Kolloquium: Gernot Akemann (Universität Bielefeld): „Universal Random Matrix Statistics in low Dimensional Quantum Systems“

Universal Random Matrix Statistics in low Dimensional Quantum Systems – Vortragender: Gernot Akemann, Universität Bielefeld – Einladender: T. Krüger

Abstract: Random matrices are used to predict spectral statistics in many areas of physics. Often these predictions are based on heuristics, sometimes a precise link can be established. I will focus on random matrices with complex eigenvalues and give an example for a precise map to ground state properties of a particular quantum system, non-interacting fermions in a two-dimensional rotating trap. On the mathematical side we find a remarkable robustness of the random matrix predictions for the mean, variance and higher order cumulants of the number of eigenvalues in a centered disc. Their independence from the distribution of matrix elements and symmetry class of the chosen ensemble is called universality.

This is based on joint work with Sungsoo Byun, Markus Ebke and Gregory Schehr.