Speaker
Description
Random matrix theory (RMT) is one of the main tools for studying quantum chaotic systems. Since quantum evolution is unitary, one can analyze the statistics of eigenvalues of the generators of unitary dynamics — for instance, energy-level statistics — and compare them with the corresponding RMT predictions.
In this talk, I will argue that a similar approach can also be applied to classical systems, as classical observables likewise evolve unitarily. I will focus on discrete classical systems, for which the relevant RMT ensemble is given by random permutations. Concentrating on one-dimensional classical brickwall circuits and employing methods of space-time duality, I will demonstrate how RMT behavior emerges in discrete classical many-body systems.