Iterative Interplay between Aharonov-Bohm Deficit Angle and Berry Phase

Binder, Bernd (2002) Iterative Interplay between Aharonov-Bohm Deficit Angle and Berry Phase.

Abstract

Geometric phases can be observed by interference as preferred
scattering directions in the Aharonov-Bohm (AB) effect or as Berry
phase shifts leading to precession on cyclic paths. Without
curvature single-valuedness is lost in both case. It is shown how
the deficit angle of the AB conic metric and the geometric
precession cone vertex angle of the Berry phase can be adjusted to
restore single-valuedness. The resulting interplay between both
phases confirms the non--linear iterative system providing for
generalized fine structure constants obtained in the preliminary
work. Topological solitons of the scalar coupling field emerge as
localized, non-dispersive and non-singular solutions of the
(complex) sine-Gordon equation with a relation to the Thirring
coupling constant and non-linear optics.