Proposal for many-body quantum chaos detection

Understand

In this work, the term ``quantum chaos'' refers to spectral correlations similar to those found in the random matrix theory.

• Quantum chaos can be diagnosed through the analysis of level statistics using e.g.~the spectral form factor, which detects both short- and long-range level correlations.
• The spectral form factor corresponds to the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole) when the system is chaotic.
• We discuss how this structure could be detected through the quench dynamics of two physical quantities accessible to experimental many-body quantum systems: the survival probability and the spin autocorrelation function.