@unpublished{51376, abstract = {{In the Bogoliubov-Fr\"ohlich model, we prove that an impurity immersed in a Bose-Einstein condensate forms a stable quasi-particle when the total momentum is less than its mass times the speed of sound. The system thus exhibits superfluid behavior, as this quasi-particle does not experience friction. We do not assume any infrared or ultraviolet regularization of the model, which contains massless excitations and point-like interactions.}}, author = {{Hinrichs, Benjamin and Lampart, Jonas}}, booktitle = {{arXiv:2311.05361}}, title = {{{A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate}}}, year = {{2023}}, } @article{31190, abstract = {{For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of arbitrary rank we determine the location of certain Ruelle-Taylor resonances for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate counting function for the Ruelle-Taylor resonances and establish a spectral gap which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is achieved by proving a quantum-classical correspondence, i.e. a 1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant states and joint eigenfunctions of the algebra of invariant differential operators on $G/K$.}}, author = {{Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}}, journal = {{Analysis & PDE}}, number = {{10}}, pages = {{2241–2265}}, publisher = {{MSP}}, title = {{{Higher rank quantum-classical correspondence}}}, volume = {{16}}, year = {{2023}}, } @unpublished{51205, abstract = {{We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dead ends. The first kind are transfer operators acting on vector spaces associated with the set of non backtracking paths in the graphs. The second kind of operators are averaging operators acting on vector spaces associated with the space of vertices of the graph. The choice of vector spaces reflects regularity properties. Our main results are correspondences between classical and quantum spectral objects as well as some automatic regularity properties for eigenfunctions of transfer operators.}}, author = {{Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}}, booktitle = {{arXiv:2307.10876}}, title = {{{Spectral correspondences for finite graphs without dead ends}}}, year = {{2023}}, } @article{31210, abstract = {{In this paper we complete the program of relating the Laplace spectrum for rank one compact locally symmetric spaces with the first band Ruelle-Pollicott resonances of the geodesic flow on its sphere bundle. This program was started by Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and Guillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for general rank one spaces. Except for the case of hyperbolic surfaces a countable set of exceptional spectral parameters always left untreated since the corresponding Poisson transforms are neither injective nor surjective. We use vector valued Poisson transforms to treat also the exceptional spectral parameters. For surfaces the exceptional spectral parameters lead to discrete series representations of $\mathrm{SL}(2,\mathbb R)$. In higher dimensions the situation is more complicated, but can be described completely.}}, author = {{Arends, Christian and Hilgert, Joachim}}, issn = {{2270-518X}}, journal = {{Journal de l’École polytechnique — Mathématiques}}, keywords = {{Ruelle resonances, Poisson transforms, locally symmetric spaces, principal series representations}}, pages = {{335--403}}, title = {{{Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters}}}, doi = {{10.5802/jep.220}}, volume = {{10}}, year = {{2023}}, } @article{51383, author = {{Hilgert, Joachim and Arends, C.}}, journal = {{J. de l'École polytechnique — Mathématiques}}, pages = {{335--403}}, title = {{{Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters}}}, volume = {{10}}, year = {{2023}}, } @article{51384, author = {{Hilgert, Joachim and Glöckner, H.}}, journal = {{J. Diff. Equations}}, pages = {{186--232}}, title = {{{Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}}}, volume = {{343}}, year = {{2023}}, } @unpublished{51499, author = {{Hilgert, Joachim and Arends, C. and Frahm, J.}}, title = {{{A pairing formula for resonant states on finite regular graphs}}}, year = {{2023}}, } @unpublished{51500, author = {{Hilgert, Joachim and Arends, C. and Frahm, J.}}, title = {{{Edge Laplacians and vector valued Poisson transforms for graphs}}}, year = {{2023}}, } @unpublished{51502, author = {{Hilgert, Joachim and Baier, T. and Kaya, O. and Mourao, J. and Nunes, J.}}, title = {{{Quantization in fibering polarizations, Mabuchi rays and geometric Peter--Weyl theorem}}}, year = {{2023}}, } @unpublished{51521, author = {{Hilgert, Joachim and Guedes Bonthonneau, Y. and Guillarmou, C. and Weich, Tobias}}, title = {{{Ruelle-Taylor resonances of Anosov actions}}}, year = {{2023}}, }