Aharonov–Anandan quantum phase from a fixed vector field background and an axial magnetic field around a cavity

By assuming a privileged direction of the spacetime yielded by a fixed vector field in the radial direction, we show that a geometric quantum phase can stem from the interaction of a neutral particle with a nonuniform magnetic field around a cylindrical cavity. This magnetic field is in the z-direction, and it is produced by a nonuniform electric current density inside a long conducting cylinder. Further, we study an Aharonov–Bohm-type effect for bound states when the neutral particle is confined to a cylindrical wire and a two-dimensional quantum ring. Then, we obtain the persistent spin currents and the revival time. We extend our discussion about the confinement of the neutral particle to a cylindrical wire and a two-dimensional quantum ring to a rotating reference frame.