Title: Geometric phases old and new
Abstract:
The waves that describe systems in quantum physics can carry information about how their environment has been altered, for example by forces acting on them. This effect is the geometric phase. It occurs in the optics of polarised light, where it goes back to the 1830s, possibly earlier. It influences wave interference; and it provides insight into the spin-statistics relation for identical quantum particles. The underlying mathematics is geometric: parallel transport, explaining how falling cats turn upright, and how to park a car. Recent results describe the typical behaviour of the geometric phase curvature and the related quantum metric. Incorporating the back-reaction of the geometric phase on the dynamics of the changing environment exposes an unsolved problem: how can a system be separated from its slowly-varying environment? The concept has a tangled history.
Bio:
Sir Michael Berry is a theoretical physicist at the University of Bristol, where he has been for more than twice as long as he has not. His research centres on the relations between physical theories at different levels of description (classical and quantum physics, ray optics and wave optics…). In addition to these deeply mathematical, often geometric, studies, he also delights in finding familiar phenomena illustrating deep concepts – the arcane in the mundane: rainbows, the sparkling of the sun on the sea, twinkling starlight, polarised light in the sky, tidal bores…