Gernot Akemann: Universality of Random Matrices: From Coulomb Gases to Quantum Systems
Random matrices represent mathematical models that are simple enough to be analytically tractable, while being rich enough to describe universal features in many applications in Physics, Mathematics, and beyond. In this talk I will focus on Gaussian random matrices with complex eigenvalues representing a two-dimensional, static Coulomb gas at a certain temperature, the Ginibre ensembles. While being partly simpler than their Hermitian counterparts, they still pose interesting open mathematical problems. Some examples will be presented where they successfully describe complex spectra in quantum field theories with chemical potential and in dissipative open quantum systems.
Professor Gernot Akemann, University of Bielefeld