181 citations · 3.2k across the 184 of their papers we have counts for
9 papers · 1 filter
Necklaces with interacting beads: isoperimetric problems
Pavel Exner
We discuss a pair of isoperimetric problems which at a glance seem to be unrelated. The first one is classical: one places identical point charges at a closed curve at the…
Inequalities for means of chords, with application to isoperimetric problems
Pavel Exner, Evans M. Harrell, Michael Loss
We consider a pair of isoperimetric problems arising in physics. The first concerns a Schrödinger operator in with an attractive interaction supported on a clos…
Approximations by graphs and emergence of global structures
Pavel Exner, Pavel Hejcik, Petr Seba
We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schroedinger e…
Absolute continuity of the spectrum for periodically modulated leaky wires in
Pavel Exner, Rupert L. Frank
We consider a model of leaky quantum wire in three dimensions. The Hamiltonian is a singular perturbation of the Laplacian supported by a line with the coupling which is bounded an…
Approximations of permutation-symmetric vertex couplings in quantum graphs
Pavel Exner, Ondrej Turek
We consider boundary conditions at the vertex of a star graph which make Schroedinger operators on the graph self-adjoint, in particular, the two-parameter family of such condition…
Spectrum of the Schrödinger operator in a perturbed periodically twisted tube
Pavel Exner, Hynek Kovařík
We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowin…