Special Condensed Matter Seminar: Amos Chan, University of Oxford - “Minimal Models and Spectral Statistics of Many-Body Quantum Chaotic Systems”

I will present two minimal models for many-body quantum chaotic systems. Each model has a q-dimensional Hilbert space at each site, and has a time evolution that is random in space but periodic in time (Floquet). I evaluate the spectral statistics of the Floquet operator and the dynamical behaviour of these models via diagrammatic techniques in the large-q limit. Using a mapping to a classical statistical model, I explore the universal behaviour in the spectral correlations of many-body quantum chaotic systems that goes beyond the random matrix theory.