
function. This allows us to show that three definitions of the jellium energy
coincide in dimensions d ≥ 2, thus extending the result of Cotar and Petrache
[“Equality of the Jellium and uniform electron gas next-order asymptotic terms
for Coulomb and Riesz potentials,” arXiv: 1707.07664 (2019)] and Lewin, Lieb,
and Seiringer [Phys. Rev. B 100, 035127 (2019)] that the three definitions coincide
in dimension d ≥ 3. We show that the jellium energy is also equivalent to a “renormalized
energy” studied in a series of papers by Serfaty and others, and thus, by the
work of Bétermin and Sandier [Constr. Approximation 47, 39–74 (2018)], we relate
the jellium energy to the order n term in the logarithmic energy of n points on
the unit 2-sphere. We improve upon known lower bounds for this renormalized energy.
Additionally, we derive formulas for the jellium energy of periodic configurations.'
acknowledgement: The author would like to thank Robert Seiringer for guidance and
many helpful comments on this project. The author would also like to thank Mathieu
Lewin for his comments on the manuscript and Lorenzo Portinale for providing his
lecture notes for the course “Mathematics of quantum many-body systems” in spring
2020, taught by Robert Seiringer. The Proof of Theorem III.1 is inspired by these
lecture notes.
article_number: '083305'
article_processing_charge: No
article_type: original
author:
- 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: Lauritsen AB. Floating Wigner crystal and periodic jellium configurations.
*Journal of Mathematical Physics*. 2021;62(8). doi:10.1063/5.0053494
apa: Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations.
*Journal of Mathematical Physics*. AIP. https://doi.org/10.1063/5.0053494
chicago: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium
Configurations.” *Journal of Mathematical Physics*. AIP, 2021. https://doi.org/10.1063/5.0053494.
ieee: A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,”
*Journal of Mathematical Physics*, vol. 62, no. 8. AIP, 2021.
ista: Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations.
Journal of Mathematical Physics. 62(8), 083305.
mla: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium
Configurations.” *Journal of Mathematical Physics*, vol. 62, no. 8, 083305,
AIP, 2021, doi:10.1063/5.0053494.
short: A.B. Lauritsen, Journal of Mathematical Physics 62 (2021).
date_created: 2021-08-12T07:08:36Z
date_published: 2021-08-01T00:00:00Z
date_updated: 2021-10-27T13:22:51Z
day: '01'
ddc:
- '530'
department:
- _id: GradSch
- _id: RoSe
doi: 10.1063/5.0053494
external_id:
arxiv:
- '2103.07975'
file:
- access_level: open_access
checksum: d035be2b894c4d50d90ac5ce252e27cd
content_type: application/pdf
creator: cziletti
date_created: 2021-10-27T12:57:06Z
date_updated: 2021-10-27T12:57:06Z
file_id: '10188'
file_name: 2021_JMathPhy_Lauritsen.pdf
file_size: 4352640
relation: main_file
success: 1
file_date_updated: 2021-10-27T12:57:06Z
has_accepted_license: '1'
intvolume: ' 62'
issue: '8'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
- 0022-2488
publication_status: published
publisher: AIP
quality_controlled: '1'
scopus_import: '1'
status: public
title: Floating Wigner crystal and periodic jellium configurations
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: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 62
year: '2021'
...
---
_id: '9973'
abstract:
- lang: eng
text: In this article we introduce a complete gradient estimate for symmetric quantum
Markov semigroups on von Neumann algebras equipped with a normal faithful tracial
state, which implies semi-convexity of the entropy with respect to the recently
introduced noncommutative 2-Wasserstein distance. We show that this complete gradient
estimate is stable under tensor products and free products and establish its validity
for a number of examples. As an application we prove a complete modified logarithmic
Sobolev inequality with optimal constant for Poisson-type semigroups on free group
factors.
acknowledgement: Both authors would like to thank Jan Maas for fruitful discussions
and helpful comments.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups.
*Communications in Mathematical Physics*. 2021;387:761–791. doi:10.1007/s00220-021-04199-4
apa: Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov
semigroups. *Communications in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4
chicago: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” *Communications in Mathematical Physics*. Springer Nature,
2021. https://doi.org/10.1007/s00220-021-04199-4.
ieee: M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,”
*Communications in Mathematical Physics*, vol. 387. Springer Nature, pp.
761–791, 2021.
ista: Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 387, 761–791.
mla: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” *Communications in Mathematical Physics*, vol. 387, Springer
Nature, 2021, pp. 761–791, doi:10.1007/s00220-021-04199-4.
short: M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.
date_created: 2021-08-30T10:07:44Z
date_published: 2021-08-30T00:00:00Z
date_updated: 2022-05-13T06:56:44Z
day: '30'
ddc:
- '621'
department:
- _id: JaMa
doi: 10.1007/s00220-021-04199-4
ec_funded: 1
external_id:
arxiv:
- '2007.13506'
file:
- access_level: open_access
checksum: 8a602f916b1c2b0dc1159708b7cb204b
content_type: application/pdf
creator: cchlebak
date_created: 2021-09-08T07:34:24Z
date_updated: 2021-09-08T09:46:34Z
file_id: '9990'
file_name: 2021_CommunMathPhys_Wirth.pdf
file_size: 505971
relation: main_file
file_date_updated: 2021-09-08T09:46:34Z
has_accepted_license: '1'
intvolume: ' 387'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 761–791
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential 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: Complete gradient estimates of quantum Markov semigroups
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: 387
year: '2021'
...
---
_id: '8415'
abstract:
- lang: eng
text: 'We consider billiards obtained by removing three strictly convex obstacles
satisfying the non-eclipse condition on the plane. The restriction of the dynamics
to the set of non-escaping orbits is conjugated to a subshift on three symbols
that provides a natural labeling of all periodic orbits. We study the following
inverse problem: does the Marked Length Spectrum (i.e., the set of lengths of
periodic orbits together with their labeling), determine the geometry of the billiard
table? We show that from the Marked Length Spectrum it is possible to recover
the curvature at periodic points of period two, as well as the Lyapunov exponent
of each periodic orbit.'
article_processing_charge: No
article_type: original
author:
- first_name: Péter
full_name: Bálint, Péter
last_name: Bálint
- first_name: Jacopo
full_name: De Simoi, Jacopo
last_name: De Simoi
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Martin
full_name: Leguil, Martin
last_name: Leguil
citation:
ama: Bálint P, De Simoi J, Kaloshin V, Leguil M. Marked length spectrum, homoclinic
orbits and the geometry of open dispersing billiards. *Communications in Mathematical
Physics*. 2019;374(3):1531-1575. doi:10.1007/s00220-019-03448-x
apa: Bálint, P., De Simoi, J., Kaloshin, V., & Leguil, M. (2019). Marked length
spectrum, homoclinic orbits and the geometry of open dispersing billiards. *Communications
in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s00220-019-03448-x
chicago: Bálint, Péter, Jacopo De Simoi, Vadim Kaloshin, and Martin Leguil. “Marked
Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.”
*Communications in Mathematical Physics*. Springer Nature, 2019. https://doi.org/10.1007/s00220-019-03448-x.
ieee: P. Bálint, J. De Simoi, V. Kaloshin, and M. Leguil, “Marked length spectrum,
homoclinic orbits and the geometry of open dispersing billiards,” *Communications
in Mathematical Physics*, vol. 374, no. 3. Springer Nature, pp. 1531–1575,
2019.
ista: Bálint P, De Simoi J, Kaloshin V, Leguil M. 2019. Marked length spectrum,
homoclinic orbits and the geometry of open dispersing billiards. Communications
in Mathematical Physics. 374(3), 1531–1575.
mla: Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry
of Open Dispersing Billiards.” *Communications in Mathematical Physics*,
vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:10.1007/s00220-019-03448-x.
short: P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical
Physics 374 (2019) 1531–1575.
date_created: 2020-09-17T10:41:27Z
date_published: 2019-05-09T00:00:00Z
date_updated: 2021-01-12T08:19:08Z
day: '09'
doi: 10.1007/s00220-019-03448-x
extern: '1'
external_id:
arxiv:
- '1809.08947'
intvolume: ' 374'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1809.08947
month: '05'
oa: 1
oa_version: Preprint
page: 1531-1575
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Marked length spectrum, homoclinic orbits and the geometry of open dispersing
billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 374
year: '2019'
...
---
_id: '8417'
abstract:
- lang: eng
text: The restricted planar elliptic three body problem (RPETBP) describes the motion
of a massless particle (a comet or an asteroid) under the gravitational field
of two massive bodies (the primaries, say the Sun and Jupiter) revolving around
their center of mass on elliptic orbits with some positive eccentricity. The aim
of this paper is to show the existence of orbits whose angular momentum performs
arbitrary excursions in a large region. In particular, there exist diffusive orbits,
that is, with a large variation of angular momentum. The leading idea of the proof
consists in analyzing parabolic motions of the comet. By a well-known result of
McGehee, the union of future (resp. past) parabolic orbits is an analytic manifold
P+ (resp. P−). In a properly chosen coordinate system these manifolds are stable
(resp. unstable) manifolds of a manifold at infinity P∞, which we call the manifold
at parabolic infinity. On P∞ it is possible to define two scattering maps, which
contain the map structure of the homoclinic trajectories to it, i.e. orbits parabolic
both in the future and the past. Since the inner dynamics inside P∞ is trivial,
two different scattering maps are used. The combination of these two scattering
maps permits the design of the desired diffusive pseudo-orbits. Using shadowing
techniques and these pseudo orbits we show the existence of true trajectories
of the RPETBP whose angular momentum varies in any predetermined fashion.
article_processing_charge: No
article_type: original
author:
- first_name: Amadeu
full_name: Delshams, Amadeu
last_name: Delshams
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Abraham
full_name: de la Rosa, Abraham
last_name: de la Rosa
- first_name: Tere M.
full_name: Seara, Tere M.
last_name: Seara
citation:
ama: Delshams A, Kaloshin V, de la Rosa A, Seara TM. Global instability in the restricted
planar elliptic three body problem. *Communications in Mathematical Physics*.
2018;366(3):1173-1228. doi:10.1007/s00220-018-3248-z
apa: Delshams, A., Kaloshin, V., de la Rosa, A., & Seara, T. M. (2018). Global
instability in the restricted planar elliptic three body problem. *Communications
in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s00220-018-3248-z
chicago: Delshams, Amadeu, Vadim Kaloshin, Abraham de la Rosa, and Tere M. Seara.
“Global Instability in the Restricted Planar Elliptic Three Body Problem.” *Communications
in Mathematical Physics*. Springer Nature, 2018. https://doi.org/10.1007/s00220-018-3248-z.
ieee: A. Delshams, V. Kaloshin, A. de la Rosa, and T. M. Seara, “Global instability
in the restricted planar elliptic three body problem,” *Communications in Mathematical
Physics*, vol. 366, no. 3. Springer Nature, pp. 1173–1228, 2018.
ista: Delshams A, Kaloshin V, de la Rosa A, Seara TM. 2018. Global instability in
the restricted planar elliptic three body problem. Communications in Mathematical
Physics. 366(3), 1173–1228.
mla: Delshams, Amadeu, et al. “Global Instability in the Restricted Planar Elliptic
Three Body Problem.” *Communications in Mathematical Physics*, vol. 366,
no. 3, Springer Nature, 2018, pp. 1173–228, doi:10.1007/s00220-018-3248-z.
short: A. Delshams, V. Kaloshin, A. de la Rosa, T.M. Seara, Communications in Mathematical
Physics 366 (2018) 1173–1228.
date_created: 2020-09-17T10:41:43Z
date_published: 2018-09-05T00:00:00Z
date_updated: 2021-01-12T08:19:08Z
day: '05'
doi: 10.1007/s00220-018-3248-z
extern: '1'
intvolume: ' 366'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '09'
oa_version: None
page: 1173-1228
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Global instability in the restricted planar elliptic three body problem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 366
year: '2018'
...
---
_id: '8420'
abstract:
- lang: eng
text: We show that in the space of all convex billiard boundaries, the set of boundaries
with rational caustics is dense. More precisely, the set of billiard boundaries
with caustics of rotation number 1/q is polynomially sense in the smooth case,
and exponentially dense in the analytic case.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Ke
full_name: Zhang, Ke
last_name: Zhang
citation:
ama: Kaloshin V, Zhang K. Density of convex billiards with rational caustics. *Nonlinearity*.
2018;31(11):5214-5234. doi:10.1088/1361-6544/aadc12
apa: Kaloshin, V., & Zhang, K. (2018). Density of convex billiards with rational
caustics. *Nonlinearity*. IOP Publishing. https://doi.org/10.1088/1361-6544/aadc12
chicago: Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational
Caustics.” *Nonlinearity*. IOP Publishing, 2018. https://doi.org/10.1088/1361-6544/aadc12.
ieee: V. Kaloshin and K. Zhang, “Density of convex billiards with rational caustics,”
*Nonlinearity*, vol. 31, no. 11. IOP Publishing, pp. 5214–5234, 2018.
ista: Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics.
Nonlinearity. 31(11), 5214–5234.
mla: Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.”
*Nonlinearity*, vol. 31, no. 11, IOP Publishing, 2018, pp. 5214–34, doi:10.1088/1361-6544/aadc12.
short: V. Kaloshin, K. Zhang, Nonlinearity 31 (2018) 5214–5234.
date_created: 2020-09-17T10:42:09Z
date_published: 2018-10-15T00:00:00Z
date_updated: 2021-01-12T08:19:10Z
day: '15'
doi: 10.1088/1361-6544/aadc12
extern: '1'
external_id:
arxiv:
- '1706.07968'
intvolume: ' 31'
issue: '11'
keyword:
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1706.07968
month: '10'
oa: 1
oa_version: Preprint
page: 5214-5234
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: Density of convex billiards with rational caustics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2018'
...
---
_id: '8498'
abstract:
- lang: eng
text: "In the present note we announce a proof of a strong form of Arnold diffusion
for smooth convex Hamiltonian systems. Let ${\\mathbb T}^2$ be a 2-dimensional
torus and B2 be the unit ball around the origin in ${\\mathbb R}^2$ . Fix ρ >
0. Our main result says that for a 'generic' time-periodic perturbation of an
integrable system of two degrees of freedom $H_0(p)+\\varepsilon H_1(\\theta,p,t),\\quad
\\ \\theta\\in {\\mathbb T}^2,\\ p\\in B^2,\\ t\\in {\\mathbb T}={\\mathbb R}/{\\mathbb
Z}$ , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in
${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ , namely, a ρ-neighborhood of
the orbit contains ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ .\r\n\r\nOur
proof is a combination of geometric and variational methods. The fundamental elements
of the construction are the usage of crumpled normally hyperbolic invariant cylinders
from [9], flower and simple normally hyperbolic invariant manifolds from [36]
as well as their kissing property at a strong double resonance. This allows us
to build a 'connected' net of three-dimensional normally hyperbolic invariant
manifolds. To construct diffusing orbits along this net we employ a version of
the Mather variational method [41] equipped with weak KAM theory [28], proposed
by Bernard in [7]."
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: K
full_name: Zhang, K
last_name: Zhang
citation:
ama: Kaloshin V, Zhang K. Arnold diffusion for smooth convex systems of two and
a half degrees of freedom. *Nonlinearity*. 2015;28(8):2699-2720. doi:10.1088/0951-7715/28/8/2699
apa: Kaloshin, V., & Zhang, K. (2015). Arnold diffusion for smooth convex systems
of two and a half degrees of freedom. *Nonlinearity*. IOP Publishing. https://doi.org/10.1088/0951-7715/28/8/2699
chicago: Kaloshin, Vadim, and K Zhang. “Arnold Diffusion for Smooth Convex Systems
of Two and a Half Degrees of Freedom.” *Nonlinearity*. IOP Publishing, 2015.
https://doi.org/10.1088/0951-7715/28/8/2699.
ieee: V. Kaloshin and K. Zhang, “Arnold diffusion for smooth convex systems of two
and a half degrees of freedom,” *Nonlinearity*, vol. 28, no. 8. IOP Publishing,
pp. 2699–2720, 2015.
ista: Kaloshin V, Zhang K. 2015. Arnold diffusion for smooth convex systems of two
and a half degrees of freedom. Nonlinearity. 28(8), 2699–2720.
mla: Kaloshin, Vadim, and K. Zhang. “Arnold Diffusion for Smooth Convex Systems
of Two and a Half Degrees of Freedom.” *Nonlinearity*, vol. 28, no. 8, IOP
Publishing, 2015, pp. 2699–720, doi:10.1088/0951-7715/28/8/2699.
short: V. Kaloshin, K. Zhang, Nonlinearity 28 (2015) 2699–2720.
date_created: 2020-09-18T10:46:43Z
date_published: 2015-06-30T00:00:00Z
date_updated: 2021-01-12T08:19:41Z
day: '30'
doi: 10.1088/0951-7715/28/8/2699
extern: '1'
intvolume: ' 28'
issue: '8'
keyword:
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '06'
oa_version: None
page: 2699-2720
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: Arnold diffusion for smooth convex systems of two and a half degrees of freedom
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2015'
...
---
_id: '8502'
abstract:
- lang: eng
text: 'The famous ergodic hypothesis suggests that for a typical Hamiltonian on
a typical energy surface nearly all trajectories are dense. KAM theory disproves
it. Ehrenfest (The Conceptual Foundations of the Statistical Approach in Mechanics.
Ithaca, NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers.
Vol 2, New York: Dover, pp 462–465, 1968) stated the quasi-ergodic hypothesis
claiming that a typical Hamiltonian on a typical energy surface has a dense orbit.
This question is wide open. Herman (Proceedings of the International Congress
of Mathematicians, Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin:
Int Math Union, pp 797–808, 1998) proposed to look for an example of a Hamiltonian
near H0(I)=⟨I,I⟩2 with a dense orbit on the unit energy surface. In this paper
we construct a Hamiltonian H0(I)+εH1(θ,I,ε) which has an orbit dense in a set
of maximal Hausdorff dimension equal to 5 on the unit energy surface.'
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Maria
full_name: Saprykina, Maria
last_name: Saprykina
citation:
ama: Kaloshin V, Saprykina M. An example of a nearly integrable Hamiltonian system
with a trajectory dense in a set of maximal Hausdorff dimension. *Communications
in Mathematical Physics*. 2012;315(3):643-697. doi:10.1007/s00220-012-1532-x
apa: Kaloshin, V., & Saprykina, M. (2012). An example of a nearly integrable
Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension.
*Communications in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s00220-012-1532-x
chicago: Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable
Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.”
*Communications in Mathematical Physics*. Springer Nature, 2012. https://doi.org/10.1007/s00220-012-1532-x.
ieee: V. Kaloshin and M. Saprykina, “An example of a nearly integrable Hamiltonian
system with a trajectory dense in a set of maximal Hausdorff dimension,” *Communications
in Mathematical Physics*, vol. 315, no. 3. Springer Nature, pp. 643–697, 2012.
ista: Kaloshin V, Saprykina M. 2012. An example of a nearly integrable Hamiltonian
system with a trajectory dense in a set of maximal Hausdorff dimension. Communications
in Mathematical Physics. 315(3), 643–697.
mla: Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian
System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” *Communications
in Mathematical Physics*, vol. 315, no. 3, Springer Nature, 2012, pp. 643–97,
doi:10.1007/s00220-012-1532-x.
short: V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012)
643–697.
date_created: 2020-09-18T10:47:16Z
date_published: 2012-11-01T00:00:00Z
date_updated: 2021-01-12T08:19:44Z
day: '01'
doi: 10.1007/s00220-012-1532-x
extern: '1'
intvolume: ' 315'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '11'
oa_version: None
page: 643-697
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: An example of a nearly integrable Hamiltonian system with a trajectory dense
in a set of maximal Hausdorff dimension
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 315
year: '2012'
...
---
_id: '8525'
abstract:
- lang: eng
text: Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be
the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism
f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points
for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms
Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points
P n f grows with a period n faster than any following sequence of numbers {a n
} n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In
the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth
of the number of periodic points is a Newhouse domain. A proof of the man result
is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of
that theorem is also presented.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Kaloshin V. Generic diffeomorphisms with superexponential growth of number
of periodic orbits. *Communications in Mathematical Physics*. 2000;211:253-271.
doi:10.1007/s002200050811
apa: Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of
number of periodic orbits. *Communications in Mathematical Physics*. Springer
Nature. https://doi.org/10.1007/s002200050811
chicago: Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth
of Number of Periodic Orbits.” *Communications in Mathematical Physics*.
Springer Nature, 2000. https://doi.org/10.1007/s002200050811.
ieee: V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number
of periodic orbits,” *Communications in Mathematical Physics*, vol. 211.
Springer Nature, pp. 253–271, 2000.
ista: Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of
number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.
mla: Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number
of Periodic Orbits.” *Communications in Mathematical Physics*, vol. 211,
Springer Nature, 2000, pp. 253–71, doi:10.1007/s002200050811.
short: V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.
date_created: 2020-09-18T10:50:20Z
date_published: 2000-04-01T00:00:00Z
date_updated: 2021-01-12T08:19:52Z
day: '01'
doi: 10.1007/s002200050811
extern: '1'
intvolume: ' 211'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '04'
oa_version: None
page: 253-271
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Generic diffeomorphisms with superexponential growth of number of periodic
orbits
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 211
year: '2000'
...
---
_id: '8527'
abstract:
- lang: eng
text: We introduce a new potential-theoretic definition of the dimension spectrum of
a probability measure for q > 1 and explain its relation to prior definitions.
We apply this definition to prove that if and is a Borel probability measure
with compact support in , then under almost every linear transformation from to
, the q-dimension of the image of is ; in particular, the q-dimension of is
preserved provided . We also present results on the preservation of information
dimension and pointwise dimension. Finally, for and q > 2 we give examples for
which is not preserved by any linear transformation into . All results for typical
linear transformations are also proved for typical (in the sense of prevalence)
continuously differentiable functions.
article_processing_charge: No
article_type: original
author:
- first_name: Brian R
full_name: Hunt, Brian R
last_name: Hunt
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal
measures. *Nonlinearity*. 1997;10(5):1031-1046. doi:10.1088/0951-7715/10/5/002
apa: Hunt, B. R., & Kaloshin, V. (1997). How projections affect the dimension
spectrum of fractal measures. *Nonlinearity*. IOP Publishing. https://doi.org/10.1088/0951-7715/10/5/002
chicago: Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension
Spectrum of Fractal Measures.” *Nonlinearity*. IOP Publishing, 1997. https://doi.org/10.1088/0951-7715/10/5/002.
ieee: B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum
of fractal measures,” *Nonlinearity*, vol. 10, no. 5. IOP Publishing, pp.
1031–1046, 1997.
ista: Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of
fractal measures. Nonlinearity. 10(5), 1031–1046.
mla: Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum
of Fractal Measures.” *Nonlinearity*, vol. 10, no. 5, IOP Publishing, 1997,
pp. 1031–46, doi:10.1088/0951-7715/10/5/002.
short: B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046.
date_created: 2020-09-18T10:50:41Z
date_published: 1997-06-19T00:00:00Z
date_updated: 2021-01-12T08:19:53Z
day: '19'
doi: 10.1088/0951-7715/10/5/002
extern: '1'
intvolume: ' 10'
issue: '5'
keyword:
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '06'
oa_version: None
page: 1031-1046
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: How projections affect the dimension spectrum of fractal measures
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10
year: '1997'
...