Point perturbation-invariant solutions of the Schrödinger equation with a magnetic field

Zero Modes in a System of Aharonov–bohm Fluxes

“…In our case, this ansatz reduces the problem of finding zero-modes to some estimates for entire functions. The mechanism of appearance of zero modes in the considered cases is close to that for a two-dimensional system in a uniform magnetic field in the presence of an infinite array of point scatterers [38,18,19,20,21,22].…”

Semiclassical reduction for magnetic Schrödinger operator with periodic zero-range potentials and applications

“…Various aspects of the spectral analysis of magnetic Hamiltonians with point perturbations were discussed in numerous works, see e.g. [4,5,14,[17][18][19]22,32] and references therein. Our principal aim in this paper is to show that the technique of Helffer and Sjöstrand is still applicable and is general enough to handle this non-standard class of operators; such a correspondence between the semiclassical analysis and solvable models seems to appear for the first time.…”

“…Helffer and K. Pankrashkin / Magnetic Schrödinger operator with periodic zero-range potentials19 Therefore, by (4.7), there exists C = C(h) > 0 such that for z < 0 one has and n, |m| + |n| > 0.…”