Quantum flux-based resonances in solitonic vortices

Working with the Nielsen–Olesen Lagrangian in static cylindric coordinates, we derive the system of coupled field equations and perform a first-order perturbative approach, pointing out an interesting contribution connected to the London–Heitler current. For an r,θ-depending scalar boson, evolving in a constant or zero magnetic field we get, besides the flux quantization and the Landau energy levels, a less expected structure of the scalar modes whose radial and azimuthal parts are decoupled by the presence of the quantized magnetic flux.