Quantum chaos and level dynamics

Abstract

We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving level dynamics such as level avoided-crossing distributions, slope and curvature of level distributions showing both the postulate of unversality and its limitations. We mention shortly the experimental confirmations of these theories. We concentrate in some detail on measures imported from quantum information approach such as the fidelity susceptibility and more generally geometric tensor matrix elements. The possible open problems are suggested.