---
_id: '63656'
article_number: '012220'
article_type: original
author:
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Julien
full_name: Pinske, Julien
last_name: Pinske
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Martin
full_name: Kolb, Martin
id: '48880'
last_name: Kolb
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Ares L, Pinske J, Hinrichs B, Kolb M, Sperling J. Restricted Monte Carlo wave-function
method and Lindblad equation for identifying entangling open-quantum-system dynamics.
Physical Review A. 2026;113(1). doi:10.1103/hcj7-8zlg
apa: Ares, L., Pinske, J., Hinrichs, B., Kolb, M., & Sperling, J. (2026). Restricted
Monte Carlo wave-function method and Lindblad equation for identifying entangling
open-quantum-system dynamics. Physical Review A, 113(1), Article
012220. https://doi.org/10.1103/hcj7-8zlg
bibtex: '@article{Ares_Pinske_Hinrichs_Kolb_Sperling_2026, title={Restricted Monte
Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system
dynamics}, volume={113}, DOI={10.1103/hcj7-8zlg},
number={1012220}, journal={Physical Review A}, publisher={American Physical Society
(APS)}, author={Ares, Laura and Pinske, Julien and Hinrichs, Benjamin and Kolb,
Martin and Sperling, Jan}, year={2026} }'
chicago: Ares, Laura, Julien Pinske, Benjamin Hinrichs, Martin Kolb, and Jan Sperling.
“Restricted Monte Carlo Wave-Function Method and Lindblad Equation for Identifying
Entangling Open-Quantum-System Dynamics.” Physical Review A 113, no. 1
(2026). https://doi.org/10.1103/hcj7-8zlg.
ieee: 'L. Ares, J. Pinske, B. Hinrichs, M. Kolb, and J. Sperling, “Restricted Monte
Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system
dynamics,” Physical Review A, vol. 113, no. 1, Art. no. 012220, 2026, doi:
10.1103/hcj7-8zlg.'
mla: Ares, Laura, et al. “Restricted Monte Carlo Wave-Function Method and Lindblad
Equation for Identifying Entangling Open-Quantum-System Dynamics.” Physical
Review A, vol. 113, no. 1, 012220, American Physical Society (APS), 2026,
doi:10.1103/hcj7-8zlg.
short: L. Ares, J. Pinske, B. Hinrichs, M. Kolb, J. Sperling, Physical Review A
113 (2026).
date_created: 2026-01-18T18:08:18Z
date_updated: 2026-01-18T18:15:01Z
department:
- _id: '799'
doi: 10.1103/hcj7-8zlg
external_id:
arxiv:
- '2412.08735'
intvolume: ' 113'
issue: '1'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
publication: Physical Review A
publication_identifier:
issn:
- 2469-9926
- 2469-9934
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Restricted Monte Carlo wave-function method and Lindblad equation for identifying
entangling open-quantum-system dynamics
type: journal_article
user_id: '99427'
volume: 113
year: '2026'
...
---
_id: '63657'
article_number: L010403
article_type: letter_note
author:
- first_name: Julien
full_name: Pinske, Julien
last_name: Pinske
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Martin
full_name: Kolb, Martin
id: '48880'
last_name: Kolb
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Pinske J, Ares L, Hinrichs B, Kolb M, Sperling J. Separability Lindblad equation for
dynamical open-system entanglement. Physical Review A. 2026;113(1). doi:10.1103/kd3b-bfxq
apa: Pinske, J., Ares, L., Hinrichs, B., Kolb, M., & Sperling, J. (2026). Separability
Lindblad equation for dynamical open-system entanglement. Physical Review A,
113(1), Article L010403. https://doi.org/10.1103/kd3b-bfxq
bibtex: '@article{Pinske_Ares_Hinrichs_Kolb_Sperling_2026, title={Separability Lindblad
equation for dynamical open-system entanglement}, volume={113}, DOI={10.1103/kd3b-bfxq},
number={1L010403}, journal={Physical Review A}, publisher={American Physical Society
(APS)}, author={Pinske, Julien and Ares, Laura and Hinrichs, Benjamin and Kolb,
Martin and Sperling, Jan}, year={2026} }'
chicago: Pinske, Julien, Laura Ares, Benjamin Hinrichs, Martin Kolb, and Jan Sperling.
“Separability Lindblad Equation for Dynamical Open-System Entanglement.” Physical
Review A 113, no. 1 (2026). https://doi.org/10.1103/kd3b-bfxq.
ieee: 'J. Pinske, L. Ares, B. Hinrichs, M. Kolb, and J. Sperling, “Separability
Lindblad equation for dynamical open-system entanglement,” Physical Review
A, vol. 113, no. 1, Art. no. L010403, 2026, doi: 10.1103/kd3b-bfxq.'
mla: Pinske, Julien, et al. “Separability Lindblad Equation for Dynamical Open-System
Entanglement.” Physical Review A, vol. 113, no. 1, L010403, American Physical
Society (APS), 2026, doi:10.1103/kd3b-bfxq.
short: J. Pinske, L. Ares, B. Hinrichs, M. Kolb, J. Sperling, Physical Review A
113 (2026).
date_created: 2026-01-18T18:11:27Z
date_updated: 2026-01-18T18:15:26Z
department:
- _id: '799'
doi: 10.1103/kd3b-bfxq
external_id:
arxiv:
- '2412.08724'
intvolume: ' 113'
issue: '1'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
publication: Physical Review A
publication_identifier:
issn:
- 2469-9926
- 2469-9934
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Separability Lindblad equation for dynamical open-system entanglement
type: journal_article
user_id: '99427'
volume: 113
year: '2026'
...
---
_id: '47534'
abstract:
- lang: eng
text: "In this proceeding we consider a translation invariant Nelson type model
in\r\ntwo spatial dimensions modeling a scalar relativistic particle in interaction\r\nwith
a massive radiation field. As is well-known, the corresponding Hamiltonian\r\ncan
be defined with the help of an energy renormalization. First, we review a\r\nFeynman-Kac
formula for the semigroup generated by this Hamiltonian proven by\r\nthe authors
in a recent preprint (where several matter particles and exterior\r\npotentials
are treated as well). After that, we employ a few technical key\r\nrelations and
estimates obtained in our preprint to present an otherwise\r\nself-contained derivation
of new Feynman-Kac formulas for the fiber\r\nHamiltonians attached to fixed total
momenta of the translation invariant\r\nsystem. We conclude by inferring an alternative
derivation of the Feynman-Kac\r\nformula for the full translation invariant Hamiltonian."
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 for fiber Hamiltonians in the relativistic
Nelson model in two spatial dimensions. In: Hiroshima F, ed. Proceedings of
the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics.”
Vol 2310. RIMS Kôkyûroku. ; 2025.'
apa: Hinrichs, B., & Matte, O. (2025). Feynman-Kac formula for fiber Hamiltonians
in the relativistic Nelson model in two spatial dimensions. In F. Hiroshima (Ed.),
Proceedings of the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields
and Related Topics” (Vol. 2310, Issue 3).
bibtex: '@inproceedings{Hinrichs_Matte_2025, series={RIMS Kôkyûroku}, title={Feynman-Kac
formula for fiber Hamiltonians in the relativistic Nelson model in two spatial
dimensions}, volume={2310}, number={3}, booktitle={Proceedings of the 2023 RIMS
Workshop “Mathematical Aspects of Quantum Fields and Related Topics”}, author={Hinrichs,
Benjamin and Matte, Oliver}, editor={Hiroshima, Fumio}, year={2025}, collection={RIMS
Kôkyûroku} }'
chicago: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians
in the Relativistic Nelson Model in Two Spatial Dimensions.” In Proceedings
of the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related
Topics,” edited by Fumio Hiroshima, Vol. 2310. RIMS Kôkyûroku, 2025.
ieee: B. Hinrichs and O. Matte, “Feynman-Kac formula for fiber Hamiltonians in the
relativistic Nelson model in two spatial dimensions,” in Proceedings of the
2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics,”
2025, vol. 2310, no. 3.
mla: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians
in the Relativistic Nelson Model in Two Spatial Dimensions.” Proceedings of
the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics,”
edited by Fumio Hiroshima, vol. 2310, no. 3, 2025.
short: 'B. Hinrichs, O. Matte, in: F. Hiroshima (Ed.), Proceedings of the 2023 RIMS
Workshop “Mathematical Aspects of Quantum Fields and Related Topics,” 2025.'
date_created: 2023-10-02T06:21:37Z
date_updated: 2026-01-16T08:55:19Z
department:
- _id: '799'
- _id: '623'
editor:
- first_name: Fumio
full_name: Hiroshima, Fumio
last_name: Hiroshima
external_id:
arxiv:
- '2309.09005'
intvolume: ' 2310'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2310.html
project:
- _id: '266'
name: 'PhoQC: PhoQC: Photonisches Quantencomputing'
publication: Proceedings of the 2023 RIMS Workshop 'Mathematical Aspects of Quantum
Fields and Related Topics'
series_title: RIMS Kôkyûroku
status: public
title: Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model
in two spatial dimensions
type: conference
user_id: '99427'
volume: 2310
year: '2025'
...
---
_id: '63642'
abstract:
- lang: eng
text: We prove absence of ground states in the infrared-divergent spin boson model
at large coupling. Our key argument reduces the proof to verifying long range
order in the dual one-dimensional continuum Ising model, i.e., to showing that
the respective two point function is lower bounded by a strictly positive constant.
We can then use known results from percolation theory to establish long range
order at large coupling. Combined with the known existence of ground states at
small coupling, our result proves that the spin boson model undergoes a phase
transition with respect to the coupling strength. We also present an expansion
for the vacuum overlap of the spin boson ground state in terms of the Ising $n$-point
functions, which implies that the phase transition is unique, i.e., that there
is a critical coupling constant below which a ground state exists and above which
none can exist.
author:
- first_name: Volker
full_name: Betz, Volker
last_name: Betz
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Mino Nicola
full_name: Kraft, Mino Nicola
last_name: Kraft
- first_name: Steffen
full_name: Polzer, Steffen
last_name: Polzer
citation:
ama: Betz V, Hinrichs B, Kraft MN, Polzer S. On the Ising Phase Transition in the
Infrared-Divergent Spin Boson Model. arXiv:250119362. Published online
2025.
apa: Betz, V., Hinrichs, B., Kraft, M. N., & Polzer, S. (2025). On the Ising
Phase Transition in the Infrared-Divergent Spin Boson Model. In arXiv:2501.19362.
bibtex: '@article{Betz_Hinrichs_Kraft_Polzer_2025, title={On the Ising Phase Transition
in the Infrared-Divergent Spin Boson Model}, journal={arXiv:2501.19362}, author={Betz,
Volker and Hinrichs, Benjamin and Kraft, Mino Nicola and Polzer, Steffen}, year={2025}
}'
chicago: Betz, Volker, Benjamin Hinrichs, Mino Nicola Kraft, and Steffen Polzer.
“On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model.” ArXiv:2501.19362,
2025.
ieee: V. Betz, B. Hinrichs, M. N. Kraft, and S. Polzer, “On the Ising Phase Transition
in the Infrared-Divergent Spin Boson Model,” arXiv:2501.19362. 2025.
mla: Betz, Volker, et al. “On the Ising Phase Transition in the Infrared-Divergent
Spin Boson Model.” ArXiv:2501.19362, 2025.
short: V. Betz, B. Hinrichs, M.N. Kraft, S. Polzer, ArXiv:2501.19362 (2025).
date_created: 2026-01-16T08:56:45Z
date_updated: 2026-01-16T08:57:21Z
department:
- _id: '799'
external_id:
arxiv:
- '2501.19362'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2501.19362
status: public
title: On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '63644'
abstract:
- lang: eng
text: We study the ultraviolet problem for models of a finite-dimensional quantum
mechanical system linearly coupled to a bosonic quantum field, such as the (many-)spin
boson model or its rotating-wave approximation. If the state change of the system
upon emission or absorption of a boson is either given by a normal matrix or by
a 2-nilpotent one, which is the case for the previously named examples, we prove
an optimal renormalization result. We complement it, by proving the norm resolvent
convergence of appropriately regularized models to the renormalized one. Our method
consists of a dressing transformation argument in the normal case and an appropriate
interior boundary condition for the 2-nilpotent case.
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Jonas
full_name: Lampart, Jonas
last_name: Lampart
- first_name: Javier
full_name: Valentín Martín, Javier
last_name: Valentín Martín
citation:
ama: Hinrichs B, Lampart J, Valentín Martín J. Ultraviolet Renormalization of Spin
Boson Models I. Normal and 2-Nilpotent Interactions. arXiv:250204876. Published
online 2025.
apa: Hinrichs, B., Lampart, J., & Valentín Martín, J. (2025). Ultraviolet Renormalization
of Spin Boson Models I. Normal and 2-Nilpotent Interactions. In arXiv:2502.04876.
bibtex: '@article{Hinrichs_Lampart_Valentín Martín_2025, title={Ultraviolet Renormalization
of Spin Boson Models I. Normal and 2-Nilpotent Interactions}, journal={arXiv:2502.04876},
author={Hinrichs, Benjamin and Lampart, Jonas and Valentín Martín, Javier}, year={2025}
}'
chicago: Hinrichs, Benjamin, Jonas Lampart, and Javier Valentín Martín. “Ultraviolet
Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions.”
ArXiv:2502.04876, 2025.
ieee: B. Hinrichs, J. Lampart, and J. Valentín Martín, “Ultraviolet Renormalization
of Spin Boson Models I. Normal and 2-Nilpotent Interactions,” arXiv:2502.04876.
2025.
mla: Hinrichs, Benjamin, et al. “Ultraviolet Renormalization of Spin Boson Models
I. Normal and 2-Nilpotent Interactions.” ArXiv:2502.04876, 2025.
short: B. Hinrichs, J. Lampart, J. Valentín Martín, ArXiv:2502.04876 (2025).
date_created: 2026-01-16T08:58:25Z
date_updated: 2026-01-16T08:59:03Z
department:
- _id: '799'
external_id:
arxiv:
- '2502.04876'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2502.04876
status: public
title: Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent
Interactions
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '63643'
abstract:
- lang: eng
text: In this short communication we discuss the ultraviolet renormalization of
the van Hove-Miyatake scalar field, generated by any distributional source. An
abstract algebraic approach, based on the study of a special class of ground states
of the van Hove-Miyatake dynamical map is compared with an Hamiltonian renormalization
that makes use of a non-unitary dressing transformation. The two approaches are
proved to yield equivalent results.
author:
- first_name: Marco
full_name: Falconi, Marco
last_name: Falconi
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
citation:
ama: 'Falconi M, Hinrichs B. Ultraviolet Renormalization of the van Hove-Miyatake
Model: an Algebraic and Hamiltonian Approach. arXiv:250519977. Published
online 2025.'
apa: 'Falconi, M., & Hinrichs, B. (2025). Ultraviolet Renormalization of the
van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach. In arXiv:2505.19977.'
bibtex: '@article{Falconi_Hinrichs_2025, title={Ultraviolet Renormalization of the
van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach}, journal={arXiv:2505.19977},
author={Falconi, Marco and Hinrichs, Benjamin}, year={2025} }'
chicago: 'Falconi, Marco, and Benjamin Hinrichs. “Ultraviolet Renormalization of
the van Hove-Miyatake Model: An Algebraic and Hamiltonian Approach.” ArXiv:2505.19977,
2025.'
ieee: 'M. Falconi and B. Hinrichs, “Ultraviolet Renormalization of the van Hove-Miyatake
Model: an Algebraic and Hamiltonian Approach,” arXiv:2505.19977. 2025.'
mla: 'Falconi, Marco, and Benjamin Hinrichs. “Ultraviolet Renormalization of the
van Hove-Miyatake Model: An Algebraic and Hamiltonian Approach.” ArXiv:2505.19977,
2025.'
short: M. Falconi, B. Hinrichs, ArXiv:2505.19977 (2025).
date_created: 2026-01-16T08:57:34Z
date_updated: 2026-01-16T08:58:12Z
department:
- _id: '799'
external_id:
arxiv:
- '2505.19977'
language:
- iso: eng
publication: arXiv:2505.19977
status: public
title: 'Ultraviolet Renormalization of the van Hove-Miyatake Model: an Algebraic and
Hamiltonian Approach'
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '63645'
abstract:
- lang: eng
text: In this paper we construct the non-trivial, renormalized Hamiltonian for a
class of spin-boson models with supercritical form factors, including the one
describing the Weisskopf-Wigner spontaneous emission. The renormalization is performed
through both a self-energy and mass renormalization, in the so-called Hamiltonian
formalism of constructive quantum field theory, implemented by a non-unitary dressing
transformation. This solves the problem of triviality for unitarily-renormalized
supercritical spin-boson models.
author:
- first_name: Marco
full_name: Falconi, Marco
last_name: Falconi
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Javier
full_name: Valentín Martín, Javier
last_name: Valentín Martín
citation:
ama: Falconi M, Hinrichs B, Valentín Martín J. Non-Trivial Renormalization of Spin-Boson
Models with Supercritical Form Factors. arXiv:250800805. Published online
2025.
apa: Falconi, M., Hinrichs, B., & Valentín Martín, J. (2025). Non-Trivial Renormalization
of Spin-Boson Models with Supercritical Form Factors. In arXiv:2508.00805.
bibtex: '@article{Falconi_Hinrichs_Valentín Martín_2025, title={Non-Trivial Renormalization
of Spin-Boson Models with Supercritical Form Factors}, journal={arXiv:2508.00805},
author={Falconi, Marco and Hinrichs, Benjamin and Valentín Martín, Javier}, year={2025}
}'
chicago: Falconi, Marco, Benjamin Hinrichs, and Javier Valentín Martín. “Non-Trivial
Renormalization of Spin-Boson Models with Supercritical Form Factors.” ArXiv:2508.00805,
2025.
ieee: M. Falconi, B. Hinrichs, and J. Valentín Martín, “Non-Trivial Renormalization
of Spin-Boson Models with Supercritical Form Factors,” arXiv:2508.00805.
2025.
mla: Falconi, Marco, et al. “Non-Trivial Renormalization of Spin-Boson Models with
Supercritical Form Factors.” ArXiv:2508.00805, 2025.
short: M. Falconi, B. Hinrichs, J. Valentín Martín, ArXiv:2508.00805 (2025).
date_created: 2026-01-16T08:59:11Z
date_updated: 2026-01-16T09:01:45Z
department:
- _id: '799'
external_id:
arxiv:
- '2508.00805'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2508.00805
status: public
title: Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '63646'
abstract:
- lang: eng
text: We study the behavior of a probability measure near the bottom of its support
in terms of time averaged quotients of its Laplace transform. We discuss how our
results are connected to both rank-one perturbation theory as well as renewal
theory. We further apply our results in order to derive criteria for the existence
and non-existence of ground states for a finite dimensional quantum system coupled
to a bosonic field.
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Steffen
full_name: Polzer, Steffen
last_name: Polzer
citation:
ama: Hinrichs B, Polzer S. Wiener-Type Theorems for the Laplace Transform. With
Applications to Ground State Problems. arXiv:251102867. Published online
2025.
apa: Hinrichs, B., & Polzer, S. (2025). Wiener-Type Theorems for the Laplace
Transform. With Applications to Ground State Problems. In arXiv:2511.02867.
bibtex: '@article{Hinrichs_Polzer_2025, title={Wiener-Type Theorems for the Laplace
Transform. With Applications to Ground State Problems}, journal={arXiv:2511.02867},
author={Hinrichs, Benjamin and Polzer, Steffen}, year={2025} }'
chicago: Hinrichs, Benjamin, and Steffen Polzer. “Wiener-Type Theorems for the Laplace
Transform. With Applications to Ground State Problems.” ArXiv:2511.02867,
2025.
ieee: B. Hinrichs and S. Polzer, “Wiener-Type Theorems for the Laplace Transform.
With Applications to Ground State Problems,” arXiv:2511.02867. 2025.
mla: Hinrichs, Benjamin, and Steffen Polzer. “Wiener-Type Theorems for the Laplace
Transform. With Applications to Ground State Problems.” ArXiv:2511.02867,
2025.
short: B. Hinrichs, S. Polzer, ArXiv:2511.02867 (2025).
date_created: 2026-01-16T08:59:45Z
date_updated: 2026-01-16T09:01:02Z
department:
- _id: '799'
external_id:
arxiv:
- '2511.02867'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2511.02867
status: public
title: Wiener-Type Theorems for the Laplace Transform. With Applications to Ground
State Problems
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '63647'
abstract:
- lang: eng
text: We study the convergence rate of translation-invariant discrete-time quantum
dynamics on a one-dimensional lattice. We prove that the cumulative distributions
function of the ballistically scaled position $\mathbb X(n)/{n}$ after $n$ steps
converges at a rate of $n^{-1/3}$ in the Lévy metric as $n\to\infty$. In the special
case of step-coin quantum walks with two-dimensional coin space, we recover the
same convergence rate for the supremum distance and prove optimality.
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Pascal
full_name: Mittenbühler, Pascal
last_name: Mittenbühler
citation:
ama: Hinrichs B, Mittenbühler P. On the Optimal Rate of Convergence for Translation-Invariant
1D Quantum Walks. arXiv:251113409. Published online 2025.
apa: Hinrichs, B., & Mittenbühler, P. (2025). On the Optimal Rate of Convergence
for Translation-Invariant 1D Quantum Walks. In arXiv:2511.13409.
bibtex: '@article{Hinrichs_Mittenbühler_2025, title={On the Optimal Rate of Convergence
for Translation-Invariant 1D Quantum Walks}, journal={arXiv:2511.13409}, author={Hinrichs,
Benjamin and Mittenbühler, Pascal}, year={2025} }'
chicago: Hinrichs, Benjamin, and Pascal Mittenbühler. “On the Optimal Rate of Convergence
for Translation-Invariant 1D Quantum Walks.” ArXiv:2511.13409, 2025.
ieee: B. Hinrichs and P. Mittenbühler, “On the Optimal Rate of Convergence for Translation-Invariant
1D Quantum Walks,” arXiv:2511.13409. 2025.
mla: Hinrichs, Benjamin, and Pascal Mittenbühler. “On the Optimal Rate of Convergence
for Translation-Invariant 1D Quantum Walks.” ArXiv:2511.13409, 2025.
short: B. Hinrichs, P. Mittenbühler, ArXiv:2511.13409 (2025).
date_created: 2026-01-16T08:59:54Z
date_updated: 2026-01-16T09:00:31Z
department:
- _id: '799'
external_id:
arxiv:
- '2511.13409'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2511.13409
status: public
title: On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '52691'
abstract:
- lang: eng
text: "We prove Feynman-Kac formulas for the semigroups generated by selfadjoint\r\noperators
in a class containing Fr\\\"ohlich Hamiltonians known from solid state\r\nphysics.
The latter model multi-polarons, i.e., a fixed number of quantum\r\nmechanical
electrons moving in a polarizable crystal and interacting with the\r\nquantized
phonon field generated by the crystal's vibrational modes. Both the\r\nelectrons
and phonons can be confined to suitable open subsets of Euclidean\r\nspace. We
also include possibly very singular magnetic vector potentials and\r\nelectrostatic
potentials. Our Feynman-Kac formulas comprise Fock space\r\noperator-valued multiplicative
functionals and can be applied to every vector\r\nin the underlying Hilbert space.
In comparison to the renormalized Nelson\r\nmodel, for which analogous Feynman-Kac
formulas are known, the analysis of the\r\ncreation and annihilation terms in
the multiplicative functionals requires\r\nnovel ideas to overcome difficulties
caused by the phonon dispersion relation\r\nbeing constant. Getting these terms
under control and generalizing other\r\nconstruction steps so as to cover confined
systems are the main achievements of\r\nthis article."
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 formulas for semigroups generated by multi-polaron
Hamiltonians in magnetic fields and on general domains. arXiv:240312147.
Published online 2024.
apa: Hinrichs, B., & Matte, O. (2024). Feynman-Kac formulas for semigroups generated
by multi-polaron Hamiltonians in magnetic fields and on general domains. In arXiv:2403.12147.
bibtex: '@article{Hinrichs_Matte_2024, title={Feynman-Kac formulas for semigroups
generated by multi-polaron Hamiltonians in magnetic fields and on general domains},
journal={arXiv:2403.12147}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2024}
}'
chicago: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups
Generated by Multi-Polaron Hamiltonians in Magnetic Fields and on General Domains.”
ArXiv:2403.12147, 2024.
ieee: B. Hinrichs and O. Matte, “Feynman-Kac formulas for semigroups generated by
multi-polaron Hamiltonians in magnetic fields and on general domains,” arXiv:2403.12147.
2024.
mla: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups
Generated by Multi-Polaron Hamiltonians in Magnetic Fields and on General Domains.”
ArXiv:2403.12147, 2024.
short: B. Hinrichs, O. Matte, ArXiv:2403.12147 (2024).
date_created: 2024-03-20T14:56:05Z
date_updated: 2024-03-20T14:56:50Z
department:
- _id: '799'
external_id:
arxiv:
- '2403.12147'
language:
- iso: eng
publication: arXiv:2403.12147
status: public
title: Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians
in magnetic fields and on general domains
type: preprint
user_id: '99427'
year: '2024'
...
---
_id: '63636'
article_type: original
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Jonas
full_name: Lampart, Jonas
last_name: Lampart
citation:
ama: Hinrichs B, Lampart J. A Lower Bound on the Critical Momentum of an Impurity
in a Bose–Einstein Condensate. Comptes Rendus Mathématique. 2024;362(G11):1399-1411.
doi:10.5802/crmath.652
apa: Hinrichs, B., & Lampart, J. (2024). A Lower Bound on the Critical Momentum
of an Impurity in a Bose–Einstein Condensate. Comptes Rendus. Mathématique,
362(G11), 1399–1411. https://doi.org/10.5802/crmath.652
bibtex: '@article{Hinrichs_Lampart_2024, title={A Lower Bound on the Critical Momentum
of an Impurity in a Bose–Einstein Condensate}, volume={362}, DOI={10.5802/crmath.652},
number={G11}, journal={Comptes Rendus. Mathématique}, publisher={MathDoc/Centre
Mersenne}, author={Hinrichs, Benjamin and Lampart, Jonas}, year={2024}, pages={1399–1411}
}'
chicago: 'Hinrichs, Benjamin, and Jonas Lampart. “A Lower Bound on the Critical
Momentum of an Impurity in a Bose–Einstein Condensate.” Comptes Rendus. Mathématique
362, no. G11 (2024): 1399–1411. https://doi.org/10.5802/crmath.652.'
ieee: 'B. Hinrichs and J. Lampart, “A Lower Bound on the Critical Momentum of an
Impurity in a Bose–Einstein Condensate,” Comptes Rendus. Mathématique,
vol. 362, no. G11, pp. 1399–1411, 2024, doi: 10.5802/crmath.652.'
mla: Hinrichs, Benjamin, and Jonas Lampart. “A Lower Bound on the Critical Momentum
of an Impurity in a Bose–Einstein Condensate.” Comptes Rendus. Mathématique,
vol. 362, no. G11, MathDoc/Centre Mersenne, 2024, pp. 1399–411, doi:10.5802/crmath.652.
short: B. Hinrichs, J. Lampart, Comptes Rendus. Mathématique 362 (2024) 1399–1411.
date_created: 2026-01-16T08:43:59Z
date_updated: 2026-01-16T08:45:25Z
department:
- _id: '799'
doi: 10.5802/crmath.652
external_id:
arxiv:
- '2311.05361'
intvolume: ' 362'
issue: G11
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 1399-1411
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: Comptes Rendus. Mathématique
publication_identifier:
issn:
- 1631-073X
- 1778-3569
publication_status: published
publisher: MathDoc/Centre Mersenne
status: public
title: A Lower Bound on the Critical Momentum of an Impurity in a Bose–Einstein Condensate
type: journal_article
user_id: '99427'
volume: 362
year: '2024'
...
---
_id: '63641'
abstract:
- lang: eng
text: We present a simple functional integration based proof that the semigroups
generated by the ultraviolet-renormalized translation-invariant non- and semi-relativistic
Nelson Hamiltonians are positivity improving (and hence ergodic) with respect
to the Fröhlich cone for arbitrary values of the total momentum. Our argument
simplifies known proofs for ergodicity and the result is new in the semi-relativistic
case.
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Fumio
full_name: Hiroshima, Fumio
last_name: Hiroshima
citation:
ama: Hinrichs B, Hiroshima F. On the Ergodicity of Renormalized Translation-Invariant
Nelson-Type Semigroups. arXiv:241209708. Published online 2024.
apa: Hinrichs, B., & Hiroshima, F. (2024). On the Ergodicity of Renormalized
Translation-Invariant Nelson-Type Semigroups. In arXiv:2412.09708.
bibtex: '@article{Hinrichs_Hiroshima_2024, title={On the Ergodicity of Renormalized
Translation-Invariant Nelson-Type Semigroups}, journal={arXiv:2412.09708}, author={Hinrichs,
Benjamin and Hiroshima, Fumio}, year={2024} }'
chicago: Hinrichs, Benjamin, and Fumio Hiroshima. “On the Ergodicity of Renormalized
Translation-Invariant Nelson-Type Semigroups.” ArXiv:2412.09708, 2024.
ieee: B. Hinrichs and F. Hiroshima, “On the Ergodicity of Renormalized Translation-Invariant
Nelson-Type Semigroups,” arXiv:2412.09708. 2024.
mla: Hinrichs, Benjamin, and Fumio Hiroshima. “On the Ergodicity of Renormalized
Translation-Invariant Nelson-Type Semigroups.” ArXiv:2412.09708, 2024.
short: B. Hinrichs, F. Hiroshima, ArXiv:2412.09708 (2024).
date_created: 2026-01-16T08:56:18Z
date_updated: 2026-01-16T08:56:37Z
department:
- _id: '799'
external_id:
arxiv:
- '2412.09708'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2412.09708
status: public
title: On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups
type: preprint
user_id: '99427'
year: '2024'
...
---
_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. Annales Henri Poincaré. 2024;26(1):41-80. doi:10.1007/s00023-024-01453-y
apa: Hinrichs, B., Lemm, M., & Siebert, O. (2024). On Lieb–Robinson Bounds for
a Class of Continuum Fermions. Annales Henri Poincaré, 26(1), 41–80.
https://doi.org/10.1007/s00023-024-01453-y
bibtex: '@article{Hinrichs_Lemm_Siebert_2024, title={On Lieb–Robinson Bounds for
a Class of Continuum Fermions}, volume={26}, DOI={10.1007/s00023-024-01453-y},
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.” Annales Henri Poincaré 26, no.
1 (2024): 41–80. https://doi.org/10.1007/s00023-024-01453-y.'
ieee: 'B. Hinrichs, M. Lemm, and O. Siebert, “On Lieb–Robinson Bounds for a Class
of Continuum Fermions,” Annales Henri Poincaré, vol. 26, no. 1, pp. 41–80,
2024, doi: 10.1007/s00023-024-01453-y.'
mla: Hinrichs, Benjamin, et al. “On Lieb–Robinson Bounds for a Class of Continuum
Fermions.” Annales Henri Poincaré, vol. 26, no. 1, Springer Science and
Business Media LLC, 2024, pp. 41–80, doi:10.1007/s00023-024-01453-y.
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: '51374'
article_number: '110319'
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. Non-Fock ground states in the translation-invariant
Nelson model revisited non-perturbatively. Journal of Functional Analysis.
2024;286(7). doi:10.1016/j.jfa.2024.110319
apa: Hasler, D., Hinrichs, B., & Siebert, O. (2024). Non-Fock ground states
in the translation-invariant Nelson model revisited non-perturbatively. Journal
of Functional Analysis, 286(7), Article 110319. https://doi.org/10.1016/j.jfa.2024.110319
bibtex: '@article{Hasler_Hinrichs_Siebert_2024, title={Non-Fock ground states in
the translation-invariant Nelson model revisited non-perturbatively}, volume={286},
DOI={10.1016/j.jfa.2024.110319},
number={7110319}, journal={Journal of Functional Analysis}, publisher={Elsevier
BV}, author={Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}, year={2024}
}'
chicago: Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “Non-Fock Ground
States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.”
Journal of Functional Analysis 286, no. 7 (2024). https://doi.org/10.1016/j.jfa.2024.110319.
ieee: 'D. Hasler, B. Hinrichs, and O. Siebert, “Non-Fock ground states in the translation-invariant
Nelson model revisited non-perturbatively,” Journal of Functional Analysis,
vol. 286, no. 7, Art. no. 110319, 2024, doi: 10.1016/j.jfa.2024.110319.'
mla: Hasler, David, et al. “Non-Fock Ground States in the Translation-Invariant
Nelson Model Revisited Non-Perturbatively.” Journal of Functional Analysis,
vol. 286, no. 7, 110319, Elsevier BV, 2024, doi:10.1016/j.jfa.2024.110319.
short: D. Hasler, B. Hinrichs, O. Siebert, Journal of Functional Analysis 286 (2024).
date_created: 2024-02-18T12:31:28Z
date_updated: 2026-01-16T09:04:51Z
department:
- _id: '799'
doi: 10.1016/j.jfa.2024.110319
extern: '1'
external_id:
arxiv:
- '2302.06998'
intvolume: ' 286'
issue: '7'
keyword:
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier BV
status: public
title: Non-Fock ground states in the translation-invariant Nelson model revisited
non-perturbatively
type: journal_article
user_id: '99427'
volume: 286
year: '2024'
...
---
_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. Annales
Henri Poincaré. 2023;25(6):2877-2940. doi:10.1007/s00023-023-01369-z
apa: Hinrichs, B., & Matte, O. (2023). Feynman–Kac Formula and Asymptotic Behavior
of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.
Annales Henri Poincaré, 25(6), 2877–2940. https://doi.org/10.1007/s00023-023-01369-z
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={10.1007/s00023-023-01369-z},
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.” Annales Henri Poincaré 25, no. 6 (2023): 2877–2940. https://doi.org/10.1007/s00023-023-01369-z.'
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,”
Annales Henri Poincaré, vol. 25, no. 6, pp. 2877–2940, 2023, doi: 10.1007/s00023-023-01369-z.'
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.”
Annales Henri Poincaré, vol. 25, no. 6, Springer Science and Business Media
LLC, 2023, pp. 2877–940, doi:10.1007/s00023-023-01369-z.
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: '46100'
article_number: '127558'
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Daan W.
full_name: Janssen, Daan W.
last_name: Janssen
- first_name: Jobst
full_name: Ziebell, Jobst
last_name: Ziebell
citation:
ama: 'Hinrichs B, Janssen DW, Ziebell J. Super-Gaussian decay of exponentials: A
sufficient condition. Journal of Mathematical Analysis and Applications.
2023;528(1). doi:10.1016/j.jmaa.2023.127558'
apa: 'Hinrichs, B., Janssen, D. W., & Ziebell, J. (2023). Super-Gaussian decay
of exponentials: A sufficient condition. Journal of Mathematical Analysis and
Applications, 528(1), Article 127558. https://doi.org/10.1016/j.jmaa.2023.127558'
bibtex: '@article{Hinrichs_Janssen_Ziebell_2023, title={Super-Gaussian decay of
exponentials: A sufficient condition}, volume={528}, DOI={10.1016/j.jmaa.2023.127558},
number={1127558}, journal={Journal of Mathematical Analysis and Applications},
publisher={Elsevier BV}, author={Hinrichs, Benjamin and Janssen, Daan W. and Ziebell,
Jobst}, year={2023} }'
chicago: 'Hinrichs, Benjamin, Daan W. Janssen, and Jobst Ziebell. “Super-Gaussian
Decay of Exponentials: A Sufficient Condition.” Journal of Mathematical Analysis
and Applications 528, no. 1 (2023). https://doi.org/10.1016/j.jmaa.2023.127558.'
ieee: 'B. Hinrichs, D. W. Janssen, and J. Ziebell, “Super-Gaussian decay of exponentials:
A sufficient condition,” Journal of Mathematical Analysis and Applications,
vol. 528, no. 1, Art. no. 127558, 2023, doi: 10.1016/j.jmaa.2023.127558.'
mla: 'Hinrichs, Benjamin, et al. “Super-Gaussian Decay of Exponentials: A Sufficient
Condition.” Journal of Mathematical Analysis and Applications, vol. 528,
no. 1, 127558, Elsevier BV, 2023, doi:10.1016/j.jmaa.2023.127558.'
short: B. Hinrichs, D.W. Janssen, J. Ziebell, Journal of Mathematical Analysis and
Applications 528 (2023).
date_created: 2023-07-20T05:08:49Z
date_updated: 2026-01-16T09:04:39Z
department:
- _id: '799'
doi: 10.1016/j.jmaa.2023.127558
external_id:
arxiv:
- '2205.09189'
intvolume: ' 528'
issue: '1'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
publication: Journal of Mathematical Analysis and Applications
publication_identifier:
issn:
- 0022-247X
publication_status: published
publisher: Elsevier BV
status: public
title: 'Super-Gaussian decay of exponentials: A sufficient condition'
type: journal_article
user_id: '99427'
volume: 528
year: '2023'
...
---
_id: '43491'
abstract:
- lang: eng
text: We consider a model for a massive uncharged non-relativistic particle interacting
with a massless bosonic field, widely referred to as the Nelson model. It is well
known that an ultraviolet renormalized Hamilton operator exists in this case.
Further, due to translation-invariance, it decomposes into fiber operators. In
this paper, we treat the renormalized fiber operators. We give a description of
the operator and form domains and prove that the fiber operators do not have a
ground state. Our results hold for any non-zero coupling constant and arbitrary
total momentum. Our proof for the absence of ground states is a new generalization
of methods recently applied to related models. A major enhancement we provide
is that the method can be applied to models with degenerate ground state eigenspaces.
article_type: original
author:
- first_name: Thomas Norman
full_name: Dam, Thomas Norman
last_name: Dam
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
citation:
ama: Dam TN, Hinrichs B. Absence of ground states in the renormalized massless translation-invariant
Nelson model. Reviews in Mathematical Physics. 2022;34(10). doi:10.1142/s0129055x22500337
apa: Dam, T. N., & Hinrichs, B. (2022). Absence of ground states in the renormalized
massless translation-invariant Nelson model. Reviews in Mathematical Physics,
34(10). https://doi.org/10.1142/s0129055x22500337
bibtex: '@article{Dam_Hinrichs_2022, title={Absence of ground states in the renormalized
massless translation-invariant Nelson model}, volume={34}, DOI={10.1142/s0129055x22500337},
number={10}, journal={Reviews in Mathematical Physics}, publisher={World Scientific
Pub Co Pte Ltd}, author={Dam, Thomas Norman and Hinrichs, Benjamin}, year={2022}
}'
chicago: Dam, Thomas Norman, and Benjamin Hinrichs. “Absence of Ground States in
the Renormalized Massless Translation-Invariant Nelson Model.” Reviews in Mathematical
Physics 34, no. 10 (2022). https://doi.org/10.1142/s0129055x22500337.
ieee: 'T. N. Dam and B. Hinrichs, “Absence of ground states in the renormalized
massless translation-invariant Nelson model,” Reviews in Mathematical Physics,
vol. 34, no. 10, 2022, doi: 10.1142/s0129055x22500337.'
mla: Dam, Thomas Norman, and Benjamin Hinrichs. “Absence of Ground States in the
Renormalized Massless Translation-Invariant Nelson Model.” Reviews in Mathematical
Physics, vol. 34, no. 10, World Scientific Pub Co Pte Ltd, 2022, doi:10.1142/s0129055x22500337.
short: T.N. Dam, B. Hinrichs, Reviews in Mathematical Physics 34 (2022).
date_created: 2023-04-14T04:49:00Z
date_updated: 2023-04-14T05:03:17Z
doi: 10.1142/s0129055x22500337
extern: '1'
external_id:
arxiv:
- '1909.07661'
intvolume: ' 34'
issue: '10'
language:
- iso: eng
publication: Reviews in Mathematical Physics
publication_identifier:
issn:
- 0129-055X
- 1793-6659
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Absence of ground states in the renormalized massless translation-invariant
Nelson model
type: journal_article
user_id: '99427'
volume: 34
year: '2022'
...
---
_id: '43496'
abstract:
- lang: eng
text: "We review recent results on the existence of ground states for the\r\ninfrared-critical
spin boson model, which describes the interaction of a\r\nmassless bosonic field
with a two-state quantum system. Explicitly, we derive a\r\ncritical coupling
$\\lambda_{\\mathsf c}>0$ such that the spin boson model\r\nexhibits a ground
state for coupling constants $\\lambda$ with\r\n$|\\lambda|<\\lambda_{\\mathsf
c}$. The proof combines a Feynman-Kac-Nelson\r\nformula for the spin boson model
with external magnetic field, a 1D-Ising model\r\ncorrelation bound and a compactness
argument in Fock space. Elaborating on the\r\nconnection to a long-range 1D-Ising
model, we briefly discuss the conjecture\r\nthat the spin boson model does not
have a ground state at large coupling. This\r\nnote is based on joint work with
David Hasler and Oliver Siebert."
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
citation:
ama: 'Hinrichs B. Existence of Ground States in the Infrared-Critial Spin Boson
Model. In: Hiroshima F, ed. Mathematical Aspects of Quantum Fields and Related
Topics. Vol 2235. RIMS Kôkyûroku. ; 2022:60-73.'
apa: Hinrichs, B. (2022). Existence of Ground States in the Infrared-Critial Spin
Boson Model. In F. Hiroshima (Ed.), Mathematical aspects of quantum fields
and related topics (Vol. 2235, pp. 60–73).
bibtex: '@inproceedings{Hinrichs_2022, series={RIMS Kôkyûroku}, title={Existence
of Ground States in the Infrared-Critial Spin Boson Model}, volume={2235}, booktitle={Mathematical
aspects of quantum fields and related topics}, author={Hinrichs, Benjamin}, editor={Hiroshima,
Fumio}, year={2022}, pages={60–73}, collection={RIMS Kôkyûroku} }'
chicago: Hinrichs, Benjamin. “Existence of Ground States in the Infrared-Critial
Spin Boson Model.” In Mathematical Aspects of Quantum Fields and Related Topics,
edited by Fumio Hiroshima, 2235:60–73. RIMS Kôkyûroku, 2022.
ieee: B. Hinrichs, “Existence of Ground States in the Infrared-Critial Spin Boson
Model,” in Mathematical aspects of quantum fields and related topics, RIMS,
Kyoto, 2022, vol. 2235, pp. 60–73.
mla: Hinrichs, Benjamin. “Existence of Ground States in the Infrared-Critial Spin
Boson Model.” Mathematical Aspects of Quantum Fields and Related Topics,
edited by Fumio Hiroshima, vol. 2235, 2022, pp. 60–73.
short: 'B. Hinrichs, in: F. Hiroshima (Ed.), Mathematical Aspects of Quantum Fields
and Related Topics, 2022, pp. 60–73.'
conference:
end_date: 2021-12-08
location: RIMS, Kyoto
name: Mathematical aspects of quantum fields and related topics
start_date: 2021-12-06
date_created: 2023-04-14T04:56:51Z
date_updated: 2026-01-16T09:03:41Z
editor:
- first_name: Fumio
full_name: Hiroshima, Fumio
last_name: Hiroshima
extern: '1'
external_id:
arxiv:
- '2204.00287'
intvolume: ' 2235'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://hdl.handle.net/2433/282934
oa: '1'
page: 60-73
publication: Mathematical aspects of quantum fields and related topics
publication_status: published
series_title: RIMS Kôkyûroku
status: public
title: Existence of Ground States in the Infrared-Critial Spin Boson Model
type: conference
user_id: '99427'
volume: 2235
year: '2022'
...
---
_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. Annales Henri Poincaré.
2022;23(8):2819-2853. doi:10.1007/s00023-022-01160-6
apa: Hasler, D., Hinrichs, B., & Siebert, O. (2022). FKN Formula and Ground
State Energy for the Spin Boson Model with External Magnetic Field. Annales
Henri Poincaré, 23(8), 2819–2853. https://doi.org/10.1007/s00023-022-01160-6
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={10.1007/s00023-022-01160-6},
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.” Annales
Henri Poincaré 23, no. 8 (2022): 2819–53. https://doi.org/10.1007/s00023-022-01160-6.'
ieee: 'D. Hasler, B. Hinrichs, and O. Siebert, “FKN Formula and Ground State Energy
for the Spin Boson Model with External Magnetic Field,” Annales Henri Poincaré,
vol. 23, no. 8, pp. 2819–2853, 2022, doi: 10.1007/s00023-022-01160-6.'
mla: Hasler, David, et al. “FKN Formula and Ground State Energy for the Spin Boson
Model with External Magnetic Field.” Annales Henri Poincaré, vol. 23, no.
8, Springer Science and Business Media LLC, 2022, pp. 2819–53, doi:10.1007/s00023-022-01160-6.
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: '43501'
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
citation:
ama: Hinrichs B. Existence of Ground States for Infrared-Critical Models of Quantum
Field Theory.; 2022. doi:10.22032/dbt.51516
apa: Hinrichs, B. (2022). Existence of Ground States for Infrared-Critical Models
of Quantum Field Theory. https://doi.org/10.22032/dbt.51516
bibtex: '@book{Hinrichs_2022, place={Jena}, title={Existence of Ground States for
Infrared-Critical Models of Quantum Field Theory}, DOI={10.22032/dbt.51516},
author={Hinrichs, Benjamin}, year={2022} }'
chicago: Hinrichs, Benjamin. Existence of Ground States for Infrared-Critical
Models of Quantum Field Theory. Jena, 2022. https://doi.org/10.22032/dbt.51516.
ieee: B. Hinrichs, Existence of Ground States for Infrared-Critical Models of
Quantum Field Theory. Jena, 2022.
mla: Hinrichs, Benjamin. Existence of Ground States for Infrared-Critical Models
of Quantum Field Theory. 2022, doi:10.22032/dbt.51516.
short: B. Hinrichs, Existence of Ground States for Infrared-Critical Models of Quantum
Field Theory, Jena, 2022.
date_created: 2023-04-14T05:09:10Z
date_updated: 2026-01-16T09:03:08Z
doi: 10.22032/dbt.51516
extern: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
place: Jena
status: public
supervisor:
- first_name: David
full_name: Hasler, David
last_name: Hasler
title: Existence of Ground States for Infrared-Critical Models of Quantum Field Theory
type: dissertation
user_id: '99427'
year: '2022'
...