Lecture: Quantum Mechanics, Chaos and the Singing of the Primes
Friday, June 1, 2012 - 3:15pm
The Maseeh Mathematics and Statistics Colloquium Series*
Sir Michael Berry
H H Wills Physics Laboratory, University of Bristol, UK
Quantum mechanics, chaos and the singing of the primes
Abstract: The Riemann hypothesis can be interpreted as stating that the prime numbers contain 'music', whose component frequencies are the Riemann zeros. The question "Frequencies of what?" leads to tantalizing connections with the energy levels of quantum systems whose corresponding classical motion is chaotic. At the level of statistics, predictions for the Riemann zeros based on semiclassical quantum asymptotics (with primes as periods of classical trajectories) have reached a high degree of accuracy and refinement. For the zeros themselves, the Riemann-Siegel formula and its improvements lead to new ways of calculating quantum levels. There are speculations about the underlying operator.
Friday, June 1st, 2012 at 3:15pm
Neuberger Hall room 454
(Refreshments served at 3:00 Neuberger Hall room 344)
* Sponsored by the Maseeh Mathematics and Statistics Colloquium Series Fund and the Fariborz Maseeh Department of Mathematics & Statistics, PSU. This event is free and open to the public.