Differentiations and Diversions
Duration: 60 mins
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About this item
| Description: |
Berry, M
Tuesday 30th March 2021 - 16:00 to 17:00 |
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| Created: | 2021-04-01 11:37 |
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| Collection: | Applicable resurgent asymptotics: towards a universal theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Berry, M |
| Language: | eng (English) |
| Abstract: | Asymptotic procedures, such as generating slowness
corrections to geometric phases, involve successive differentiations. For a large class of functions, the universal attractor of the differentiation map is, when suitably scaled, locally trigonometric/exponential; nontrivial examples illustrate this. For geometric phases, the series must diverge, reflecting the exponentially small final transition amplitude. Evolution of the amplitude towards this final velue depends sensitively on the representation used. If this is optimal, the transition takes place rapidly and universally across a Stokes line emanating from a degeneracy in the complex time plane. But some Hamiltonian ODE systems do not generate transitions; this is because the complex-plane degeneracies have a peculiar structure, for which there is no Stokes phenomenon. Oscillating high derivatives (asymptotic monochromaticity) and superoscillations (extreme polychromaticity) are in a sense opposite mathematical phenomena. |
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