Geometric Phase Locked in Fine Structure

Binder, Bernd (2002) Geometric Phase Locked in Fine Structure.

Abstract

Berry's phase carries physical information coded as topological
and geometrical objects that can be directly verified in
measurements. In some cases the situation can be reduced to an
irrational phase shift, that can be usually obtained by an
iterative process. Take the Berry phase as the geometric object
and let the iterative process be a non-linear phase-locked
feedback mechanism defined by spin-orbit coupling and precession,
a coupling of fast and slow rotating vectors. For spin-orbit
coupling the realization is easy and fast generating irrational
and rational numbers: generalized fine structure constants. As a
result, this paper provides for additional evidence, that the Sommerfeld
fine structure constant <FONT FACE="Symbol">a</FONT> carries a Berry phase component
2<FONT FACE="Symbol">p</FONT>(1-137<FONT FACE="Symbol">a</FONT>).