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The geometric phase
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Geometric Phases and the Separation of the World by Michael Berry
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- 1 Prehistory: The first geometric phase, discovered in the optics of crystals in 1830
- 2 "The radiant Stranger", TrinityCollege Dublin, 24 May 2018
- 3 Phase: Describes the stages of any cyclic process
- 4 Underlying mathematics Gauss approximate 1800: parallel transport in the presence of curvature
- 5 Foucault pendulum
- 6 Underlying parallel transport: Anholonomy
- 7 The geometric phase
- 8 Dynamical phase and geometric phase
- 9 Measure the geometric phase by interference
- 10 Polarisation rotation in a coiled optical fiber
- 11 Polarisation rotation of spinning neutrons
- 12 Why is the phase geometric?
- 13 Exchange sign is a topological phase Pi for Pauli
- 14 A new calculation, with Pragya Shukla: probability distribution of curvature C for random parameter-dependent states
- 15 Numerical simulation, 10000 sample hamiltonians
- 16 Real symmetric matrix, eg. time-reversal symmetry
- 17 Beyond adiabatic i driven parameters Rt
- 18 Represent solution by unit spin expectation vector
- 19 The series eventually diverges, because higher terms involve higher derivatives
- 20 Divergence is inevitable, in order to accommodate transitions - exponentially weak, i.e beyond all orders epsilon power n
- 21 Optimal truncation: smoothest birth of the transition
- 22 Where is the phase?
- 23 Beyond adiabatic 2: dynamics of parameters Rt
- 24 Pi is a special case of the phase, amounting to a reversal
- 25 Geometric magnetism from the polarisation-rotation phase of light
- 26 Separation is fundamental to the practice of science
- 27 Geometric phase timeline
- 28 1983. Simon: connection with fiber bundles, Chern class
- 29 Eponymous nomenclature
- 30 Back to the beginning: easy way to see hamilton's cone and its geometric phase: do-it-yourself cononscopy
- 31 Fringes are contours of cone separation
- 32 Some references, all downloadable from http://michaelberryphisics.wordpress.com
