"Geometric Phase Patterns and Holography- Encoding Model for Charge and Spin", invited poster (below are computer-generated toy patterns, "charged" with a little thought provocation), presented at the "Aharonov-Bohm Effect and Berry Phase Anniversary 50/25 2009, Dec., 14-15, University Bristol", GB (2009) .
Geometric phases arise from interference, where the interference of spatial separated interference patterns shows a characteristic correlation or interaction. Consider overlapping holographic interference patterns of topological charges (local twists and phase singularities). The local interference patterns of these topological patterns arising in the overlap region are proposed to be neutral Berry's phase patterns related to strong interaction. It seems that a stable configuration requires that all neutral patterns connecting charged patterns are in phase.
SPESIF 2010, Washington, JHU
(Rolling oscillators. Geometrically Induced Interactions and Bifurcations)
"Geodesic Holonomy Attractor between
Surfaces of Different Curvature Signs relevant
to Spin Transport", CHAOS2009, Chania, Crete (2009).
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.
At the CHAOS2009 conference I met Alfred Inselberg who recently published the book "Parallel Coordinates" at Springer This highly recommendable book is about visualization, systematically incorporating the fantastic human pattern recognition into the problem-solving. I got interested in his visualization of a higher-dimensional rotation-translation duality (surely part of MAP) and other dualities (btw, he "immensely enjoyed" the poster/paper above).
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 Books, p.31-42 (2008), (Amazon).
"Berry's Phase and Fine Structure", preprint (2002), (PhilSci archive).
"Friedmann Propulsion in a Flat Holographic Universe" (Advanced Gauss Unit Scale Flux Normalization), STAIF 2008, New Mexico. In "Space Technology and Applications International Forum-STAIF 2008", Editor M. S. El Genk, AIP Conference Series 969, p.1146-1153 (2008).
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), Aharonov-Bohm Effect and Berry Phase Anniversary 50/25 2009 (Bristol, UK), SPESIF 2010 John Hopkins University (Washington, USA)
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