181 citations · 3.2k across the 184 of their papers we have counts for
7 papers · 2 filters
Asymptotic eigenvalue estimates for a Robin problem with a large parameter
Pavel Exner, Alexander Minakov, Leonid Parnovski
Robin problem for the Laplacian in a bounded planar domain with a smooth boundary and a large parameter in the boundary condition is considered. We prove a two-sided three-term asy…
A regular version of Smilansky model
Diana Barseghyan, Pavel Exner
We discuss a modification of Smilansky model in which a singular potential `channel' is replaced by a regular, below unbounded potential which shrinks as it becomes deeper. We demo…
Schrödinger operators with δ- and δ'-interactions on Lipschitz surfaces and chromatic numbers of associated partitions
Jussi Behrndt, Pavel Exner, Vladimir Lotoreichik
We investigate Schrödinger operators with δ- and δ'-interactions supported on hypersurfaces, which separate the Euclidean space into finitely many bounded and unbounded Lipschitz d…
Approximations of quantum-graph vertex couplings by singularly scaled potentials
Pavel Exner, Stepan S. Manko
We investigate the limit properties of a family of Schrödinger operators of the form $H_\varepsilon= -\frac{\mathrm{d}^2}{\mathrm{d}x^2}+ \frac{λ(\varepsilon)}{\varepsilon^2}Q \big…
Spectral asymptotics of a strong interaction on a planar loop
Pavel Exner, Michal Jex
We consider a generalized Schrödinger operator in with an attractive strongly singular interaction of type characterized by the coupling parameter and suppor…
Resonances on hedgehog manifolds
Pavel Exner, Jiri Lipovsky
We discuss resonances for a nonrelativistic and spinless quantum particle confined to a two- or three-dimensional Riemannian manifold to which a finite number of semiinfinite leads…