Lensing of Dirac monopole in Berry's phase
Abstract
Berry's phase, which is associated with the slow cyclic motion with a finite period, looks like a Dirac monopole when seen from far away but smoothly changes to a dipole near the level crossing point in the parameter space in an exactly solvable model. This topology change of Berry's phase is visualized as a result of lensing effect; the monopole supposed to be located at the level crossing point appears at the displaced point when the variables of the model deviate from the precisely adiabatic movement. The effective magnetic field generated by Berry's phase is determined by a simple geometrical consideration of the magnetic flux coming from the displaced Dirac monopole.
Keywords
Cite
@article{arxiv.2101.10541,
title = {Lensing of Dirac monopole in Berry's phase},
author = {Kazuo Fujikawa and Koichiro Umetsu},
journal= {arXiv preprint arXiv:2101.10541},
year = {2021}
}
Comments
14 pages, 4 figures. The agreement of Berry's phase with the solid angle drawn by a spin vector in the case of a two-component spinor is explained in connection with the lensing effect. This version is going to appear in Phys. Rev. D