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 or "rolling" a rotator or wave packet over regions with alternating curvature, I propose special lossless quantum states called "Magic Angle Precession", which are characterized by a linear spin-precession coupling with proper revival due to a recurrent rolling holonomy (Berry phase). The corresponding geometric phase patterns carry holographic information about spin and charge.

Current Interests

Aharonov-Bohm Effect and Berry Phase Anniversary 50/25 event, 2009, Dec., 14-15, Univ. Bristol, GB
SPESIF 2010, Washington, JHU
(Rolling oscillators. Geometrically Induced Interactions and Bifurcations)

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) are considered, where an 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. 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 hypergeometric functions related by inversion and can be described by 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. In the classical range the correspondence to the quantum 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.

Publications

Harvard SAO/NASA Astrophysics Data System (ADS)

"Magic Angle Chaotic Precession", in "Topics on Chaotic Systems: Selected Papers from CHAOS 2008 International Conference", Editor Ch. Skiadas, Singapore, World Scientific (2008)

Philosophy of Science (PhilSci) Archive, preprints

Using Java in scientific research (1999)

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Conferences with Contributions

STAIF 2007 Albuquerque (New Mexico, USA), QUANTUM MIND 2007 Salzburg (Austria), STAIF 2008 Albuquerque (New Mexico, USA), CHAOS2008 Chania (Crete, Greece), SPESIF 2009 Huntsville (Alabama, USA), CHAOS2009 Chania (Crete, Greece)

Simulations

Berry's Phase & Fine Structure Constant Java simulation, some screenshots

Geometric Phase Bifurcation near Z=115

Parallel Transport and Precession

Quantum Precession or Quantum Gyroscope with Magic Angle Precession (MAP)

Quark Model: Three Space-like Cones Rolling on a Common Time-like Cone

MAP part of a Chua oscillator showing "charged" bifurcation singularities