40 citations · 107 across the 8 of their papers we have counts for
24 papers
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…
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…
On relations between stable and Zeno dynamics in a leaky graph decay model
Pavel Exner, Takashi Ichinose, Sylwia Kondej
We use a caricature model of a system consisting of a quantum wire and a finite number of quantum dots, to discuss relation between the Zeno dynamics and the stable one which gover…
Sufficient conditions for the anti-Zeno effect
Pavel Exner
The ideal anti-Zeno effect means that a perpetual observation leads to an immediate disappearance of the unstable system. We present a straightforward way to derive sufficient cond…
Leaky quantum wire and dots: a resonance model
Pavel Exner, Sylwia Kondej
We discuss a model of a leaky quantum wire and a family of quantum dots described by Laplacian in with an attractive singular perturbation supported by a line a…
Absolute continuity in periodic thin tubes and strongly coupled leaky wires
Francois Bentosela, Pierre Duclos, Pavel Exner
Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or t…