Now showing items 1-5 of 5
Spectral asymptotics for $\delta$-interactions on sharp cones
We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ...
A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions
We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $C^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the ...
Spectral Transitions for Aharonov-Bohm Laplacians on Conical Layers
We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary ...
On the bound states of Schrödinger operators with $\delta$-interactions on conical surfaces
In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$-interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ...
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for ...