NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (3), P. 309–319
Topological damping of Aharonov-Bohm effect: quantum graphs and vertex conditions
P. Kurasov – Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden; email@example.com
A. Serio – Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
The magnetic Schrödinger operator was studied on a figure 8-shaped graph. It is shown that for specially chosen vertex conditions, the spectrum of the magnetic operator is independent of the flux through one of the loops, provided the flux through the other loop is zero. Topological reasons for this effect are explained.
Keywords: Quantum graphs, Magnetic field, Trace formula.
PACS 02.30.Tb, 03.65.Vf, 05.60.Gg