Quantum graph resonances by cut-off technique
We demonstrate how resonances in a quantum graph consisting of a compact core and semi-infinite leads can be identified from the eigenvalue behavior of the cut-off system.
quant-ph↗
arXiv subjects
Jan Pekař
Publications and source records attributed to Jan Pekař.
Spectral properties of hexagonal lattices with the -R coupling
We analyze the spectrum of the hexagonal lattice graph with a vertex coupling which manifestly violates the time reversal invariance and at high energies it asymptotically decouples edges at even degree vertices; a comparison is made to the case when such a decoupling occurs at odd degree vertices. We also show that the spectral character does not change if the equilateral elementary cell of the lattice is dilated to have three different edge lengths, except that flat bands are absent if those are incommensurate.
math-ph↗
Vertex coupling interpolation in quantum chain graphs
We analyze band spectrum of the periodic quantum graph in the form of a chain of rings connected by line segments with the vertex coupling which violates the time reversal invariance, interpolating between the $δ$ coupling and the one determined by a simple circulant matrix. We find that flat bands are generically absent and that the negative spectrum is nonempty even for interpolation with a non-attractive $δ$ coupling; we also determine the high-energy asymptotic behavior of the bands.
math-ph↗