25 citations · 158 across the 37 of their papers we have counts for
38 papers
Existence and absence of Bose-Einstein condensation in the interacting random Kac-Luttinger model
C. Boccato, J. Kerner, M. Pechmann +1
In this paper, we study interacting bosons at zero temperature in a random and higher-dimensional continuum model introduced by Kac and Luttinger. For weak interactions we prove th…
Ambarzumian-type theorems for Hermitian matrices with applications
Matthias Hofmann, Joachim Kerner
A foundational result in inverse spectral theory due to Ambarzumian (1929) states that the Neumann Laplacian on an interval is not isospectral to the Neumann Laplacian with an addi…
On the asymptotic behavior of the spectral gap for discrete Schrödinger operators
Matthias Hofmann, Joachim Kerner, Maximilian Pechmann
In this note we elaborate on the asymptotic behavior of the spectral gap of a class of discrete Schrödinger operators defined on a path graph in the limit of infinite volume. We co…
On Bose-Einstein condensation in interacting Bose gases in the Kac-Luttinger model
Chiara Boccato, Joachim Kerner, Maximilian Pechmann
We study interacting Bose gases of dimensions at zero temperature in a random model known as the Kac-Luttinger model. Choosing the pair-interaction between t…
Some spectral comparison results on infinite quantum graphs
Patrizio Bifulco, Joachim Kerner
In this paper we establish spectral comparison results for Schrödinger operators on a certain class of infinite quantum graphs, using recent results obtained in the finite setting.…
A note on Ambarzumian's theorem for quantum graphs
Patrizio Bifulco, Joachim Kerner
Based on the main result presented in a recent paper, we derive Ambarzumian-type theorems for Schrödinger operators defined on quantum graphs. We recover existing results such as t…
On the surface area of graphs, related connectivity measures and spectral estimates
Patrizio Bifulco, Joachim Kerner
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 conne…
Robustness of flat bands on the perturbed Kagome and the perturbed Super-Kagome lattice
Joachim Kerner, Matthias Täufer, Jens Wintermayr
We study spectral properties of perturbed discrete Laplacians on two-dimensional Archimedean tilings. The perturbation manifests itself in the introduction of non-trivial edge weig…
Comparing the spectrum of Schrödinger operators on quantum graphs
Patrizio Bifulco, Joachim Kerner
We study Schrödinger operators on compact finite metric graphs subject to -coupling and standard boundary conditions. We compare the -th eigenvalues of those self-adjoint rea…
On the spectral gap of higher-dimensional Schrödinger operators on large domains
Joachim Kerner, Matthias Täufer
We study the asymptotic behaviour of the spectral gap of Schrödinger operators in two and higher dimensions and in a limit where the volume of the domain tends to infinity. Dependi…
Bose--Einstein condensation for particles with repulsive short-range pair interactions in a Poisson random external potential in
Joachim Kerner, Maximilian Pechmann
We study Bose gases in dimensions, , with short-range repulsive pair interactions, at positive temperature, in the canonical ensemble and in the thermodynamic limit. W…
On the spectral gap of the path graph in the limit of large volume
Joachim Kerner, Pavlo Yatsyna
In this paper we study the spectral gap of the path graph and illustrate an interesting effect which has been described recently in the continuous setting. More explicitly, in the…
A lower bound on the spectral gap of one-dimensional Schrödinger operators
Joachim Kerner
In this note we provide an explicit lower bound on the spectral gap of one-dimensional Schrödinger operators with non-negative bounded potentials and subject to Neumann boundary co…
A lower bound on the spectral gap of Schrödinger operators with weak potentials of compact support
Joachim Kerner
In this paper we continue the study of the spectral gap of Schrödinger operators on large intervals and subject to Neumann boundary conditions. The main goal is to derive a lower b…
On the spectral gap of one-dimensional Schrödinger operators on large intervals
Joachim Kerner, Matthias Täufer
We study the effect of non-negative potentials on the spectral gap of one-dimensional Schrödinger operators in the limit of large intervals. In particular, we derive upper and lowe…
On the effect of repulsive interactions on Bose-Einstein condensation in the Luttinger-Sy model
Joachim Kerner, Maximilian Pechmann
In this paper we investigate the effect of repulsive pair interactions on Bose-Einstein condensation in a well-established random one-dimensional system known as the Luttinger-Sy m…
On a condition for type-I Bose-Einstein condensation in random potentials in dimensions
Joachim Kerner, Maximilian Pechmann, Wolfgang Spitzer
In this paper we discuss Bose-Einstein condensation (BEC) in systems of pairwise non-interacting bosons in random potentials in dimensions. Working in a rather general framewor…
Attractive conical surfaces create infinitely many bound states
Sebastian Egger, Joachim Kerner, Konstantin Pankrashkin
In this paper we study spectral properties of a three-dimensional Schrödinger operator with a potential given, modulo rapidly decaying terms, by a function of the distan…
On the number of isolated eigenvalues of a pair of particles in a quantum wire
Joachim Kerner
In this note we consider a pair of particles moving on the positive half-line with the pairing generated by a hard-wall potential. This model was first introduced in [arXiv:1604.06…
Bound states of a pair of particles on the half-line with a general interaction potential
Sebastian Egger, Joachim Kerner, Konstantin Pankrashkin
In this paper we study an interacting two-particle system on the positive half-line. We focus on spectral properties of the Hamiltonian for a large class of two-particle potentials…
On Bose-Einstein condensation in the Luttinger-Sy model with finite interaction strength
Joachim Kerner, Maximilian Pechmann, Wolfgang Spitzer
We study Bose-Einstein condensation (BEC) in the Luttinger-Sy model. Here, Bose point particles in one spatial dimension do not interact with each other, but, through a positive (r…
Many-particle quantum graphs: A review
Jens Bolte, Joachim Kerner
In this paper we review recent work that has been done on quantum many-particle systems on metric graphs. Topics include the implementation of singular interactions, Bose-Einstein…
On Lennard-Jones-type potentials on the half-line
Federica Gregorio, Joachim Kerner
In this paper we study a particle under the influence of a Lennard-Jones potential moving in a simple quantum wire modelled by the positive half-line. Despite its physical signific…
Bose--Einstein condensation in the Luttinger--Sy model with contact interaction
Joachim Kerner, Maximilian Pechmann, Wolfgang Spitzer
We study bosons on the real line in a Poisson random potential (Luttinger--Sy model) with contact interaction in the thermodynamic limit at absolute zero temperature. We prove that…