Aharonov-Anandan quantum phases and Landau quantization associated with a magnetic quadrupole moment

The arising of geometric quantum phases in the wave function of a moving particle possessing a magnetic quadrupole moment is investigated. It is shown that an Aharonov-Anandan quantum phase (Aharonov and Anandan, 1987) can be obtained in the quantum dynamics of a moving particle with a magnetic quadrupole moment. In particular, it is obtained as an analogue of the scalar Aharonov-Bohm effect for a neutral particle (Anandan, 1989). Besides, by confining the quantum particle to a hard-wall confining potential, the dependence of the energy levels on the geometric quantum phase is discussed and, as a consequence, persistent currents can arise from this dependence. Finally, an analogue of the Landau quantization is discussed.