Mathematical model of weakly coupled spherical resonator chains under the influence of external magnetic field

The Schrödinger operators with constant magnetic field in a bent chain and Y-type chain of coupled balls are considered. Coupling exists due to point-like openings at the touching points of neighbor spheres. The mathematical background of the model is the theory of self-adjoint extensions of symmetric operators. The spectral equations for the model operators in each case were derived and analyzed.