## Heilborn Lectures

**2017-18 Heilborn Lecturer**

**Sir Michael Berry**

Melville Wills Professor of Physics (Emeritus)

H H Wills Physics Laboratory

University of Bristol, UK

**Sir Michael Berry**

After graduating from Exeter and St Andrews, Michael Berry entered Bristol University, where he has been for more than twice as long he has not. He is a physicist, focusing on the physics of the mathematics...of the physics. Applications include the geometry of singularities (caustics on large scales, vortices on fine scales) in optics and other waves, connections between classical and quantum physics, and the physical asymptotics of divergent series. He delights in finding the arcane in the mundane – abstract and subtle concepts in familiar or dramatic phenomena:

Singularities of smooth gradient maps in rainbows and tsunamis; The Laplace operator in oriental magic mirrors; Elliptic integrals in the polarization pattern of the clear blue sky; Geometry of twists and turns in quantum indistinguishability; Matrix degeneracies in overhead-projector transparencies; Gauss sums in the light beyond a humble diffraction grating.

**Monday, April 9, 4:00 pm, Tech LR4 **

**"Nature’s optics and our understanding of light"**

Optical phenomena visible to everyone abundantly illustrate important ideas in science and mathematics. The phenomena considered include rainbows, sparkling reflections on water, green flashes, earthlight on the moon, glories, daylight, crystals, and the squint moon. The concepts include refraction, wave interference, numerical experiments, asymptotics, Regge poles, polarization singularities, conical intersections, and visual illusions.

**Tuesday, April 10, 11:00 am, Tech F160**

*“Variations on a theme of Aharonov and Bohm"*

The Aharonov-Bohm effect (AB) concerns the role in quantum physics of the magnetic vector potential of an impenetrable line of magnetic flux. Its partial anticipation by Ehrenberg and Siday, in terms of interference, was an approximation whose wavefunction was not singlevalued, and whose connection with the singlevalued AB wave involves topology: ‘whirling waves’ winding round the flux. AB is a fine illustration of idealization in physics. There are four AB effects, depending on whether the waves and the flux are classical or quantum. In the classical-classical case, many details of the AB wavefunction have been explored experimentally in ripples scattered by a water vortex, where the flow velocity of the water corresponds to the vector potential. The AB wave possesses a phase singularity, and there is a similar phenomenon in general interferometers. Gauge-invariant AB streamlines exhibit extraordinary sub-wavelength structure. Connections between the AB wave and the Cornu spiral describing edge diffraction lead to extremely accurate approximations.

**Wednesday, April 11, 4:00 pm, Tech Ryan Auditorium **

** ***“Faster than Fourier: superoscillations, weak measurement, vorticulture..."*

Band-limited functions can oscillate arbitrarily faster than their fastest Fourier component over arbitrarily long intervals. In quantum mechanics, such ‘superoscillations’ correspond to weak measurements, resulting in ‘weak values’ of observables (e.g photon momenta) far outside the spectrum of the operator being measured. Superoscillations were anticipated in optical vortices and in radar theory. The phenomenon has implications for signal processing, and enable sub-wavelength resolution microscopy without evanescent waves. Where superoscillations occur, functions are exponentially weak and vulnerable to noise. Superoscillations are unexpectedly common: in typical monochromatic optical fields, approximately one-third of the domain is superoscillatory.

**Thursday, April 12, 4:00 pm, Tech F160**

*“Chasing the dragon: tidal bores in the UK and elsewhere; quantum and Hawking radiation analogies"*

In some of the world's rivers, an incoming high tide can arrive as a breaking wave, or as a smooth jump decorated by waves. An apporximate theory illustrates hamiltonians in quantum mechanics, and an analogy with Hawking radiation in relativity. This dramatic phenomenon, in which the river flows backwards, illustrates the first unification in physics: the same force - gravity - keeps us on the ground, holds the moon in its orbit, and pulls the tides.

**Friday, April 13, 4:00 pm, Tech Ryan Auditorium**

*“How quantum physics democratized music: a meditation on physics and technology"*

Connections between physics and technological invention and aspects of human life that seem far from science are both unexpected and unexpectedly common. And rather than flowing one way - from physics to gadgets - the connections form an intricate web, linking all aspects of human culture, in unexpected ways that frustrate our convenient compartmentalisations and coarse interventions aimed at promoting technology transfer. I will discuss this theme not abstractly but with examples, ranging from music to the colour of gold, and explain how quantum physics helps me do quantum physics (sic).

To learn more about the Heilborn Lecture and for a full description of the Lectures, click here.