Spectral filtering in quantum Y-junction (2009)
Cheon, Taksu, Exner, Pavel, Turek, Ondrej
We examine scattering properties of singular vertex of degree $n=2$ and $n=3$, taking advantage of a new form of representing the vertex boundary condition, which has been devised to approximate a...
Approximation of a general singular vertex coupling in quantum graphs (2009)
Cheon, Taksu, Exner, Pavel, Turek, Ondrej
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 of their endpoints...
On the spectrum of a bent chain graph (2008)
Duclos, Pierre, Exner, Pavel, Turek, Ondrej
We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$....
Approximations of singular vertex couplings in quantum graphs (2007)
We discuss approximations of the vertex coupling on a star-shaped quantum graph of $n$ edges in the singular case when the wave functions are not continuous at the vertex and no edge-permutation...
Approximations of permutation-symmetric vertex couplings in quantum graphs (2005)
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 conditions invariant with...