13 citations · 38 across the 5 of their papers we have counts for
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math-ph2015★ 4 cited
Spectral properties of magnetic chain graphs
Pavel Exner, Stepan Manko
We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a -c…
math-ph2014★ 7 cited
Spectra of magnetic chain graphs: coupling constant perturbations
Pavel Exner, Stepan S. Manko
We analyze spectral properties of a quantum graph in the form of a ring chain with a coupling in the vertices exposed to a homogeneous magnetic field perpendicular to the graph…
math-ph2013★ 7 cited
Approximations of quantum-graph vertex couplings by singularly scaled potentials
Pavel Exner, Stepan S. Manko
We investigate the limit properties of a family of Schrödinger operators of the form $H_\varepsilon= -\frac{\mathrm{d}^2}{\mathrm{d}x^2}+ \frac{λ(\varepsilon)}{\varepsilon^2}Q \big…