Berry's Phase & Fine Structure Constant Java simulation

Bernd Binder, 9.8.2002 and 24.10.2006

To visualize the surprisingly simple model of fine structure and spin-orbit coupling in Berry's Phase and Fine Structure (pdf 333kb), a small Java simulation is loaded to this page. The geometric phase couples back to the round trip frequency or path length such, that the resulting non-linear feedback loop provides for the spin-orbit coupling constant a = cos(pa)/M that can be solved iteratively. The total phase is defined by two parts: the Berry phase p(1-Ma), and the dynamical phase pMa, where a is the orbital wavenumber divided by the Compton wavenumber and M the magnetic quantum number. The geometric phase (from "parallel transport") is responsible for 1/a-M >0. The radius of blue circle corresponds to cos(pa). Moving the slide bar of the Java applet changes M up to 150. Displayed in the applet are the epicycloidal and hypocycloidal values of M, 1/a, and the ratio dynamical to geometric phase (winding) separated by commas.

The applet is written using Java. You must have a Java enabled browser to be able to see the applet right here.

The source of this applet is here. The physics behind 1/a can be modelled by classical mechanics (rolling cones or balls) and fits to a general spin-orbit coupling relation (that covers also the gravitomagnetic case). The coupling is polar (sign of M) and carries a Dirac monopole with half spin magnetic charge M/2 on SU(2)/U(1) = S^2. a (M=137) with hypo=epi and free running iteration can be considered as a candidate for the Sommerfeld fine structure constant measured with neutrons.

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