Andrea Serio: Quantum graphs: spectrum and magnetic fields

For particular properly connecting matching conditions on the eight-shape quantum graph equipped with the magnetic Schrödinger operator it occurs that if one of the two fluxes is a multiple of pi, then the spectrum does not depend on the other one. There is a double check of this property: through the characteristic equation and the trace formula. There is also an interpretation via the set of the closed paths along the graph. Furthermore the effect has been recognized as a topological damping of the Aharonov-Bohm effect. This phenomenon is unexpected and occurs due to a nontrivial interplay between the topology of the graph and matching conditions involved.