The interplay between quantum chaos and integrability has been extensively studied in the past decades. We approach this topic from the point of view of complexity of adiabatic transformations, which in turn is related to the long time low-frequency response of physical observables.. I will argue that there is no direct transition from integrable to ergodic regimes. Instead there is always a universal slow glassy regime separating the two. In the case of disordered systems this (transient) regime was mistakenly identified as MBL. I will show that integrable points play the role analogous to critical points in continuous phase transitions and that integrability is attractive both from the point of view of quantum-information geometry and of dynamics.
Host: Nir Navon (nir.navon@yale.edu)