---
_id: '10176'
abstract:
- lang: eng
  text: "We give a combinatorial model for r-spin surfaces with parameterized boundary
    based on Novak (“Lattice topological field theories in two dimensions,” Ph.D.
    thesis, Universität Hamburg, 2015). The r-spin structure is encoded in terms of
    ℤ\U0001D45F-valued indices assigned to the edges of a polygonal decomposition.
    This combinatorial model is designed for our state-sum construction of two-dimensional
    topological field theories on r-spin surfaces. We show that an example of such
    a topological field theory computes the Arf-invariant of an r-spin surface as
    introduced by Randal-Williams [J. Topol. 7, 155 (2014)] and Geiges et al. [Osaka
    J. Math. 49, 449 (2012)]. This implies, in particular, that the r-spin Arf-invariant
    is constant on orbits of the mapping class group, providing an alternative proof
    of that fact."
acknowledgement: We would like to thank Nils Carqueville, Tobias Dyckerhoff, Jan Hesse,
  Ehud Meir, Sebastian Novak, Louis-Hadrien Robert, Nick Salter, Walker Stern, and
  Lukas Woike for helpful discussions and comments. L.S. was supported by the DFG
  Research Training Group 1670 “Mathematics Inspired by String Theory and Quantum
  Field Theory.”
article_number: '102302'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ingo
  full_name: Runkel, Ingo
  last_name: Runkel
- first_name: Lorant
  full_name: Szegedy, Lorant
  id: 7943226E-220E-11EA-94C7-D59F3DDC885E
  last_name: Szegedy
  orcid: 0000-0003-2834-5054
citation:
  ama: Runkel I, Szegedy L. Topological field theory on r-spin surfaces and the Arf-invariant.
    <i>Journal of Mathematical Physics</i>. 2021;62(10). doi:<a href="https://doi.org/10.1063/5.0037826">10.1063/5.0037826</a>
  apa: Runkel, I., &#38; Szegedy, L. (2021). Topological field theory on r-spin surfaces
    and the Arf-invariant. <i>Journal of Mathematical Physics</i>. AIP Publishing.
    <a href="https://doi.org/10.1063/5.0037826">https://doi.org/10.1063/5.0037826</a>
  chicago: Runkel, Ingo, and Lorant Szegedy. “Topological Field Theory on R-Spin Surfaces
    and the Arf-Invariant.” <i>Journal of Mathematical Physics</i>. AIP Publishing,
    2021. <a href="https://doi.org/10.1063/5.0037826">https://doi.org/10.1063/5.0037826</a>.
  ieee: I. Runkel and L. Szegedy, “Topological field theory on r-spin surfaces and
    the Arf-invariant,” <i>Journal of Mathematical Physics</i>, vol. 62, no. 10. AIP
    Publishing, 2021.
  ista: Runkel I, Szegedy L. 2021. Topological field theory on r-spin surfaces and
    the Arf-invariant. Journal of Mathematical Physics. 62(10), 102302.
  mla: Runkel, Ingo, and Lorant Szegedy. “Topological Field Theory on R-Spin Surfaces
    and the Arf-Invariant.” <i>Journal of Mathematical Physics</i>, vol. 62, no. 10,
    102302, AIP Publishing, 2021, doi:<a href="https://doi.org/10.1063/5.0037826">10.1063/5.0037826</a>.
  short: I. Runkel, L. Szegedy, Journal of Mathematical Physics 62 (2021).
date_created: 2021-10-24T22:01:32Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2023-08-14T08:04:12Z
day: '01'
department:
- _id: MiLe
doi: 10.1063/5.0037826
external_id:
  arxiv:
  - '1802.09978'
  isi:
  - '000755638500010'
intvolume: '        62'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1802.09978
month: '10'
oa: 1
oa_version: Preprint
publication: Journal of Mathematical Physics
publication_identifier:
  issn:
  - '00222488'
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological field theory on r-spin surfaces and the Arf-invariant
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 62
year: '2021'
...
---
_id: '8134'
abstract:
- lang: eng
  text: We prove an upper bound on the free energy of a two-dimensional homogeneous
    Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the
    free energy per unit volume differs from the one of the non-interacting system
    by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]2+) to leading order, where a is the scattering
    length of the two-body interaction potential, ρ is the density, β is the inverse
    temperature, and βc is the inverse Berezinskii–Kosterlitz–Thouless critical temperature
    for superfluidity. In combination with the corresponding matching lower bound
    proved by Deuchert et al. [Forum Math. Sigma 8, e20 (2020)], this shows equality
    in the asymptotic expansion.
article_number: '061901'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Simon
  full_name: Mayer, Simon
  id: 30C4630A-F248-11E8-B48F-1D18A9856A87
  last_name: Mayer
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas.
    II. Upper bound. <i>Journal of Mathematical Physics</i>. 2020;61(6). doi:<a href="https://doi.org/10.1063/5.0005950">10.1063/5.0005950</a>
  apa: Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional
    dilute Bose gas. II. Upper bound. <i>Journal of Mathematical Physics</i>. AIP
    Publishing. <a href="https://doi.org/10.1063/5.0005950">https://doi.org/10.1063/5.0005950</a>
  chicago: Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional
    Dilute Bose Gas. II. Upper Bound.” <i>Journal of Mathematical Physics</i>. AIP
    Publishing, 2020. <a href="https://doi.org/10.1063/5.0005950">https://doi.org/10.1063/5.0005950</a>.
  ieee: S. Mayer and R. Seiringer, “The free energy of the two-dimensional dilute
    Bose gas. II. Upper bound,” <i>Journal of Mathematical Physics</i>, vol. 61, no.
    6. AIP Publishing, 2020.
  ista: Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute
    Bose gas. II. Upper bound. Journal of Mathematical Physics. 61(6), 061901.
  mla: Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional
    Dilute Bose Gas. II. Upper Bound.” <i>Journal of Mathematical Physics</i>, vol.
    61, no. 6, 061901, AIP Publishing, 2020, doi:<a href="https://doi.org/10.1063/5.0005950">10.1063/5.0005950</a>.
  short: S. Mayer, R. Seiringer, Journal of Mathematical Physics 61 (2020).
date_created: 2020-07-19T22:00:59Z
date_published: 2020-06-22T00:00:00Z
date_updated: 2023-08-22T08:12:40Z
day: '22'
department:
- _id: RoSe
doi: 10.1063/5.0005950
ec_funded: 1
external_id:
  arxiv:
  - '2002.08281'
  isi:
  - '000544595100001'
intvolume: '        61'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2002.08281
month: '06'
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: Journal of Mathematical Physics
publication_identifier:
  issn:
  - '00222488'
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The free energy of the two-dimensional dilute Bose gas. II. Upper bound
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 61
year: '2020'
...
---
_id: '8670'
abstract:
- lang: eng
  text: The α–z Rényi relative entropies are a two-parameter family of Rényi relative
    entropies that are quantum generalizations of the classical α-Rényi relative entropies.
    In the work [Adv. Math. 365, 107053 (2020)], we decided the full range of (α,
    z) for which the data processing inequality (DPI) is valid. In this paper, we
    give algebraic conditions for the equality in DPI. For the full range of parameters
    (α, z), we give necessary conditions and sufficient conditions. For most parameters,
    we give equivalent conditions. This generalizes and strengthens the results of
    Leditzky et al. [Lett. Math. Phys. 107, 61–80 (2017)].
acknowledgement: This research was supported by the European Union’s Horizon 2020
  research and innovation program under the Marie Skłodowska-Curie Grant Agreement
  No. 754411. The author would like to thank Anna Vershynina and Sarah Chehade for
  their helpful comments.
article_number: '102201'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Haonan
  full_name: Zhang, Haonan
  id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
  last_name: Zhang
citation:
  ama: Zhang H. Equality conditions of data processing inequality for α-z Rényi relative
    entropies. <i>Journal of Mathematical Physics</i>. 2020;61(10). doi:<a href="https://doi.org/10.1063/5.0022787">10.1063/5.0022787</a>
  apa: Zhang, H. (2020). Equality conditions of data processing inequality for α-z
    Rényi relative entropies. <i>Journal of Mathematical Physics</i>. AIP Publishing.
    <a href="https://doi.org/10.1063/5.0022787">https://doi.org/10.1063/5.0022787</a>
  chicago: Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z
    Rényi Relative Entropies.” <i>Journal of Mathematical Physics</i>. AIP Publishing,
    2020. <a href="https://doi.org/10.1063/5.0022787">https://doi.org/10.1063/5.0022787</a>.
  ieee: H. Zhang, “Equality conditions of data processing inequality for α-z Rényi
    relative entropies,” <i>Journal of Mathematical Physics</i>, vol. 61, no. 10.
    AIP Publishing, 2020.
  ista: Zhang H. 2020. Equality conditions of data processing inequality for α-z Rényi
    relative entropies. Journal of Mathematical Physics. 61(10), 102201.
  mla: Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi
    Relative Entropies.” <i>Journal of Mathematical Physics</i>, vol. 61, no. 10,
    102201, AIP Publishing, 2020, doi:<a href="https://doi.org/10.1063/5.0022787">10.1063/5.0022787</a>.
  short: H. Zhang, Journal of Mathematical Physics 61 (2020).
date_created: 2020-10-18T22:01:36Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2023-08-22T10:32:29Z
day: '01'
department:
- _id: JaMa
doi: 10.1063/5.0022787
ec_funded: 1
external_id:
  arxiv:
  - '2007.06644'
  isi:
  - '000578529200001'
intvolume: '        61'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2007.06644
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Journal of Mathematical Physics
publication_identifier:
  issn:
  - '00222488'
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equality conditions of data processing inequality for α-z Rényi relative entropies
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 61
year: '2020'
...
---
_id: '7226'
article_number: '123504'
article_processing_charge: No
article_type: letter_note
author:
- first_name: Vojkan
  full_name: Jaksic, Vojkan
  last_name: Jaksic
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: 'Jaksic V, Seiringer R. Introduction to the Special Collection: International
    Congress on Mathematical Physics (ICMP) 2018. <i>Journal of Mathematical Physics</i>.
    2019;60(12). doi:<a href="https://doi.org/10.1063/1.5138135">10.1063/1.5138135</a>'
  apa: 'Jaksic, V., &#38; Seiringer, R. (2019). Introduction to the Special Collection:
    International Congress on Mathematical Physics (ICMP) 2018. <i>Journal of Mathematical
    Physics</i>. AIP Publishing. <a href="https://doi.org/10.1063/1.5138135">https://doi.org/10.1063/1.5138135</a>'
  chicago: 'Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection:
    International Congress on Mathematical Physics (ICMP) 2018.” <i>Journal of Mathematical
    Physics</i>. AIP Publishing, 2019. <a href="https://doi.org/10.1063/1.5138135">https://doi.org/10.1063/1.5138135</a>.'
  ieee: 'V. Jaksic and R. Seiringer, “Introduction to the Special Collection: International
    Congress on Mathematical Physics (ICMP) 2018,” <i>Journal of Mathematical Physics</i>,
    vol. 60, no. 12. AIP Publishing, 2019.'
  ista: 'Jaksic V, Seiringer R. 2019. Introduction to the Special Collection: International
    Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical Physics.
    60(12), 123504.'
  mla: 'Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection:
    International Congress on Mathematical Physics (ICMP) 2018.” <i>Journal of Mathematical
    Physics</i>, vol. 60, no. 12, 123504, AIP Publishing, 2019, doi:<a href="https://doi.org/10.1063/1.5138135">10.1063/1.5138135</a>.'
  short: V. Jaksic, R. Seiringer, Journal of Mathematical Physics 60 (2019).
date_created: 2020-01-05T23:00:46Z
date_published: 2019-12-01T00:00:00Z
date_updated: 2024-02-28T13:01:45Z
day: '01'
ddc:
- '500'
department:
- _id: RoSe
doi: 10.1063/1.5138135
external_id:
  isi:
  - '000505529800002'
file:
- access_level: open_access
  checksum: bbd12ad1999a9ad7ba4d3c6f2e579c22
  content_type: application/pdf
  creator: dernst
  date_created: 2020-01-07T14:59:13Z
  date_updated: 2020-07-14T12:47:54Z
  file_id: '7244'
  file_name: 2019_JournalMathPhysics_Jaksic.pdf
  file_size: 1025015
  relation: main_file
file_date_updated: 2020-07-14T12:47:54Z
has_accepted_license: '1'
intvolume: '        60'
isi: 1
issue: '12'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Physics
publication_identifier:
  issn:
  - '00222488'
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Introduction to the Special Collection: International Congress on Mathematical
  Physics (ICMP) 2018'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 60
year: '2019'
...
---
_id: '912'
abstract:
- lang: eng
  text: "We consider a many-body system of fermionic atoms interacting via a local
    pair potential and subject to an external potential within the framework of Bardeen-Cooper-Schrieffer
    (BCS) theory. We measure the free energy of the whole sample with respect to the
    free energy of a reference state which allows us to define a BCS functional with
    boundary conditions at infinity. Our main result is a lower bound for this energy
    functional in terms of expressions that typically appear in Ginzburg-Landau functionals.\r\n"
article_number: '081901'
article_processing_charge: No
author:
- first_name: Andreas
  full_name: Deuchert, Andreas
  id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
  last_name: Deuchert
  orcid: 0000-0003-3146-6746
citation:
  ama: Deuchert A. A lower bound for the BCS functional with boundary conditions at
    infinity. <i> Journal of Mathematical Physics</i>. 2017;58(8). doi:<a href="https://doi.org/10.1063/1.4996580">10.1063/1.4996580</a>
  apa: Deuchert, A. (2017). A lower bound for the BCS functional with boundary conditions
    at infinity. <i> Journal of Mathematical Physics</i>. AIP Publishing. <a href="https://doi.org/10.1063/1.4996580">https://doi.org/10.1063/1.4996580</a>
  chicago: Deuchert, Andreas. “A Lower Bound for the BCS Functional with Boundary
    Conditions at Infinity.” <i> Journal of Mathematical Physics</i>. AIP Publishing,
    2017. <a href="https://doi.org/10.1063/1.4996580">https://doi.org/10.1063/1.4996580</a>.
  ieee: A. Deuchert, “A lower bound for the BCS functional with boundary conditions
    at infinity,” <i> Journal of Mathematical Physics</i>, vol. 58, no. 8. AIP Publishing,
    2017.
  ista: Deuchert A. 2017. A lower bound for the BCS functional with boundary conditions
    at infinity.  Journal of Mathematical Physics. 58(8), 081901.
  mla: Deuchert, Andreas. “A Lower Bound for the BCS Functional with Boundary Conditions
    at Infinity.” <i> Journal of Mathematical Physics</i>, vol. 58, no. 8, 081901,
    AIP Publishing, 2017, doi:<a href="https://doi.org/10.1063/1.4996580">10.1063/1.4996580</a>.
  short: A. Deuchert,  Journal of Mathematical Physics 58 (2017).
date_created: 2018-12-11T11:49:10Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2024-02-28T13:07:56Z
day: '01'
department:
- _id: RoSe
doi: 10.1063/1.4996580
ec_funded: 1
external_id:
  isi:
  - '000409197200015'
intvolume: '        58'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1703.04616
month: '08'
oa: 1
oa_version: Submitted Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: ' Journal of Mathematical Physics'
publication_identifier:
  issn:
  - '00222488'
publication_status: published
publisher: AIP Publishing
publist_id: '6531'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A lower bound for the BCS functional with boundary conditions at infinity
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2017'
...