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 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.
If the simulations does not start automatically check your Java security settings.
There are more simulations:
home
| Fine Structure Java simulation
| Geometric Phase
Bifurcation
| Quantum
Precession
| Dirac
Hyperdiamond
| Quantum/Cosmic Vortex Pair Simulation
(c) Bernd Binder 2002-2008