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The study of spectral statistics is of importance due to its universality and utility as a robust diagnostic of quantum chaos. For closed many-body quantum chaotic systems, I will present two results: (i) a quantum-classical mapping that connects the Thouless time, which characterizes the onset of RMT of the spectral form factor (SFF); and the spectral gap of a dual classical stochastic system; (ii) a set of Lyapunov exponents which characterize the spectral statistics in the thermodynamic limit. For open quantum systems with complex spectra, I will propose and analyze a generalized SFF, and show that dissipative quantum chaotic systems display a “dip-ramp-plateau” behaviour with a quadratic ramp.
Amos Chan finished his DPhil from the University of Oxford in 2019, and is currently a postdoctoral fellow at the Princeton Center for Theoretical Science. Amos is interested in strongly correlated many-body quantum systems, particularly in out-of-equilibrium quantum dynamics, disordered quantum systems and statistical mechanics.