18/07/2016, 10:00 — 11:00 — Amphitheatre Ea1, North Tower, IST
Michael Berry, Bristol University

Two Physical Applications of Divergent Series: The Aharonov-Bohm Wave, and Exquisite Sensitivity of Optical Polarization

1. Approximate connections between the Aharonov-Bohm wave (AB) scattered by a magnetic flux line and the Fresnel-Sommerfeld edge-diffracted wave have been known for decades. The connection can be made precise by representing AB as a series whose large parameter is distance from the flux; the Erf-based approximation is uniform in angle and flux. The series diverges, and can be resummed to give additional accuracy, even within one wavelength of the flux.
2. Divergent series and nonhermitian degeneracies combine in the optics of polarized light traversing a slowly-twisted anisotropic absorbing material, leading to a prediction that the emergent polarization is extraordinarily sensitive to the incident polarization - a dramatic violation of adiabatic intuition, explained by the Stokes phenomenon.