---
_id: '63637'
article_type: original
author:
- first_name: Benjamin
  full_name: Hinrichs, Benjamin
  id: '99427'
  last_name: Hinrichs
  orcid: 0000-0001-9074-1205
- first_name: Marius
  full_name: Lemm, Marius
  last_name: Lemm
- first_name: Oliver
  full_name: Siebert, Oliver
  last_name: Siebert
citation:
  ama: Hinrichs B, Lemm M, Siebert O. On Lieb–Robinson Bounds for a Class of Continuum
    Fermions. <i>Annales Henri Poincaré</i>. 2024;26(1):41-80. doi:<a href="https://doi.org/10.1007/s00023-024-01453-y">10.1007/s00023-024-01453-y</a>
  apa: Hinrichs, B., Lemm, M., &#38; Siebert, O. (2024). On Lieb–Robinson Bounds for
    a Class of Continuum Fermions. <i>Annales Henri Poincaré</i>, <i>26</i>(1), 41–80.
    <a href="https://doi.org/10.1007/s00023-024-01453-y">https://doi.org/10.1007/s00023-024-01453-y</a>
  bibtex: '@article{Hinrichs_Lemm_Siebert_2024, title={On Lieb–Robinson Bounds for
    a Class of Continuum Fermions}, volume={26}, DOI={<a href="https://doi.org/10.1007/s00023-024-01453-y">10.1007/s00023-024-01453-y</a>},
    number={1}, journal={Annales Henri Poincaré}, publisher={Springer Science and
    Business Media LLC}, author={Hinrichs, Benjamin and Lemm, Marius and Siebert,
    Oliver}, year={2024}, pages={41–80} }'
  chicago: 'Hinrichs, Benjamin, Marius Lemm, and Oliver Siebert. “On Lieb–Robinson
    Bounds for a Class of Continuum Fermions.” <i>Annales Henri Poincaré</i> 26, no.
    1 (2024): 41–80. <a href="https://doi.org/10.1007/s00023-024-01453-y">https://doi.org/10.1007/s00023-024-01453-y</a>.'
  ieee: 'B. Hinrichs, M. Lemm, and O. Siebert, “On Lieb–Robinson Bounds for a Class
    of Continuum Fermions,” <i>Annales Henri Poincaré</i>, vol. 26, no. 1, pp. 41–80,
    2024, doi: <a href="https://doi.org/10.1007/s00023-024-01453-y">10.1007/s00023-024-01453-y</a>.'
  mla: Hinrichs, Benjamin, et al. “On Lieb–Robinson Bounds for a Class of Continuum
    Fermions.” <i>Annales Henri Poincaré</i>, vol. 26, no. 1, Springer Science and
    Business Media LLC, 2024, pp. 41–80, doi:<a href="https://doi.org/10.1007/s00023-024-01453-y">10.1007/s00023-024-01453-y</a>.
  short: B. Hinrichs, M. Lemm, O. Siebert, Annales Henri Poincaré 26 (2024) 41–80.
date_created: 2026-01-16T08:46:12Z
date_updated: 2026-01-16T09:05:58Z
department:
- _id: '799'
doi: 10.1007/s00023-024-01453-y
external_id:
  arxiv:
  - '2310.17736'
intvolume: '        26'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 41-80
project:
- _id: '266'
  name: 'PhoQC: Photonisches Quantencomputing'
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On Lieb–Robinson Bounds for a Class of Continuum Fermions
type: journal_article
user_id: '99427'
volume: 26
year: '2024'
...
---
_id: '53410'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We consider a geodesic billiard system
    consisting of a complete Riemannian manifold and an obstacle submanifold with
    boundary at which the trajectories of the geodesic flow experience specular reflections.
    We show that if the geodesic billiard system is hyperbolic on its trapped set
    and the latter is compact and non-grazing, the techniques for open hyperbolic
    systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146,
    2016) can be applied to a smooth model for the discontinuous flow defined by the
    non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent
    for the generator of the billiard flow. As an application we prove a meromorphic
    continuation of weighted zeta functions together with explicit residue formulae.
    In particular, our results apply to scattering by convex obstacles in the Euclidean
    plane.</jats:p>
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Philipp
  full_name: Schütte, Philipp
  id: '50168'
  last_name: Schütte
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Delarue B, Schütte P, Weich T. Resonances and Weighted Zeta Functions for Obstacle
    Scattering via Smooth Models. <i>Annales Henri Poincaré</i>. 2023;25(2):1607-1656.
    doi:<a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>
  apa: Delarue, B., Schütte, P., &#38; Weich, T. (2023). Resonances and Weighted Zeta
    Functions for Obstacle Scattering via Smooth Models. <i>Annales Henri Poincaré</i>,
    <i>25</i>(2), 1607–1656. <a href="https://doi.org/10.1007/s00023-023-01379-x">https://doi.org/10.1007/s00023-023-01379-x</a>
  bibtex: '@article{Delarue_Schütte_Weich_2023, title={Resonances and Weighted Zeta
    Functions for Obstacle Scattering via Smooth Models}, volume={25}, DOI={<a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>},
    number={2}, journal={Annales Henri Poincaré}, publisher={Springer Science and
    Business Media LLC}, author={Delarue, Benjamin and Schütte, Philipp and Weich,
    Tobias}, year={2023}, pages={1607–1656} }'
  chicago: 'Delarue, Benjamin, Philipp Schütte, and Tobias Weich. “Resonances and
    Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” <i>Annales
    Henri Poincaré</i> 25, no. 2 (2023): 1607–56. <a href="https://doi.org/10.1007/s00023-023-01379-x">https://doi.org/10.1007/s00023-023-01379-x</a>.'
  ieee: 'B. Delarue, P. Schütte, and T. Weich, “Resonances and Weighted Zeta Functions
    for Obstacle Scattering via Smooth Models,” <i>Annales Henri Poincaré</i>, vol.
    25, no. 2, pp. 1607–1656, 2023, doi: <a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>.'
  mla: Delarue, Benjamin, et al. “Resonances and Weighted Zeta Functions for Obstacle
    Scattering via Smooth Models.” <i>Annales Henri Poincaré</i>, vol. 25, no. 2,
    Springer Science and Business Media LLC, 2023, pp. 1607–56, doi:<a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>.
  short: B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.
date_created: 2024-04-11T12:30:14Z
date_updated: 2024-04-11T12:37:34Z
department:
- _id: '548'
doi: 10.1007/s00023-023-01379-x
intvolume: '        25'
issue: '2'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 1607-1656
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models
type: journal_article
user_id: '70575'
volume: 25
year: '2023'
...
---
_id: '63635'
article_type: original
author:
- first_name: Benjamin
  full_name: Hinrichs, Benjamin
  id: '99427'
  last_name: Hinrichs
  orcid: 0000-0001-9074-1205
- first_name: Oliver
  full_name: Matte, Oliver
  last_name: Matte
citation:
  ama: Hinrichs B, Matte O. Feynman–Kac Formula and Asymptotic Behavior of the Minimal
    Energy for the Relativistic Nelson Model in Two Spatial Dimensions. <i>Annales
    Henri Poincaré</i>. 2023;25(6):2877-2940. doi:<a href="https://doi.org/10.1007/s00023-023-01369-z">10.1007/s00023-023-01369-z</a>
  apa: Hinrichs, B., &#38; Matte, O. (2023). Feynman–Kac Formula and Asymptotic Behavior
    of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.
    <i>Annales Henri Poincaré</i>, <i>25</i>(6), 2877–2940. <a href="https://doi.org/10.1007/s00023-023-01369-z">https://doi.org/10.1007/s00023-023-01369-z</a>
  bibtex: '@article{Hinrichs_Matte_2023, title={Feynman–Kac Formula and Asymptotic
    Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial
    Dimensions}, volume={25}, DOI={<a href="https://doi.org/10.1007/s00023-023-01369-z">10.1007/s00023-023-01369-z</a>},
    number={6}, journal={Annales Henri Poincaré}, publisher={Springer Science and
    Business Media LLC}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2023},
    pages={2877–2940} }'
  chicago: 'Hinrichs, Benjamin, and Oliver Matte. “Feynman–Kac Formula and Asymptotic
    Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial
    Dimensions.” <i>Annales Henri Poincaré</i> 25, no. 6 (2023): 2877–2940. <a href="https://doi.org/10.1007/s00023-023-01369-z">https://doi.org/10.1007/s00023-023-01369-z</a>.'
  ieee: 'B. Hinrichs and O. Matte, “Feynman–Kac Formula and Asymptotic Behavior of
    the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions,”
    <i>Annales Henri Poincaré</i>, vol. 25, no. 6, pp. 2877–2940, 2023, doi: <a href="https://doi.org/10.1007/s00023-023-01369-z">10.1007/s00023-023-01369-z</a>.'
  mla: Hinrichs, Benjamin, and Oliver Matte. “Feynman–Kac Formula and Asymptotic Behavior
    of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.”
    <i>Annales Henri Poincaré</i>, vol. 25, no. 6, Springer Science and Business Media
    LLC, 2023, pp. 2877–940, doi:<a href="https://doi.org/10.1007/s00023-023-01369-z">10.1007/s00023-023-01369-z</a>.
  short: B. Hinrichs, O. Matte, Annales Henri Poincaré 25 (2023) 2877–2940.
date_created: 2026-01-16T08:39:40Z
date_updated: 2026-01-16T09:05:26Z
department:
- _id: '799'
doi: 10.1007/s00023-023-01369-z
extern: '1'
external_id:
  arxiv:
  - '2211.14046'
intvolume: '        25'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 2877-2940
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic
  Nelson Model in Two Spatial Dimensions
type: journal_article
user_id: '99427'
volume: 25
year: '2023'
...
---
_id: '43492'
abstract:
- lang: eng
  text: We consider the spin boson model with external magnetic field. We prove a
    path integral formula for the heat kernel, known as Feynman–Kac–Nelson (FKN) formula.
    We use this path integral representation to express the ground state energy as
    a stochastic integral. Based on this connection, we determine the expansion coefficients
    of the ground state energy with respect to the magnetic field strength and express
    them in terms of correlation functions of a continuous Ising model. From a recently
    proven correlation inequality, we can then deduce that the second order derivative
    is finite. As an application, we show existence of ground states in infrared-singular
    situations.
article_type: original
author:
- first_name: David
  full_name: Hasler, David
  last_name: Hasler
- first_name: Benjamin
  full_name: Hinrichs, Benjamin
  id: '99427'
  last_name: Hinrichs
  orcid: 0000-0001-9074-1205
- first_name: Oliver
  full_name: Siebert, Oliver
  last_name: Siebert
citation:
  ama: Hasler D, Hinrichs B, Siebert O. FKN Formula and Ground State Energy for the
    Spin Boson Model with External Magnetic Field. <i>Annales Henri Poincaré</i>.
    2022;23(8):2819-2853. doi:<a href="https://doi.org/10.1007/s00023-022-01160-6">10.1007/s00023-022-01160-6</a>
  apa: Hasler, D., Hinrichs, B., &#38; Siebert, O. (2022). FKN Formula and Ground
    State Energy for the Spin Boson Model with External Magnetic Field. <i>Annales
    Henri Poincaré</i>, <i>23</i>(8), 2819–2853. <a href="https://doi.org/10.1007/s00023-022-01160-6">https://doi.org/10.1007/s00023-022-01160-6</a>
  bibtex: '@article{Hasler_Hinrichs_Siebert_2022, title={FKN Formula and Ground State
    Energy for the Spin Boson Model with External Magnetic Field}, volume={23}, DOI={<a
    href="https://doi.org/10.1007/s00023-022-01160-6">10.1007/s00023-022-01160-6</a>},
    number={8}, journal={Annales Henri Poincaré}, publisher={Springer Science and
    Business Media LLC}, author={Hasler, David and Hinrichs, Benjamin and Siebert,
    Oliver}, year={2022}, pages={2819–2853} }'
  chicago: 'Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “FKN Formula and
    Ground State Energy for the Spin Boson Model with External Magnetic Field.” <i>Annales
    Henri Poincaré</i> 23, no. 8 (2022): 2819–53. <a href="https://doi.org/10.1007/s00023-022-01160-6">https://doi.org/10.1007/s00023-022-01160-6</a>.'
  ieee: 'D. Hasler, B. Hinrichs, and O. Siebert, “FKN Formula and Ground State Energy
    for the Spin Boson Model with External Magnetic Field,” <i>Annales Henri Poincaré</i>,
    vol. 23, no. 8, pp. 2819–2853, 2022, doi: <a href="https://doi.org/10.1007/s00023-022-01160-6">10.1007/s00023-022-01160-6</a>.'
  mla: Hasler, David, et al. “FKN Formula and Ground State Energy for the Spin Boson
    Model with External Magnetic Field.” <i>Annales Henri Poincaré</i>, vol. 23, no.
    8, Springer Science and Business Media LLC, 2022, pp. 2819–53, doi:<a href="https://doi.org/10.1007/s00023-022-01160-6">10.1007/s00023-022-01160-6</a>.
  short: D. Hasler, B. Hinrichs, O. Siebert, Annales Henri Poincaré 23 (2022) 2819–2853.
date_created: 2023-04-14T04:49:36Z
date_updated: 2026-01-16T09:02:30Z
doi: 10.1007/s00023-022-01160-6
extern: '1'
external_id:
  arxiv:
  - '2106.08659 '
intvolume: '        23'
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 2819-2853
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: FKN Formula and Ground State Energy for the Spin Boson Model with External
  Magnetic Field
type: journal_article
user_id: '99427'
volume: 23
year: '2022'
...
---
_id: '32006'
author:
- first_name: Colin
  full_name: Guillarmou, Colin
  last_name: Guillarmou
- first_name: Benjamin
  full_name: Küster, Benjamin
  last_name: Küster
citation:
  ama: Guillarmou C, Küster B. Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds.
    <i>Annales Henri Poincaré</i>. 2021;22(11):3565-3617. doi:<a href="https://doi.org/10.1007/s00023-021-01068-7">10.1007/s00023-021-01068-7</a>
  apa: Guillarmou, C., &#38; Küster, B. (2021). Spectral Theory of the Frame Flow
    on Hyperbolic 3-Manifolds. <i>Annales Henri Poincaré</i>, <i>22</i>(11), 3565–3617.
    <a href="https://doi.org/10.1007/s00023-021-01068-7">https://doi.org/10.1007/s00023-021-01068-7</a>
  bibtex: '@article{Guillarmou_Küster_2021, title={Spectral Theory of the Frame Flow
    on Hyperbolic 3-Manifolds}, volume={22}, DOI={<a href="https://doi.org/10.1007/s00023-021-01068-7">10.1007/s00023-021-01068-7</a>},
    number={11}, journal={Annales Henri Poincaré}, publisher={Springer Science and
    Business Media LLC}, author={Guillarmou, Colin and Küster, Benjamin}, year={2021},
    pages={3565–3617} }'
  chicago: 'Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame
    Flow on Hyperbolic 3-Manifolds.” <i>Annales Henri Poincaré</i> 22, no. 11 (2021):
    3565–3617. <a href="https://doi.org/10.1007/s00023-021-01068-7">https://doi.org/10.1007/s00023-021-01068-7</a>.'
  ieee: 'C. Guillarmou and B. Küster, “Spectral Theory of the Frame Flow on Hyperbolic
    3-Manifolds,” <i>Annales Henri Poincaré</i>, vol. 22, no. 11, pp. 3565–3617, 2021,
    doi: <a href="https://doi.org/10.1007/s00023-021-01068-7">10.1007/s00023-021-01068-7</a>.'
  mla: Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame Flow
    on Hyperbolic 3-Manifolds.” <i>Annales Henri Poincaré</i>, vol. 22, no. 11, Springer
    Science and Business Media LLC, 2021, pp. 3565–617, doi:<a href="https://doi.org/10.1007/s00023-021-01068-7">10.1007/s00023-021-01068-7</a>.
  short: C. Guillarmou, B. Küster, Annales Henri Poincaré 22 (2021) 3565–3617.
date_created: 2022-06-20T08:37:52Z
date_updated: 2024-04-11T12:39:23Z
department:
- _id: '548'
doi: 10.1007/s00023-021-01068-7
intvolume: '        22'
issue: '11'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 3565-3617
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds
type: journal_article
user_id: '70575'
volume: 22
year: '2021'
...
---
_id: '31289'
author:
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Weich T. On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows.
    <i>Annales Henri Poincaré</i>. 2016;18(1):37-52. doi:<a href="https://doi.org/10.1007/s00023-016-0514-5">10.1007/s00023-016-0514-5</a>
  apa: Weich, T. (2016). On the Support of Pollicott–Ruelle Resonanant States for
    Anosov Flows. <i>Annales Henri Poincaré</i>, <i>18</i>(1), 37–52. <a href="https://doi.org/10.1007/s00023-016-0514-5">https://doi.org/10.1007/s00023-016-0514-5</a>
  bibtex: '@article{Weich_2016, title={On the Support of Pollicott–Ruelle Resonanant
    States for Anosov Flows}, volume={18}, DOI={<a href="https://doi.org/10.1007/s00023-016-0514-5">10.1007/s00023-016-0514-5</a>},
    number={1}, journal={Annales Henri Poincaré}, publisher={Springer Science and
    Business Media LLC}, author={Weich, Tobias}, year={2016}, pages={37–52} }'
  chicago: 'Weich, Tobias. “On the Support of Pollicott–Ruelle Resonanant States for
    Anosov Flows.” <i>Annales Henri Poincaré</i> 18, no. 1 (2016): 37–52. <a href="https://doi.org/10.1007/s00023-016-0514-5">https://doi.org/10.1007/s00023-016-0514-5</a>.'
  ieee: 'T. Weich, “On the Support of Pollicott–Ruelle Resonanant States for Anosov
    Flows,” <i>Annales Henri Poincaré</i>, vol. 18, no. 1, pp. 37–52, 2016, doi: <a
    href="https://doi.org/10.1007/s00023-016-0514-5">10.1007/s00023-016-0514-5</a>.'
  mla: Weich, Tobias. “On the Support of Pollicott–Ruelle Resonanant States for Anosov
    Flows.” <i>Annales Henri Poincaré</i>, vol. 18, no. 1, Springer Science and Business
    Media LLC, 2016, pp. 37–52, doi:<a href="https://doi.org/10.1007/s00023-016-0514-5">10.1007/s00023-016-0514-5</a>.
  short: T. Weich, Annales Henri Poincaré 18 (2016) 37–52.
date_created: 2022-05-17T12:53:51Z
date_updated: 2022-05-19T10:15:36Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: 10.1007/s00023-016-0514-5
external_id:
  arxiv:
  - '1511.08338'
intvolume: '        18'
issue: '1'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 37-52
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows
type: journal_article
user_id: '49178'
volume: 18
year: '2016'
...