[{"date_created":"2026-01-18T18:08:18Z","publisher":"American Physical Society (APS)","title":"Restricted Monte Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system dynamics","issue":"1","year":"2026","external_id":{"arxiv":["2412.08735"]},"language":[{"iso":"eng"}],"publication":"Physical Review A","author":[{"first_name":"Laura","last_name":"Ares","full_name":"Ares, Laura"},{"first_name":"Julien","full_name":"Pinske, Julien","last_name":"Pinske"},{"orcid":"0000-0001-9074-1205","last_name":"Hinrichs","full_name":"Hinrichs, Benjamin","id":"99427","first_name":"Benjamin"},{"first_name":"Martin","id":"48880","full_name":"Kolb, Martin","last_name":"Kolb"},{"first_name":"Jan","last_name":"Sperling","orcid":"0000-0002-5844-3205","full_name":"Sperling, Jan","id":"75127"}],"volume":113,"date_updated":"2026-01-18T18:15:01Z","doi":"10.1103/hcj7-8zlg","publication_status":"published","publication_identifier":{"issn":["2469-9926","2469-9934"]},"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. <i>Physical Review A</i>. 2026;113(1). doi:<a href=\"https://doi.org/10.1103/hcj7-8zlg\">10.1103/hcj7-8zlg</a>","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.” <i>Physical Review A</i> 113, no. 1 (2026). <a href=\"https://doi.org/10.1103/hcj7-8zlg\">https://doi.org/10.1103/hcj7-8zlg</a>.","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,” <i>Physical Review A</i>, vol. 113, no. 1, Art. no. 012220, 2026, doi: <a href=\"https://doi.org/10.1103/hcj7-8zlg\">10.1103/hcj7-8zlg</a>.","short":"L. Ares, J. Pinske, B. Hinrichs, M. Kolb, J. Sperling, Physical Review A 113 (2026).","mla":"Ares, Laura, et al. “Restricted Monte Carlo Wave-Function Method and Lindblad Equation for Identifying Entangling Open-Quantum-System Dynamics.” <i>Physical Review A</i>, vol. 113, no. 1, 012220, American Physical Society (APS), 2026, doi:<a href=\"https://doi.org/10.1103/hcj7-8zlg\">10.1103/hcj7-8zlg</a>.","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={<a href=\"https://doi.org/10.1103/hcj7-8zlg\">10.1103/hcj7-8zlg</a>}, 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} }","apa":"Ares, L., Pinske, J., Hinrichs, B., Kolb, M., &#38; Sperling, J. (2026). Restricted Monte Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system dynamics. <i>Physical Review A</i>, <i>113</i>(1), Article 012220. <a href=\"https://doi.org/10.1103/hcj7-8zlg\">https://doi.org/10.1103/hcj7-8zlg</a>"},"intvolume":"       113","user_id":"99427","department":[{"_id":"799"}],"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"}],"_id":"63656","article_number":"012220","article_type":"original","type":"journal_article","status":"public"},{"publication":"Physical Review A","external_id":{"arxiv":["2412.08724"]},"language":[{"iso":"eng"}],"issue":"1","year":"2026","date_created":"2026-01-18T18:11:27Z","publisher":"American Physical Society (APS)","title":"Separability Lindblad equation for dynamical open-system entanglement","type":"journal_article","status":"public","department":[{"_id":"799"}],"user_id":"99427","_id":"63657","project":[{"name":"PhoQC: Photonisches Quantencomputing","_id":"266"},{"_id":"174","name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse"}],"article_number":"L010403","article_type":"letter_note","publication_identifier":{"issn":["2469-9926","2469-9934"]},"publication_status":"published","intvolume":"       113","citation":{"ieee":"J. Pinske, L. Ares, B. Hinrichs, M. Kolb, and J. Sperling, “Separability Lindblad equation for dynamical open-system entanglement,” <i>Physical Review A</i>, vol. 113, no. 1, Art. no. L010403, 2026, doi: <a href=\"https://doi.org/10.1103/kd3b-bfxq\">10.1103/kd3b-bfxq</a>.","chicago":"Pinske, Julien, Laura Ares, Benjamin Hinrichs, Martin Kolb, and Jan Sperling. “Separability Lindblad Equation for Dynamical Open-System Entanglement.” <i>Physical Review A</i> 113, no. 1 (2026). <a href=\"https://doi.org/10.1103/kd3b-bfxq\">https://doi.org/10.1103/kd3b-bfxq</a>.","ama":"Pinske J, Ares L, Hinrichs B, Kolb M, Sperling J. Separability Lindblad equation for dynamical open-system entanglement. <i>Physical Review A</i>. 2026;113(1). doi:<a href=\"https://doi.org/10.1103/kd3b-bfxq\">10.1103/kd3b-bfxq</a>","apa":"Pinske, J., Ares, L., Hinrichs, B., Kolb, M., &#38; Sperling, J. (2026). Separability Lindblad equation for dynamical open-system entanglement. <i>Physical Review A</i>, <i>113</i>(1), Article L010403. <a href=\"https://doi.org/10.1103/kd3b-bfxq\">https://doi.org/10.1103/kd3b-bfxq</a>","short":"J. Pinske, L. Ares, B. Hinrichs, M. Kolb, J. Sperling, Physical Review A 113 (2026).","mla":"Pinske, Julien, et al. “Separability Lindblad Equation for Dynamical Open-System Entanglement.” <i>Physical Review A</i>, vol. 113, no. 1, L010403, American Physical Society (APS), 2026, doi:<a href=\"https://doi.org/10.1103/kd3b-bfxq\">10.1103/kd3b-bfxq</a>.","bibtex":"@article{Pinske_Ares_Hinrichs_Kolb_Sperling_2026, title={Separability Lindblad equation for dynamical open-system entanglement}, volume={113}, DOI={<a href=\"https://doi.org/10.1103/kd3b-bfxq\">10.1103/kd3b-bfxq</a>}, 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} }"},"volume":113,"author":[{"full_name":"Pinske, Julien","last_name":"Pinske","first_name":"Julien"},{"first_name":"Laura","last_name":"Ares","full_name":"Ares, Laura"},{"first_name":"Benjamin","last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","id":"99427"},{"first_name":"Martin","full_name":"Kolb, Martin","id":"48880","last_name":"Kolb"},{"full_name":"Sperling, Jan","id":"75127","last_name":"Sperling","orcid":"0000-0002-5844-3205","first_name":"Jan"}],"date_updated":"2026-01-18T18:15:26Z","doi":"10.1103/kd3b-bfxq"},{"abstract":[{"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.","lang":"eng"}],"publication":"Proceedings of the 2023 RIMS Workshop 'Mathematical Aspects of Quantum Fields and Related Topics'","language":[{"iso":"eng"}],"external_id":{"arxiv":["2309.09005"]},"year":"2025","issue":"3","title":"Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson  model in two spatial dimensions","date_created":"2023-10-02T06:21:37Z","status":"public","editor":[{"first_name":"Fumio","full_name":"Hiroshima, Fumio","last_name":"Hiroshima"}],"type":"conference","department":[{"_id":"799"},{"_id":"623"}],"series_title":"RIMS Kôkyûroku","user_id":"99427","_id":"47534","project":[{"name":"PhoQC: PhoQC: Photonisches Quantencomputing","_id":"266"}],"intvolume":"      2310","citation":{"mla":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians in the Relativistic Nelson  Model in Two Spatial Dimensions.” <i>Proceedings of the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics,”</i> edited by Fumio Hiroshima, vol. 2310, no. 3, 2025.","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} }","short":"B. Hinrichs, O. Matte, in: F. Hiroshima (Ed.), Proceedings of the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics,” 2025.","apa":"Hinrichs, B., &#38; Matte, O. (2025). Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson  model in two spatial dimensions. In F. Hiroshima (Ed.), <i>Proceedings of the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics”</i> (Vol. 2310, Issue 3).","ama":"Hinrichs B, Matte O. Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson  model in two spatial dimensions. In: Hiroshima F, ed. <i>Proceedings of the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics.”</i> Vol 2310. RIMS Kôkyûroku. ; 2025.","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians in the Relativistic Nelson  Model in Two Spatial Dimensions.” In <i>Proceedings of the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics,”</i> 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 <i>Proceedings of the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics,”</i> 2025, vol. 2310, no. 3."},"main_file_link":[{"url":"https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2310.html"}],"volume":2310,"author":[{"id":"99427","full_name":"Hinrichs, Benjamin","last_name":"Hinrichs","orcid":"0000-0001-9074-1205","first_name":"Benjamin"},{"last_name":"Matte","full_name":"Matte, Oliver","first_name":"Oliver"}],"date_updated":"2026-01-16T08:55:19Z"},{"citation":{"ama":"Betz V, Hinrichs B, Kraft MN, Polzer S. On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model. <i>arXiv:250119362</i>. Published online 2025.","ieee":"V. Betz, B. Hinrichs, M. N. Kraft, and S. Polzer, “On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model,” <i>arXiv:2501.19362</i>. 2025.","chicago":"Betz, Volker, Benjamin Hinrichs, Mino Nicola Kraft, and Steffen Polzer. “On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model.” <i>ArXiv:2501.19362</i>, 2025.","mla":"Betz, Volker, et al. “On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model.” <i>ArXiv:2501.19362</i>, 2025.","short":"V. Betz, B. Hinrichs, M.N. Kraft, S. Polzer, ArXiv:2501.19362 (2025).","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} }","apa":"Betz, V., Hinrichs, B., Kraft, M. N., &#38; Polzer, S. (2025). On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model. In <i>arXiv:2501.19362</i>."},"year":"2025","title":"On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model","date_created":"2026-01-16T08:56:45Z","author":[{"first_name":"Volker","full_name":"Betz, Volker","last_name":"Betz"},{"first_name":"Benjamin","id":"99427","full_name":"Hinrichs, Benjamin","last_name":"Hinrichs","orcid":"0000-0001-9074-1205"},{"first_name":"Mino Nicola","last_name":"Kraft","full_name":"Kraft, Mino Nicola"},{"first_name":"Steffen","last_name":"Polzer","full_name":"Polzer, Steffen"}],"date_updated":"2026-01-16T08:57:21Z","status":"public","abstract":[{"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.","lang":"eng"}],"type":"preprint","publication":"arXiv:2501.19362","language":[{"iso":"eng"}],"user_id":"99427","department":[{"_id":"799"}],"project":[{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"}],"_id":"63642","external_id":{"arxiv":["2501.19362"]}},{"language":[{"iso":"eng"}],"external_id":{"arxiv":["2502.04876"]},"_id":"63644","project":[{"name":"PhoQC: Photonisches Quantencomputing","_id":"266"}],"department":[{"_id":"799"}],"user_id":"99427","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."}],"status":"public","publication":"arXiv:2502.04876","type":"preprint","title":"Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions","date_updated":"2026-01-16T08:59:03Z","author":[{"last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","id":"99427","first_name":"Benjamin"},{"first_name":"Jonas","full_name":"Lampart, Jonas","last_name":"Lampart"},{"last_name":"Valentín Martín","full_name":"Valentín Martín, Javier","first_name":"Javier"}],"date_created":"2026-01-16T08:58:25Z","year":"2025","citation":{"apa":"Hinrichs, B., Lampart, J., &#38; Valentín Martín, J. (2025). Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions. In <i>arXiv:2502.04876</i>.","mla":"Hinrichs, Benjamin, et al. “Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions.” <i>ArXiv:2502.04876</i>, 2025.","short":"B. Hinrichs, J. Lampart, J. Valentín Martín, ArXiv:2502.04876 (2025).","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.” <i>ArXiv:2502.04876</i>, 2025.","ieee":"B. Hinrichs, J. Lampart, and J. Valentín Martín, “Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions,” <i>arXiv:2502.04876</i>. 2025.","ama":"Hinrichs B, Lampart J, Valentín Martín J. Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions. <i>arXiv:250204876</i>. Published online 2025."}},{"language":[{"iso":"eng"}],"department":[{"_id":"799"}],"user_id":"99427","external_id":{"arxiv":["2505.19977"]},"_id":"63643","status":"public","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."}],"publication":"arXiv:2505.19977","type":"preprint","title":"Ultraviolet Renormalization of the van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach","date_created":"2026-01-16T08:57:34Z","author":[{"first_name":"Marco","full_name":"Falconi, Marco","last_name":"Falconi"},{"first_name":"Benjamin","last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","id":"99427"}],"date_updated":"2026-01-16T08:58:12Z","citation":{"ieee":"M. Falconi and B. Hinrichs, “Ultraviolet Renormalization of the van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach,” <i>arXiv:2505.19977</i>. 2025.","chicago":"Falconi, Marco, and Benjamin Hinrichs. “Ultraviolet Renormalization of the van Hove-Miyatake Model: An Algebraic and Hamiltonian Approach.” <i>ArXiv:2505.19977</i>, 2025.","ama":"Falconi M, Hinrichs B. Ultraviolet Renormalization of the van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach. <i>arXiv:250519977</i>. Published online 2025.","short":"M. Falconi, B. Hinrichs, ArXiv:2505.19977 (2025).","mla":"Falconi, Marco, and Benjamin Hinrichs. “Ultraviolet Renormalization of the van Hove-Miyatake Model: An Algebraic and Hamiltonian Approach.” <i>ArXiv:2505.19977</i>, 2025.","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} }","apa":"Falconi, M., &#38; Hinrichs, B. (2025). Ultraviolet Renormalization of the van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach. In <i>arXiv:2505.19977</i>."},"year":"2025"},{"year":"2025","citation":{"chicago":"Falconi, Marco, Benjamin Hinrichs, and Javier Valentín Martín. “Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors.” <i>ArXiv:2508.00805</i>, 2025.","ieee":"M. Falconi, B. Hinrichs, and J. Valentín Martín, “Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors,” <i>arXiv:2508.00805</i>. 2025.","ama":"Falconi M, Hinrichs B, Valentín Martín J. Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors. <i>arXiv:250800805</i>. Published online 2025.","apa":"Falconi, M., Hinrichs, B., &#38; Valentín Martín, J. (2025). Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors. In <i>arXiv:2508.00805</i>.","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} }","short":"M. Falconi, B. Hinrichs, J. Valentín Martín, ArXiv:2508.00805 (2025).","mla":"Falconi, Marco, et al. “Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors.” <i>ArXiv:2508.00805</i>, 2025."},"title":"Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors","date_updated":"2026-01-16T09:01:45Z","author":[{"full_name":"Falconi, Marco","last_name":"Falconi","first_name":"Marco"},{"full_name":"Hinrichs, Benjamin","id":"99427","last_name":"Hinrichs","orcid":"0000-0001-9074-1205","first_name":"Benjamin"},{"full_name":"Valentín Martín, Javier","last_name":"Valentín Martín","first_name":"Javier"}],"date_created":"2026-01-16T08:59:11Z","abstract":[{"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.","lang":"eng"}],"status":"public","publication":"arXiv:2508.00805","type":"preprint","language":[{"iso":"eng"}],"_id":"63645","external_id":{"arxiv":["2508.00805"]},"project":[{"name":"PhoQC: Photonisches Quantencomputing","_id":"266"}],"department":[{"_id":"799"}],"user_id":"99427"},{"type":"preprint","publication":"arXiv:2511.02867","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."}],"status":"public","project":[{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"}],"_id":"63646","external_id":{"arxiv":["2511.02867"]},"user_id":"99427","department":[{"_id":"799"}],"language":[{"iso":"eng"}],"year":"2025","citation":{"ama":"Hinrichs B, Polzer S. Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems. <i>arXiv:251102867</i>. Published online 2025.","chicago":"Hinrichs, Benjamin, and Steffen Polzer. “Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems.” <i>ArXiv:2511.02867</i>, 2025.","ieee":"B. Hinrichs and S. Polzer, “Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems,” <i>arXiv:2511.02867</i>. 2025.","apa":"Hinrichs, B., &#38; Polzer, S. (2025). Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems. In <i>arXiv:2511.02867</i>.","short":"B. Hinrichs, S. Polzer, ArXiv:2511.02867 (2025).","mla":"Hinrichs, Benjamin, and Steffen Polzer. “Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems.” <i>ArXiv:2511.02867</i>, 2025.","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} }"},"date_updated":"2026-01-16T09:01:02Z","date_created":"2026-01-16T08:59:45Z","author":[{"last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","id":"99427","first_name":"Benjamin"},{"full_name":"Polzer, Steffen","last_name":"Polzer","first_name":"Steffen"}],"title":"Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems"},{"citation":{"ieee":"B. Hinrichs and P. Mittenbühler, “On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks,” <i>arXiv:2511.13409</i>. 2025.","chicago":"Hinrichs, Benjamin, and Pascal Mittenbühler. “On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks.” <i>ArXiv:2511.13409</i>, 2025.","ama":"Hinrichs B, Mittenbühler P. On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks. <i>arXiv:251113409</i>. Published online 2025.","apa":"Hinrichs, B., &#38; Mittenbühler, P. (2025). On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks. In <i>arXiv:2511.13409</i>.","mla":"Hinrichs, Benjamin, and Pascal Mittenbühler. “On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks.” <i>ArXiv:2511.13409</i>, 2025.","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} }","short":"B. Hinrichs, P. Mittenbühler, ArXiv:2511.13409 (2025)."},"year":"2025","title":"On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks","date_created":"2026-01-16T08:59:54Z","author":[{"first_name":"Benjamin","id":"99427","full_name":"Hinrichs, Benjamin","last_name":"Hinrichs","orcid":"0000-0001-9074-1205"},{"first_name":"Pascal","full_name":"Mittenbühler, Pascal","last_name":"Mittenbühler"}],"date_updated":"2026-01-16T09:00:31Z","status":"public","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."}],"type":"preprint","publication":"arXiv:2511.13409","language":[{"iso":"eng"}],"user_id":"99427","department":[{"_id":"799"}],"project":[{"name":"PhoQC: Photonisches Quantencomputing","_id":"266"}],"_id":"63647","external_id":{"arxiv":["2511.13409"]}},{"title":"Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains","author":[{"last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","id":"99427","first_name":"Benjamin"},{"first_name":"Oliver","last_name":"Matte","full_name":"Matte, Oliver"}],"date_created":"2024-03-20T14:56:05Z","date_updated":"2024-03-20T14:56:50Z","citation":{"apa":"Hinrichs, B., &#38; Matte, O. (2024). Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains. In <i>arXiv:2403.12147</i>.","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} }","short":"B. Hinrichs, O. Matte, 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.” <i>ArXiv:2403.12147</i>, 2024.","ama":"Hinrichs B, Matte O. Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains. <i>arXiv:240312147</i>. Published online 2024.","ieee":"B. Hinrichs and O. Matte, “Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains,” <i>arXiv:2403.12147</i>. 2024.","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups Generated by Multi-Polaron  Hamiltonians in Magnetic Fields and on General Domains.” <i>ArXiv:2403.12147</i>, 2024."},"year":"2024","language":[{"iso":"eng"}],"department":[{"_id":"799"}],"user_id":"99427","external_id":{"arxiv":["2403.12147"]},"_id":"52691","status":"public","abstract":[{"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.","lang":"eng"}],"publication":"arXiv:2403.12147","type":"preprint"},{"date_updated":"2026-01-16T08:45:25Z","oa":"1","author":[{"orcid":"0000-0001-9074-1205","last_name":"Hinrichs","full_name":"Hinrichs, Benjamin","id":"99427","first_name":"Benjamin"},{"first_name":"Jonas","last_name":"Lampart","full_name":"Lampart, Jonas"}],"volume":362,"main_file_link":[{"open_access":"1"}],"doi":"10.5802/crmath.652","publication_status":"published","publication_identifier":{"issn":["1631-073X","1778-3569"]},"citation":{"apa":"Hinrichs, B., &#38; Lampart, J. (2024). A Lower Bound on the Critical Momentum of an Impurity in a Bose–Einstein Condensate. <i>Comptes Rendus. Mathématique</i>, <i>362</i>(G11), 1399–1411. <a href=\"https://doi.org/10.5802/crmath.652\">https://doi.org/10.5802/crmath.652</a>","short":"B. Hinrichs, J. Lampart, Comptes Rendus. Mathématique 362 (2024) 1399–1411.","bibtex":"@article{Hinrichs_Lampart_2024, title={A Lower Bound on the Critical Momentum of an Impurity in a Bose–Einstein Condensate}, volume={362}, DOI={<a href=\"https://doi.org/10.5802/crmath.652\">10.5802/crmath.652</a>}, number={G11}, journal={Comptes Rendus. Mathématique}, publisher={MathDoc/Centre Mersenne}, author={Hinrichs, Benjamin and Lampart, Jonas}, year={2024}, pages={1399–1411} }","mla":"Hinrichs, Benjamin, and Jonas Lampart. “A Lower Bound on the Critical Momentum of an Impurity in a Bose–Einstein Condensate.” <i>Comptes Rendus. Mathématique</i>, vol. 362, no. G11, MathDoc/Centre Mersenne, 2024, pp. 1399–411, doi:<a href=\"https://doi.org/10.5802/crmath.652\">10.5802/crmath.652</a>.","ieee":"B. Hinrichs and J. Lampart, “A Lower Bound on the Critical Momentum of an Impurity in a Bose–Einstein Condensate,” <i>Comptes Rendus. Mathématique</i>, vol. 362, no. G11, pp. 1399–1411, 2024, doi: <a href=\"https://doi.org/10.5802/crmath.652\">10.5802/crmath.652</a>.","chicago":"Hinrichs, Benjamin, and Jonas Lampart. “A Lower Bound on the Critical Momentum of an Impurity in a Bose–Einstein Condensate.” <i>Comptes Rendus. Mathématique</i> 362, no. G11 (2024): 1399–1411. <a href=\"https://doi.org/10.5802/crmath.652\">https://doi.org/10.5802/crmath.652</a>.","ama":"Hinrichs B, Lampart J. A Lower Bound on the Critical Momentum of an Impurity in a Bose–Einstein Condensate. <i>Comptes Rendus Mathématique</i>. 2024;362(G11):1399-1411. doi:<a href=\"https://doi.org/10.5802/crmath.652\">10.5802/crmath.652</a>"},"page":"1399-1411","intvolume":"       362","project":[{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"}],"_id":"63636","user_id":"99427","department":[{"_id":"799"}],"article_type":"original","type":"journal_article","status":"public","publisher":"MathDoc/Centre Mersenne","date_created":"2026-01-16T08:43:59Z","title":"A Lower Bound on the Critical Momentum of an Impurity in a Bose–Einstein Condensate","issue":"G11","year":"2024","external_id":{"arxiv":["2311.05361"]},"language":[{"iso":"eng"}],"publication":"Comptes Rendus. Mathématique"},{"status":"public","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."}],"publication":"arXiv:2412.09708","type":"preprint","language":[{"iso":"eng"}],"department":[{"_id":"799"}],"user_id":"99427","_id":"63641","external_id":{"arxiv":["2412.09708"]},"project":[{"name":"PhoQC: Photonisches Quantencomputing","_id":"266"}],"citation":{"apa":"Hinrichs, B., &#38; Hiroshima, F. (2024). On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups. In <i>arXiv:2412.09708</i>.","short":"B. Hinrichs, F. Hiroshima, ArXiv:2412.09708 (2024).","mla":"Hinrichs, Benjamin, and Fumio Hiroshima. “On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups.” <i>ArXiv:2412.09708</i>, 2024.","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} }","ieee":"B. Hinrichs and F. Hiroshima, “On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups,” <i>arXiv:2412.09708</i>. 2024.","chicago":"Hinrichs, Benjamin, and Fumio Hiroshima. “On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups.” <i>ArXiv:2412.09708</i>, 2024.","ama":"Hinrichs B, Hiroshima F. On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups. <i>arXiv:241209708</i>. Published online 2024."},"year":"2024","title":"On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups","date_created":"2026-01-16T08:56:18Z","author":[{"first_name":"Benjamin","last_name":"Hinrichs","orcid":"0000-0001-9074-1205","id":"99427","full_name":"Hinrichs, Benjamin"},{"full_name":"Hiroshima, Fumio","last_name":"Hiroshima","first_name":"Fumio"}],"date_updated":"2026-01-16T08:56:37Z"},{"article_type":"original","department":[{"_id":"799"}],"user_id":"99427","_id":"63637","project":[{"name":"PhoQC: Photonisches Quantencomputing","_id":"266"}],"status":"public","type":"journal_article","doi":"10.1007/s00023-024-01453-y","main_file_link":[{"open_access":"1"}],"volume":26,"author":[{"id":"99427","full_name":"Hinrichs, Benjamin","orcid":"0000-0001-9074-1205","last_name":"Hinrichs","first_name":"Benjamin"},{"first_name":"Marius","last_name":"Lemm","full_name":"Lemm, Marius"},{"first_name":"Oliver","full_name":"Siebert, Oliver","last_name":"Siebert"}],"date_updated":"2026-01-16T09:05:58Z","oa":"1","page":"41-80","intvolume":"        26","citation":{"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>.","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>","short":"B. Hinrichs, M. Lemm, O. Siebert, Annales Henri Poincaré 26 (2024) 41–80.","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} }","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>.","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>"},"publication_identifier":{"issn":["1424-0637","1424-0661"]},"publication_status":"published","language":[{"iso":"eng"}],"external_id":{"arxiv":["2310.17736"]},"publication":"Annales Henri Poincaré","title":"On Lieb–Robinson Bounds for a Class of Continuum Fermions","date_created":"2026-01-16T08:46:12Z","publisher":"Springer Science and Business Media LLC","year":"2024","issue":"1"},{"type":"journal_article","status":"public","department":[{"_id":"799"}],"user_id":"99427","_id":"51374","extern":"1","article_number":"110319","publication_identifier":{"issn":["0022-1236"]},"publication_status":"published","intvolume":"       286","citation":{"apa":"Hasler, D., Hinrichs, B., &#38; Siebert, O. (2024). Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively. <i>Journal of Functional Analysis</i>, <i>286</i>(7), Article 110319. <a href=\"https://doi.org/10.1016/j.jfa.2024.110319\">https://doi.org/10.1016/j.jfa.2024.110319</a>","mla":"Hasler, David, et al. “Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.” <i>Journal of Functional Analysis</i>, vol. 286, no. 7, 110319, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110319\">10.1016/j.jfa.2024.110319</a>.","short":"D. Hasler, B. Hinrichs, O. Siebert, Journal of Functional Analysis 286 (2024).","bibtex":"@article{Hasler_Hinrichs_Siebert_2024, title={Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively}, volume={286}, DOI={<a href=\"https://doi.org/10.1016/j.jfa.2024.110319\">10.1016/j.jfa.2024.110319</a>}, number={7110319}, journal={Journal of Functional Analysis}, publisher={Elsevier BV}, author={Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}, year={2024} }","ieee":"D. Hasler, B. Hinrichs, and O. Siebert, “Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively,” <i>Journal of Functional Analysis</i>, vol. 286, no. 7, Art. no. 110319, 2024, doi: <a href=\"https://doi.org/10.1016/j.jfa.2024.110319\">10.1016/j.jfa.2024.110319</a>.","chicago":"Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.” <i>Journal of Functional Analysis</i> 286, no. 7 (2024). <a href=\"https://doi.org/10.1016/j.jfa.2024.110319\">https://doi.org/10.1016/j.jfa.2024.110319</a>.","ama":"Hasler D, Hinrichs B, Siebert O. Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively. <i>Journal of Functional Analysis</i>. 2024;286(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110319\">10.1016/j.jfa.2024.110319</a>"},"volume":286,"author":[{"full_name":"Hasler, David","last_name":"Hasler","first_name":"David"},{"first_name":"Benjamin","full_name":"Hinrichs, Benjamin","id":"99427","last_name":"Hinrichs","orcid":"0000-0001-9074-1205"},{"first_name":"Oliver","last_name":"Siebert","full_name":"Siebert, Oliver"}],"date_updated":"2026-01-16T09:04:51Z","oa":"1","doi":"10.1016/j.jfa.2024.110319","main_file_link":[{"open_access":"1"}],"publication":"Journal of Functional Analysis","external_id":{"arxiv":["2302.06998"]},"language":[{"iso":"eng"}],"keyword":["Analysis"],"issue":"7","year":"2024","date_created":"2024-02-18T12:31:28Z","publisher":"Elsevier BV","title":"Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively"},{"year":"2023","issue":"6","title":"Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions","date_created":"2026-01-16T08:39:40Z","publisher":"Springer Science and Business Media LLC","publication":"Annales Henri Poincaré","language":[{"iso":"eng"}],"external_id":{"arxiv":["2211.14046"]},"citation":{"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>.","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>.","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>","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.","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} }","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>"},"intvolume":"        25","page":"2877-2940","publication_status":"published","publication_identifier":{"issn":["1424-0637","1424-0661"]},"main_file_link":[{"open_access":"1"}],"doi":"10.1007/s00023-023-01369-z","author":[{"first_name":"Benjamin","full_name":"Hinrichs, Benjamin","id":"99427","orcid":"0000-0001-9074-1205","last_name":"Hinrichs"},{"first_name":"Oliver","full_name":"Matte, Oliver","last_name":"Matte"}],"volume":25,"oa":"1","date_updated":"2026-01-16T09:05:26Z","status":"public","type":"journal_article","extern":"1","article_type":"original","user_id":"99427","department":[{"_id":"799"}],"_id":"63635"},{"publication":"Journal of Mathematical Analysis and Applications","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Analysis"],"external_id":{"arxiv":["2205.09189"]},"year":"2023","issue":"1","title":"Super-Gaussian decay of exponentials: A sufficient condition","date_created":"2023-07-20T05:08:49Z","publisher":"Elsevier BV","status":"public","type":"journal_article","article_number":"127558","department":[{"_id":"799"}],"user_id":"99427","_id":"46100","intvolume":"       528","citation":{"ama":"Hinrichs B, Janssen DW, Ziebell J. Super-Gaussian decay of exponentials: A sufficient condition. <i>Journal of Mathematical Analysis and Applications</i>. 2023;528(1). doi:<a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>","ieee":"B. Hinrichs, D. W. Janssen, and J. Ziebell, “Super-Gaussian decay of exponentials: A sufficient condition,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 528, no. 1, Art. no. 127558, 2023, doi: <a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>.","chicago":"Hinrichs, Benjamin, Daan W. Janssen, and Jobst Ziebell. “Super-Gaussian Decay of Exponentials: A Sufficient Condition.” <i>Journal of Mathematical Analysis and Applications</i> 528, no. 1 (2023). <a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">https://doi.org/10.1016/j.jmaa.2023.127558</a>.","bibtex":"@article{Hinrichs_Janssen_Ziebell_2023, title={Super-Gaussian decay of exponentials: A sufficient condition}, volume={528}, DOI={<a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>}, number={1127558}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Hinrichs, Benjamin and Janssen, Daan W. and Ziebell, Jobst}, year={2023} }","mla":"Hinrichs, Benjamin, et al. “Super-Gaussian Decay of Exponentials: A Sufficient Condition.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 528, no. 1, 127558, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>.","short":"B. Hinrichs, D.W. Janssen, J. Ziebell, Journal of Mathematical Analysis and Applications 528 (2023).","apa":"Hinrichs, B., Janssen, D. W., &#38; Ziebell, J. (2023). Super-Gaussian decay of exponentials: A sufficient condition. <i>Journal of Mathematical Analysis and Applications</i>, <i>528</i>(1), Article 127558. <a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">https://doi.org/10.1016/j.jmaa.2023.127558</a>"},"publication_identifier":{"issn":["0022-247X"]},"publication_status":"published","doi":"10.1016/j.jmaa.2023.127558","main_file_link":[{"open_access":"1"}],"volume":528,"author":[{"last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","id":"99427","first_name":"Benjamin"},{"full_name":"Janssen, Daan W.","last_name":"Janssen","first_name":"Daan W."},{"first_name":"Jobst","full_name":"Ziebell, Jobst","last_name":"Ziebell"}],"date_updated":"2026-01-16T09:04:39Z","oa":"1"},{"publication_identifier":{"issn":["0129-055X","1793-6659"]},"publication_status":"published","intvolume":"        34","citation":{"chicago":"Dam, Thomas Norman, and Benjamin Hinrichs. “Absence of Ground States in the Renormalized Massless Translation-Invariant Nelson Model.” <i>Reviews in Mathematical Physics</i> 34, no. 10 (2022). <a href=\"https://doi.org/10.1142/s0129055x22500337\">https://doi.org/10.1142/s0129055x22500337</a>.","ieee":"T. N. Dam and B. Hinrichs, “Absence of ground states in the renormalized massless translation-invariant Nelson model,” <i>Reviews in Mathematical Physics</i>, vol. 34, no. 10, 2022, doi: <a href=\"https://doi.org/10.1142/s0129055x22500337\">10.1142/s0129055x22500337</a>.","ama":"Dam TN, Hinrichs B. Absence of ground states in the renormalized massless translation-invariant Nelson model. <i>Reviews in Mathematical Physics</i>. 2022;34(10). doi:<a href=\"https://doi.org/10.1142/s0129055x22500337\">10.1142/s0129055x22500337</a>","mla":"Dam, Thomas Norman, and Benjamin Hinrichs. “Absence of Ground States in the Renormalized Massless Translation-Invariant Nelson Model.” <i>Reviews in Mathematical Physics</i>, vol. 34, no. 10, World Scientific Pub Co Pte Ltd, 2022, doi:<a href=\"https://doi.org/10.1142/s0129055x22500337\">10.1142/s0129055x22500337</a>.","bibtex":"@article{Dam_Hinrichs_2022, title={Absence of ground states in the renormalized massless translation-invariant Nelson model}, volume={34}, DOI={<a href=\"https://doi.org/10.1142/s0129055x22500337\">10.1142/s0129055x22500337</a>}, number={10}, journal={Reviews in Mathematical Physics}, publisher={World Scientific Pub Co Pte Ltd}, author={Dam, Thomas Norman and Hinrichs, Benjamin}, year={2022} }","short":"T.N. Dam, B. Hinrichs, Reviews in Mathematical Physics 34 (2022).","apa":"Dam, T. N., &#38; Hinrichs, B. (2022). Absence of ground states in the renormalized massless translation-invariant Nelson model. <i>Reviews in Mathematical Physics</i>, <i>34</i>(10). <a href=\"https://doi.org/10.1142/s0129055x22500337\">https://doi.org/10.1142/s0129055x22500337</a>"},"volume":34,"author":[{"last_name":"Dam","full_name":"Dam, Thomas Norman","first_name":"Thomas Norman"},{"full_name":"Hinrichs, Benjamin","id":"99427","orcid":"0000-0001-9074-1205","last_name":"Hinrichs","first_name":"Benjamin"}],"date_updated":"2023-04-14T05:03:17Z","doi":"10.1142/s0129055x22500337","type":"journal_article","status":"public","user_id":"99427","_id":"43491","extern":"1","article_type":"original","issue":"10","year":"2022","date_created":"2023-04-14T04:49:00Z","publisher":"World Scientific Pub Co Pte Ltd","title":"Absence of ground states in the renormalized massless translation-invariant Nelson model","publication":"Reviews in Mathematical Physics","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."}],"external_id":{"arxiv":["1909.07661"]},"language":[{"iso":"eng"}]},{"type":"conference","status":"public","editor":[{"last_name":"Hiroshima","full_name":"Hiroshima, Fumio","first_name":"Fumio"}],"series_title":"RIMS Kôkyûroku","user_id":"99427","_id":"43496","extern":"1","publication_status":"published","citation":{"short":"B. Hinrichs, in: F. Hiroshima (Ed.), Mathematical Aspects of Quantum Fields and Related Topics, 2022, 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} }","mla":"Hinrichs, Benjamin. “Existence of Ground States in the Infrared-Critial Spin Boson Model.” <i>Mathematical Aspects of Quantum Fields and Related Topics</i>, edited by Fumio Hiroshima, vol. 2235, 2022, pp. 60–73.","apa":"Hinrichs, B. (2022). Existence of Ground States in the Infrared-Critial Spin Boson Model. In F. Hiroshima (Ed.), <i>Mathematical aspects of quantum fields and related topics</i> (Vol. 2235, pp. 60–73).","ieee":"B. Hinrichs, “Existence of Ground States in the Infrared-Critial Spin Boson Model,” in <i>Mathematical aspects of quantum fields and related topics</i>, RIMS, Kyoto, 2022, vol. 2235, pp. 60–73.","chicago":"Hinrichs, Benjamin. “Existence of Ground States in the Infrared-Critial Spin Boson Model.” In <i>Mathematical Aspects of Quantum Fields and Related Topics</i>, edited by Fumio Hiroshima, 2235:60–73. RIMS Kôkyûroku, 2022.","ama":"Hinrichs B. Existence of Ground States in the Infrared-Critial Spin Boson Model. In: Hiroshima F, ed. <i>Mathematical Aspects of Quantum Fields and Related Topics</i>. Vol 2235. RIMS Kôkyûroku. ; 2022:60-73."},"page":"60-73","intvolume":"      2235","author":[{"first_name":"Benjamin","orcid":"0000-0001-9074-1205","last_name":"Hinrichs","full_name":"Hinrichs, Benjamin","id":"99427"}],"volume":2235,"date_updated":"2026-01-16T09:03:41Z","oa":"1","main_file_link":[{"open_access":"1","url":"http://hdl.handle.net/2433/282934"}],"conference":{"name":"Mathematical aspects of quantum fields and related topics","start_date":"2021-12-06","end_date":"2021-12-08","location":"RIMS, Kyoto"},"publication":"Mathematical aspects of quantum fields and related topics","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."}],"external_id":{"arxiv":["2204.00287"]},"language":[{"iso":"eng"}],"year":"2022","date_created":"2023-04-14T04:56:51Z","title":"Existence of Ground States in the Infrared-Critial Spin Boson Model"},{"oa":"1","date_updated":"2026-01-16T09:02:30Z","author":[{"full_name":"Hasler, David","last_name":"Hasler","first_name":"David"},{"id":"99427","full_name":"Hinrichs, Benjamin","last_name":"Hinrichs","orcid":"0000-0001-9074-1205","first_name":"Benjamin"},{"last_name":"Siebert","full_name":"Siebert, Oliver","first_name":"Oliver"}],"volume":23,"main_file_link":[{"open_access":"1"}],"doi":"10.1007/s00023-022-01160-6","publication_status":"published","publication_identifier":{"issn":["1424-0637","1424-0661"]},"citation":{"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>","short":"D. Hasler, B. Hinrichs, O. Siebert, Annales Henri Poincaré 23 (2022) 2819–2853.","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} }","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>.","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>","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>.","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>."},"page":"2819-2853","intvolume":"        23","_id":"43492","user_id":"99427","article_type":"original","extern":"1","type":"journal_article","status":"public","publisher":"Springer Science and Business Media LLC","date_created":"2023-04-14T04:49:36Z","title":"FKN Formula and Ground State Energy for the Spin Boson Model with External Magnetic Field","issue":"8","year":"2022","external_id":{"arxiv":["2106.08659 "]},"language":[{"iso":"eng"}],"publication":"Annales Henri Poincaré","abstract":[{"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.","lang":"eng"}]},{"citation":{"ieee":"B. Hinrichs, <i>Existence of Ground States for Infrared-Critical Models of Quantum Field Theory</i>. Jena, 2022.","chicago":"Hinrichs, Benjamin. <i>Existence of Ground States for Infrared-Critical Models of Quantum Field Theory</i>. Jena, 2022. <a href=\"https://doi.org/10.22032/dbt.51516\">https://doi.org/10.22032/dbt.51516</a>.","ama":"Hinrichs B. <i>Existence of Ground States for Infrared-Critical Models of Quantum Field Theory</i>.; 2022. doi:<a href=\"https://doi.org/10.22032/dbt.51516\">10.22032/dbt.51516</a>","short":"B. Hinrichs, Existence of Ground States for Infrared-Critical Models of Quantum Field Theory, Jena, 2022.","mla":"Hinrichs, Benjamin. <i>Existence of Ground States for Infrared-Critical Models of Quantum Field Theory</i>. 2022, doi:<a href=\"https://doi.org/10.22032/dbt.51516\">10.22032/dbt.51516</a>.","bibtex":"@book{Hinrichs_2022, place={Jena}, title={Existence of Ground States for Infrared-Critical Models of Quantum Field Theory}, DOI={<a href=\"https://doi.org/10.22032/dbt.51516\">10.22032/dbt.51516</a>}, author={Hinrichs, Benjamin}, year={2022} }","apa":"Hinrichs, B. (2022). <i>Existence of Ground States for Infrared-Critical Models of Quantum Field Theory</i>. <a href=\"https://doi.org/10.22032/dbt.51516\">https://doi.org/10.22032/dbt.51516</a>"},"place":"Jena","year":"2022","supervisor":[{"first_name":"David","last_name":"Hasler","full_name":"Hasler, David"}],"date_created":"2023-04-14T05:09:10Z","author":[{"first_name":"Benjamin","full_name":"Hinrichs, Benjamin","id":"99427","orcid":"0000-0001-9074-1205","last_name":"Hinrichs"}],"date_updated":"2026-01-16T09:03:08Z","oa":"1","doi":"10.22032/dbt.51516","main_file_link":[{"open_access":"1"}],"title":"Existence of Ground States for Infrared-Critical Models of Quantum Field Theory","type":"dissertation","status":"public","user_id":"99427","_id":"43501","extern":"1","language":[{"iso":"eng"}]}]