Distribution of equilibrium currents of magnetization in systems with dimensional quantization in finite magnetic field

The distribution of the equilibrium magnetization currents in the two-dimensionally limited systems, placed in the external magnetic field, is considered. The cases of the half plane, quantum disk and broad quantum ring are considered. The transition from the classical to quantum magnetic fields is studied, It is shown, that the marginal currents at the half plane boundary are subjected to the spatial oscillations, related to the Fermi waves length, attenuating far away from the boundaries. It is established, that the area, occupied by the currents, narrows with the increase in the field. It is shown, that the current spatial distribution in the circular disk and ring significantly depends on the Fermi level position