79 citations · 481 across the 62 of their papers we have counts for
55 papers · 1 filter
On the discrete spectrum of Dirac operators with Lorentz-scalar -shell interactions supported on unbounded curves
Markus Holzmann, Vladimir Lotoreichik, Marco Vogel
We consider the massive Dirac operator (with positive mass) in the plane with an attractive Lorentz-scalar -shell interaction of strength suppor…
On shape optimization with large magnetic fields in two dimensions
Vladimir Lotoreichik, Léo Morin
This paper aims to show that, in the limit of strong magnetic fields, the optimal domains for eigenvalues of magnetic Laplacians tend to exhibit symmetry. We establish several asym…
Convergence of Schrödinger operators on domains with scaled resonant potentials
Vladimir Lotoreichik, Olaf Post
We consider Schrödinger operators on a bounded, smooth domain of dimension with Dirichlet boundary conditions and a properly scaled potential, which depends only on the d…
A note on optimization of the second positive Neumann eigenvalue for parallelograms
Vladimir Lotoreichik, Jonathan Rohleder
It has recently been conjectured by Bogosel, Henrot, and Michetti that the second positive eigenvalue of the Neumann Laplacian is maximized, among all planar convex domains of fixe…
On the Laplace operator with a weak magnetic field in exterior domains
Ayman Kachmar, Vladimir Lotoreichik, Mikael Sundqvist
We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate…
Inequalities between Dirichlet and Neumann eigenvalues of the magnetic Laplacian
Vladimir Lotoreichik
We consider the magnetic Laplacian with the homogeneous magnetic field in two and three dimensions. We prove that the -th magnetic Neumann eigenvalue of a bounded convex pla…