@article{63656, author = {{Ares, Laura and Pinske, Julien and Hinrichs, Benjamin and Kolb, Martin and Sperling, Jan}}, issn = {{2469-9926}}, journal = {{Physical Review A}}, number = {{1}}, publisher = {{American Physical Society (APS)}}, title = {{{Restricted Monte Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system dynamics}}}, doi = {{10.1103/hcj7-8zlg}}, volume = {{113}}, year = {{2026}}, } @article{63657, author = {{Pinske, Julien and Ares, Laura and Hinrichs, Benjamin and Kolb, Martin and Sperling, Jan}}, issn = {{2469-9926}}, journal = {{Physical Review A}}, number = {{1}}, publisher = {{American Physical Society (APS)}}, title = {{{Separability Lindblad equation for dynamical open-system entanglement}}}, doi = {{10.1103/kd3b-bfxq}}, volume = {{113}}, year = {{2026}}, } @inproceedings{47534, abstract = {{In this proceeding we consider a translation invariant Nelson type model in two spatial dimensions modeling a scalar relativistic particle in interaction with a massive radiation field. As is well-known, the corresponding Hamiltonian can be defined with the help of an energy renormalization. First, we review a Feynman-Kac formula for the semigroup generated by this Hamiltonian proven by the authors in a recent preprint (where several matter particles and exterior potentials are treated as well). After that, we employ a few technical key relations and estimates obtained in our preprint to present an otherwise self-contained derivation of new Feynman-Kac formulas for the fiber Hamiltonians attached to fixed total momenta of the translation invariant system. We conclude by inferring an alternative derivation of the Feynman-Kac formula for the full translation invariant Hamiltonian.}}, author = {{Hinrichs, Benjamin and Matte, Oliver}}, booktitle = {{Proceedings of the 2023 RIMS Workshop 'Mathematical Aspects of Quantum Fields and Related Topics'}}, editor = {{Hiroshima, Fumio}}, number = {{3}}, title = {{{Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions}}}, volume = {{2310}}, year = {{2025}}, } @unpublished{63642, abstract = {{We prove absence of ground states in the infrared-divergent spin boson model at large coupling.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 = {{Betz, Volker and Hinrichs, Benjamin and Kraft, Mino Nicola and Polzer, Steffen}}, booktitle = {{arXiv:2501.19362}}, title = {{{On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model}}}, year = {{2025}}, } @unpublished{63644, abstract = {{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 = {{Hinrichs, Benjamin and Lampart, Jonas and Valentín Martín, Javier}}, booktitle = {{arXiv:2502.04876}}, title = {{{Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions}}}, year = {{2025}}, } @unpublished{63643, abstract = {{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 = {{Falconi, Marco and Hinrichs, Benjamin}}, booktitle = {{arXiv:2505.19977}}, title = {{{Ultraviolet Renormalization of the van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach}}}, year = {{2025}}, } @unpublished{63645, abstract = {{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 = {{Falconi, Marco and Hinrichs, Benjamin and Valentín Martín, Javier}}, booktitle = {{arXiv:2508.00805}}, title = {{{Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors}}}, year = {{2025}}, } @unpublished{63646, abstract = {{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 = {{Hinrichs, Benjamin and Polzer, Steffen}}, booktitle = {{arXiv:2511.02867}}, title = {{{Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems}}}, year = {{2025}}, } @unpublished{63647, abstract = {{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 = {{Hinrichs, Benjamin and Mittenbühler, Pascal}}, booktitle = {{arXiv:2511.13409}}, title = {{{On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks}}}, year = {{2025}}, } @unpublished{52691, abstract = {{We prove Feynman-Kac formulas for the semigroups generated by selfadjoint operators in a class containing Fr\"ohlich Hamiltonians known from solid state physics. The latter model multi-polarons, i.e., a fixed number of quantum mechanical electrons moving in a polarizable crystal and interacting with the quantized phonon field generated by the crystal's vibrational modes. Both the electrons and phonons can be confined to suitable open subsets of Euclidean space. We also include possibly very singular magnetic vector potentials and electrostatic potentials. Our Feynman-Kac formulas comprise Fock space operator-valued multiplicative functionals and can be applied to every vector in the underlying Hilbert space. In comparison to the renormalized Nelson model, for which analogous Feynman-Kac formulas are known, the analysis of the creation and annihilation terms in the multiplicative functionals requires novel ideas to overcome difficulties caused by the phonon dispersion relation being constant. Getting these terms under control and generalizing other construction steps so as to cover confined systems are the main achievements of this article.}}, author = {{Hinrichs, Benjamin and Matte, Oliver}}, booktitle = {{arXiv:2403.12147}}, title = {{{Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains}}}, year = {{2024}}, } @article{63636, author = {{Hinrichs, Benjamin and Lampart, Jonas}}, issn = {{1631-073X}}, journal = {{Comptes Rendus. Mathématique}}, number = {{G11}}, pages = {{1399--1411}}, publisher = {{MathDoc/Centre Mersenne}}, title = {{{A Lower Bound on the Critical Momentum of an Impurity in a Bose–Einstein Condensate}}}, doi = {{10.5802/crmath.652}}, volume = {{362}}, year = {{2024}}, } @unpublished{63641, abstract = {{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 = {{Hinrichs, Benjamin and Hiroshima, Fumio}}, booktitle = {{arXiv:2412.09708}}, title = {{{On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups}}}, year = {{2024}}, } @article{63637, author = {{Hinrichs, Benjamin and Lemm, Marius and Siebert, Oliver}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, number = {{1}}, pages = {{41--80}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{On Lieb–Robinson Bounds for a Class of Continuum Fermions}}}, doi = {{10.1007/s00023-024-01453-y}}, volume = {{26}}, year = {{2024}}, } @article{51374, author = {{Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}}, issn = {{0022-1236}}, journal = {{Journal of Functional Analysis}}, keywords = {{Analysis}}, number = {{7}}, publisher = {{Elsevier BV}}, title = {{{Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively}}}, doi = {{10.1016/j.jfa.2024.110319}}, volume = {{286}}, year = {{2024}}, } @article{63635, author = {{Hinrichs, Benjamin and Matte, Oliver}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, number = {{6}}, pages = {{2877--2940}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions}}}, doi = {{10.1007/s00023-023-01369-z}}, volume = {{25}}, year = {{2023}}, } @article{46100, author = {{Hinrichs, Benjamin and Janssen, Daan W. and Ziebell, Jobst}}, issn = {{0022-247X}}, journal = {{Journal of Mathematical Analysis and Applications}}, keywords = {{Applied Mathematics, Analysis}}, number = {{1}}, publisher = {{Elsevier BV}}, title = {{{Super-Gaussian decay of exponentials: A sufficient condition}}}, doi = {{10.1016/j.jmaa.2023.127558}}, volume = {{528}}, year = {{2023}}, } @article{43491, abstract = {{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.}}, author = {{Dam, Thomas Norman and Hinrichs, Benjamin}}, issn = {{0129-055X}}, journal = {{Reviews in Mathematical Physics}}, number = {{10}}, publisher = {{World Scientific Pub Co Pte Ltd}}, title = {{{Absence of ground states in the renormalized massless translation-invariant Nelson model}}}, doi = {{10.1142/s0129055x22500337}}, volume = {{34}}, year = {{2022}}, } @inproceedings{43496, abstract = {{We review recent results on the existence of ground states for the infrared-critical spin boson model, which describes the interaction of a massless bosonic field with a two-state quantum system. Explicitly, we derive a critical coupling $\lambda_{\mathsf c}>0$ such that the spin boson model exhibits a ground state for coupling constants $\lambda$ with $|\lambda|<\lambda_{\mathsf c}$. The proof combines a Feynman-Kac-Nelson formula for the spin boson model with external magnetic field, a 1D-Ising model correlation bound and a compactness argument in Fock space. Elaborating on the connection to a long-range 1D-Ising model, we briefly discuss the conjecture that the spin boson model does not have a ground state at large coupling. This note is based on joint work with David Hasler and Oliver Siebert.}}, author = {{Hinrichs, Benjamin}}, booktitle = {{Mathematical aspects of quantum fields and related topics}}, editor = {{Hiroshima, Fumio}}, location = {{RIMS, Kyoto}}, pages = {{60--73}}, title = {{{Existence of Ground States in the Infrared-Critial Spin Boson Model}}}, volume = {{2235}}, year = {{2022}}, } @article{43492, abstract = {{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.}}, author = {{Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, number = {{8}}, pages = {{2819--2853}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{FKN Formula and Ground State Energy for the Spin Boson Model with External Magnetic Field}}}, doi = {{10.1007/s00023-022-01160-6}}, volume = {{23}}, year = {{2022}}, } @phdthesis{43501, author = {{Hinrichs, Benjamin}}, title = {{{Existence of Ground States for Infrared-Critical Models of Quantum Field Theory}}}, doi = {{10.22032/dbt.51516}}, year = {{2022}}, }