Speaker: Lior Silberman (Princeton)
Title: Finding Arithmetic Flavor in Quantum Chaos
Abstract: The motion of a mechanical system can be described from the points of view of both Classical and Quantum Mechanics. Observing that classical, Newtonian, mechanics offers an excellent approximation to the motion of everyday objects, we expect Quantum Mechanics to do the same. I will describe attempts to formalize this expectation, known as the "correspondence principle", and study its implications. In particular, sufficiently complicated (chaotic) behaviour of the classical dynamics should be visible in the quantum mechanical description, at least in limit of sufficiently high energy.
I will first give a general introduction to this problem, known as the "Quantum Chaos" problem. Most investigation has been numerical, but some analytical results are known.
Secondly, I will describe recent advances on this problem in a class of very special cases where the systems exhibit additional symmetries associated with an additional "arithmetic" structure. Time permitting I will explore connections to analytic number theory and combinatorics.