Magic Angle Precession (MAP) and Advanced Gauss Unit Scale Flux Normalization

"It is a miracle that curiosity survives formal education." Albert Einstein

Concepts

It is shown how a purely geometric kind of strange attractor can arise between spaces of different curvature. Transporting a rotator over periodic curvature steps, the resulting linear spin-precession coupling corresponds to a lossless quantum state with discrete solutions called "Magic Angle Precession".

Current Interests

CHAOS2009 conference:
We consider nonlinear holonomy effects -especially the spin dissipation dynamics- arising in the transport of a linear rotator between metric spaces with different curvature (positive, zero, negative). The extra 3D spin vector current induced by curvature or metric distortion provides for a holonomic attractor called "Magic Angle Precession" (MAP). Limitations and instabilities of the spin current exchange are assigned to bifurcations at high precession loads as the driving gauge potential. In the classical range the chaotic dynamics can be verified with a mechanical toy gyroscope with built-in spin-precession coupling that could also be modeled by a Chua-type electronic circuit. Transporting vector currents composed by spin and precession is treated by Schwarz-Christoffel triangle conformal maps with constant Schwarzian derivative and hypergeometric monodromy. Handling both curvatures simultaneously as a metric distortion is possible by a composite hypergeometric mapping function linearly composed as a ladder/recurrence relation between dual hypergeometric functions related by inversion. This leads to the well known Schroedinger hypergeometric quantum mechanical solution providing for Poeschl-Teller type potentials, quantization, factorization, and ladder operators. By pull-back we get the generalized Gauss linking number density differential form.

Publications

Harvard SAO/NASA Astrophysics Data System (ADS), older

Simulations (Java applets)

Parallel Transport and Precession Java simulation

Using Java in scientific research

Fine structure Geometric Phase Java simulation, some screenshots

Fine structure bifurcations Java simulation

Quantum gyroscopic precession Java simulation

MAP Dirac Quark Java simulation

MAP Quantum/Cosmic Vortex Pair Simulation Java simulation