Many-Body Quantum Chaos and Spectral Form Factor
Amos Chan Princeton University
Collection
Talk Type
Scientific Series
Subject
Abstract
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.