@unpublished{63642,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@unpublished{63644,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@unpublished{63643,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}},
}
@article{63649,
author = {{Glöckner, Helge and Schmeding, Alexander and Suri, Ali}},
issn = {{2972-4589}},
journal = {{Geometric Mechanics}},
number = {{04}},
pages = {{383--437}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Manifolds of continuous BV-functions and vector measure regularity of Banach–Lie groups}}},
doi = {{10.1142/s2972458925500029}},
volume = {{01}},
year = {{2025}},
}
@article{56717,
abstract = {{We establish a multiresolution analysis on the space $\text{Herm}(n)$ of
$n\times n$ complex Hermitian matrices which is adapted to invariance under
conjugation by the unitary group $U(n).$ The orbits under this action are
parametrized by the possible ordered spectra of Hermitian matrices, which
constitute a closed Weyl chamber of type $A_{n-1}$ in $\mathbb R^n.$ The space
$L^2(\text{Herm}(n))^{U(n)}$ of radial, i.e. $U(n)$-invariant $L^2$-functions
on $\text{Herm}(n)$ is naturally identified with a certain weighted $L^2$-space
on this chamber.
The scale spaces of our multiresolution analysis are obtained by usual dyadic
dilations as well as generalized translations of a scaling function, where the
generalized translation is a hypergroup translation which respects the radial
geometry. We provide a concise criterion to characterize orthonormal wavelet
bases and show that such bases always exist. They provide natural orthonormal
bases of the space $L^2(\text{Herm}(n))^{U(n)}.$
Furthermore, we show how to obtain radial scaling functions from classical
scaling functions on $\mathbb R^{n}$. Finally, generalizations related to the
Cartan decompositions for general compact Lie groups are indicated.}},
author = {{Langen, Lukas and Rösler, Margit}},
journal = {{Indagationes Mathematicae}},
number = {{6}},
pages = {{1671--1694}},
publisher = {{Elsevier}},
title = {{{Multiresolution analysis on spectra of hermitian matrices}}},
volume = {{36}},
year = {{2025}},
}
@article{64289,
abstract = {{Abstract
Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations
$$\overline{\rho }$$
ρ
¯
of the Lie group
$${{\,\textrm{Diff}\,}}_c(M)$$
Diff
c
(
M
)
of compactly supported diffeomorphisms of a smooth manifold M that satisfy a so-called generalized positive energy condition. In particular, this captures representations that are in a suitable sense compatible with a KMS state on the von Neumann algebra generated by
$$\overline{\rho }$$
ρ
¯
. We show that if M is connected and
$$\dim (M) > 1$$
dim
(
M
)
>
1
, then any such representation is necessarily trivial on the identity component
$${{\,\textrm{Diff}\,}}_c(M)_0$$
Diff
c
(
M
)
0
. As an intermediate step towards this result, we determine the continuous second Lie algebra cohomology
$$H^2_\textrm{ct}(\mathcal {X}_c(M), \mathbb {R})$$
H
ct
2
(
X
c
(
M
)
,
R
)
of the Lie algebra of compactly supported vector fields. This is subtly different from Gelfand–Fuks cohomology in view of the compact support condition.}},
author = {{Janssens, Bas and Niestijl, Milan}},
issn = {{0010-3616}},
journal = {{Communications in Mathematical Physics}},
number = {{2}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms}}},
doi = {{10.1007/s00220-024-05226-w}},
volume = {{406}},
year = {{2025}},
}
@article{59258,
author = {{Winkler, Michael}},
issn = {{0095-4616}},
journal = {{Applied Mathematics & Optimization}},
number = {{2}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters}}},
doi = {{10.1007/s00245-025-10243-9}},
volume = {{91}},
year = {{2025}},
}
@misc{64736,
booktitle = {{J. Lie Theory}},
editor = {{Frahm, Jan and Glöckner, Helge and Hilgert, Joachim and Olafsson, Gestur}},
number = {{4}},
title = {{{Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday}}},
volume = {{35}},
year = {{2025}},
}
@phdthesis{64770,
author = {{Pinaud, Matthieu}},
title = {{{Manifold of mappings and regularity properties of half-Lie groups}}},
doi = {{10.17619/UNIPB/1-2211}},
year = {{2025}},
}
@article{34807,
abstract = {{Let $M$ be a compact, real analytic manifold and $G$ be the Lie group of all
real-analytic diffeomorphisms of $M$, which is modelled on the (DFS)-space
${\mathfrak g}$ of real-analytic vector fields on $M$. We study flows of
time-dependent real-analytic vector fields on $M$ which are integrable
functions in time, and their dependence on the time-dependent vector field.
Notably, we show that the Lie group $G$ is $L^1$-regular in the sense that each
$[\gamma]$ in $L^1([0,1],{\mathfrak g})$ has an evolution which is an
absolutely continuous $G$-valued function on $[0,1]$ and smooth in $[\gamma]$.
As tools for the proof, we develop several new results concerning
$L^p$-regularity of infinite-dimensional Lie groups, for $1\leq p\leq \infty$,
which will be useful also for the discussion of other classes of groups.
Moreover, we obtain new results concerning the continuity and complex
analyticity of non-linear mappings on open subsets of locally convex direct
limits.}},
author = {{Glöckner, Helge}},
journal = {{Nonlinear Analysis}},
title = {{{Lie groups of real analytic diffeomorphisms are L^1-regular}}},
doi = {{10.1016/j.na.2024.113690}},
volume = {{252}},
year = {{2025}},
}
@article{60205,
author = {{Black, Tobias}},
issn = {{0022-0396}},
journal = {{Journal of Differential Equations}},
publisher = {{Elsevier BV}},
title = {{{Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system}}},
doi = {{10.1016/j.jde.2025.113555}},
volume = {{443}},
year = {{2025}},
}
@article{54837,
author = {{Claes, Leander and Lankeit, Johannes and Winkler, Michael}},
issn = {{1793-6314}},
journal = {{Mathematical Models and Methods in Applied Sciences}},
number = {{11}},
pages = {{2465--2512}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions}}},
doi = {{10.1142/s0218202525500447}},
volume = {{35}},
year = {{2025}},
}
@article{53414,
abstract = {{By constructing a non-empty domain of discontinuity in a suitable homogeneous
space, we prove that every torsion-free projective Anosov subgroup is the
monodromy group of a locally homogeneous contact Axiom A dynamical system with
a unique basic hyperbolic set on which the flow is conjugate to the refraction
flow of Sambarino. Under the assumption of irreducibility, we utilize the work
of Stoyanov to establish spectral estimates for the associated complex Ruelle
transfer operators, and by way of corollary: exponential mixing, exponentially
decaying error term in the prime orbit theorem, and a spectral gap for the
Ruelle zeta function. With no irreducibility assumption, results of
Dyatlov-Guillarmou imply the global meromorphic continuation of zeta functions
with smooth weights, as well as the existence of a discrete spectrum of
Ruelle-Pollicott resonances and (co)-resonant states. We apply our results to
space-like geodesic flows for the convex cocompact pseudo-Riemannian manifolds
of Danciger-Gu\'eritaud-Kassel, and the Benoist-Hilbert geodesic flow for
strictly convex real projective manifolds.}},
author = {{Delarue, Benjamin and Monclair, Daniel and Sanders, Andrew}},
journal = {{Geometric and Functional Analysis (GAFA)}},
pages = {{673–735}},
title = {{{Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing}}},
doi = {{10.1007/s00039-025-00712-2}},
volume = {{35}},
year = {{2025}},
}
@article{53412,
abstract = {{Let $M$ be a symplectic manifold carrying a Hamiltonian $S^1$-action with
momentum map $J:M \rightarrow \mathbb{R}$ and consider the corresponding
symplectic quotient $\mathcal{M}_0:=J^{-1}(0)/S^1$. We extend Sjamaar's complex
of differential forms on $\mathcal{M}_0$, whose cohomology is isomorphic to the
singular cohomology $H(\mathcal{M}_0;\mathbb{R})$ of $\mathcal{M}_0$ with real
coefficients, to a complex of differential forms on $\mathcal{M}_0$ associated
with a partial desingularization $\widetilde{\mathcal{M}}_0$, which we call
resolution differential forms. The cohomology of that complex turns out to be
isomorphic to the de Rham cohomology $H(\widetilde{ \mathcal{M}}_0)$ of
$\widetilde{\mathcal{M}}_0$. Based on this, we derive a long exact sequence
involving both $H(\mathcal{M}_0;\mathbb{R})$ and $H(\widetilde{
\mathcal{M}}_0)$ and give conditions for its splitting. We then define a Kirwan
map $\mathcal{K}:H_{S^1}(M) \rightarrow H(\widetilde{\mathcal{M}}_0)$ from the
equivariant cohomology $H_{S^1}(M)$ of $M$ to $H(\widetilde{\mathcal{M}}_0)$
and show that its image contains the image of $H(\mathcal{M}_0;\mathbb{R})$ in
$H(\widetilde{\mathcal{M}}_0)$ under the natural inclusion. Combining both
results in the case that all fixed point components of $M$ have vanishing odd
cohomology we obtain a surjection $\check \kappa:H^\textrm{ev}_{S^1}(M)
\rightarrow H^\textrm{ev}(\mathcal{M}_0;\mathbb{R})$ in even degrees, while
already simple examples show that a similar surjection in odd degrees does not
exist in general. As an interesting class of examples we study abelian polygon
spaces.}},
author = {{Delarue, Benjamin and Ramacher, Pablo and Schmitt, Maximilian}},
journal = {{Transformation Groups}},
title = {{{Singular cohomology of symplectic quotients by circle actions and Kirwan surjectivity}}},
doi = {{10.1007/s00031-025-09924-0}},
year = {{2025}},
}
@unpublished{63569,
abstract = {{Let $G$ be a totally disconnected locally compact (tdlc) group. The contraction group $\mathrm{con}(g)$ of an element $g\in G$ is the set of all $h\in G$ such that $g^n h g^{-n} \to 1_G$ as $n \to \infty$. The nub of $g$ can then be characterized as the intersection $\mathrm{nub}(g)$ of the closures of $\mathrm{con}(g)$ and $\mathrm{con}(g^{-1})$.
Contraction groups and nubs provide important tools in the study of the structure of tdlc groups, as already evidenced in the work of G. Willis. It is known that $\mathrm{nub}(g) = \{1\}$ if and only if $\mathrm{con}(g)$ is closed. In general, contraction groups are not closed and computing the nub is typically a challenging problem.
Maximal Kac-Moody groups over finite fields form a prominent family of non-discrete compactly generated simple tdlc groups. In this paper we give a complete description of the nub of any element in these groups.}},
author = {{Bischof, Sebastian and Marquis, Timothée}},
title = {{{Describing the nub in maximal Kac-Moody groups}}},
year = {{2025}},
}
@unpublished{63568,
abstract = {{In this article we work out the details of flat groups of the automorphism group of locally finite Bruhat-Tits buildings.}},
author = {{Bischof, Sebastian}},
title = {{{On flat groups in affine buildings}}},
year = {{2025}},
}
@article{53413,
abstract = {{For negatively curved symmetric spaces it is known that the poles of the
scattering matrices defined via the standard intertwining operators for the
spherical principal representations of the isometry group are either given as
poles of the intertwining operators or as quantum resonances, i.e. poles of the
meromorphically continued resolvents of the Laplace-Beltrami operator. We
extend this result to classical locally symmetric spaces of negative curvature
with convex-cocompact fundamental group using results of Bunke and Olbrich. The
method of proof forces us to exclude the spectral parameters corresponding to
singular Poisson transforms.}},
author = {{Delarue, Benjamin and Hilgert, Joachim}},
issn = {{0949-5932}},
journal = {{Journal of Lie Theory}},
number = {{(4)}},
pages = {{787----804}},
title = {{{Quantum resonances and scattering poles of classical rank one locally symmetric spaces}}},
volume = {{35}},
year = {{2025}},
}