181 citations · 3.2k across the 184 of their papers we have counts for
22 papers · 1 filter
Quantum graphs with the Bethe-Sommerfeld property
Pavel Exner, Ondřej Turek
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have…
Inverse scattering problem for quantum graph vertices
Taksu Cheon, Pavel Exner, Ondrej Turek
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of Hermitian unitary matrix when the vertex coupling is of the s…
Tripartite connection condition for quantum graph vertex
Taksu Cheon, Pavel Exner, Ondrej Turek
We discuss formulations of boundary conditions in a quantum graph vertex and demonstrate that the so-called -form can be further reduced up to a form more effective in certain…
Spectral filtering in quantum Y-junction
Taksu Cheon, Pavel Exner, Ondrej Turek
We examine scattering properties of singular vertex of degree and , taking advantage of a new form of representing the vertex boundary condition, which has been devised…
Approximation of a general singular vertex coupling in quantum graphs
Taksu Cheon, Pavel Exner, Ondrej Turek
The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair…
A remark on helical waveguides
Pavel Exner, Martin Fraas
Motivated by a proposal to create an optical helix-shaped waveguides for cold atoms and molecules, we discuss local perturbations which can create bound states in such a setting. T…