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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 ...
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 ...