Zobrazeno 1 - 10
of 122
pro vyhledávání: '"Kerner, Joachim"'
Autor:
Bifulco, Patrizio, Kerner, Joachim
We study Schr\"odinger operators on compact finite metric graphs subject to $\delta'$-coupling conditions. Based on a novel modified local Weyl law, we derive an explicit expression for the limiting mean eigenvalue distance of two different self-adjo
Externí odkaz:
http://arxiv.org/abs/2407.21719
Publikováno v:
J. Math. Pures Appl. (2024)
We study interacting Bose gases of dimensions $2\le d \in \mathbb N$ at zero temperature in a random model known as the Kac-Luttinger model. Choosing the pair-interaction between the bosons to be of a mean-field type, we prove (complete) Bose-Einstei
Externí odkaz:
http://arxiv.org/abs/2312.14357
Autor:
Bifulco, Patrizio, Kerner, Joachim
Publikováno v:
J. Math. Phys. (2024)
In this paper we establish spectral comparison results for Schr\"odinger operators on a certain class of infinite quantum graphs, using recent results obtained in the finite setting. We also show that new features do appear on infinite quantum graphs
Externí odkaz:
http://arxiv.org/abs/2308.16869
Autor:
Bifulco, Patrizio, Kerner, Joachim
Publikováno v:
Archiv der Mathematik (2024)
Based on the main result presented in a recent paper, we derive Ambarzumian-type theorems for Schr\"odinger operators defined on quantum graphs. We recover existing results such as the classical theorem by Ambarzumian and establish some seemingly new
Externí odkaz:
http://arxiv.org/abs/2308.10881
Autor:
Bifulco, Patrizio, Kerner, Joachim
In this note we elaborate on some notions of surface area for discrete graphs which are closely related to the inverse degree. These notions then naturally lead to associated connectivity measures of graphs and to the definition of a special class of
Externí odkaz:
http://arxiv.org/abs/2305.06290
Publikováno v:
Ann. Henri Poincar\'e (2023)
We study spectral properties of perturbed discrete Laplacians on two-dimensional Archimedean tilings. The perturbation manifests itself in the introduction of non-trivial edge weights. We focus on the two lattices on which the unperturbed Laplacian e
Externí odkaz:
http://arxiv.org/abs/2301.05076
Autor:
Bifulco, Patrizio, Kerner, Joachim
Publikováno v:
Proc. Amer. Math. Soc. (2023)
We study Schr\"odinger operators on compact finite metric graphs subject to $\delta$-coupling and standard boundary conditions. We compare the $n$-th eigenvalues of those self-adjoint realizations and derive an asymptotic result for the mean value of
Externí odkaz:
http://arxiv.org/abs/2212.13954
Publikováno v:
In Journal de mathématiques pures et appliquées September 2024 189
Autor:
Kerner, Joachim, Täufer, Matthias
Publikováno v:
Asymptotic Analysis (2022)
We study the asymptotic behaviour of the spectral gap of Schr\"odinger operators in two and higher dimensions and in a limit where the volume of the domain tends to infinity. Depending on properties of the underlying potential, we will find different
Externí odkaz:
http://arxiv.org/abs/2110.15110