Willard/Physical Seminar: Sir Michael Berry (University of Bristol)

1315 Seminar Hall
@ 3:30 pm

Title: Quantum chaology and the singing of the primes

Abstract: 
Although envisaged by Einstein in 1917, it was only in the 1970s that the implications for quantum mechanics of chaos in the classical limiting dynamics was recognised as a problem. The solution emerged from several directions. There is no sharp quantum-classical boundary; instead, rich borderland physics. I will concentrate on the arrangement of energy levels. Semiclassical asymptotics, in the form of Gutzwiller’s trace formula, gives the quantum spectral density as a sum over classical periodic orbits. Long periodic orbits enjoy a universal phase space democracy, leading to statistics between close- lying levels described by random-matrix theory (RMT). Short orbits give nonuniversal correlations between more distant levels, and the failure of RMT. A bonus was the discovery that the Riemann zeros share the same statistics: RMT and its failure. If time permits, I will discuss wavefunctions, for which semiclassical asymptotics implies gaussian random functions with a particular spatial correlation, occasionally decorated by scars from unstable periodic orbits. For many-body quantum chaos, large dimension D will involve asymptotics additional to semiclassical, possibly clashing (cf P W Anderson, ‘More is different’).

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…