Super-maximal chaos and instability

Abstract

An upper bound on Lyapunov exponent of a thermal many body quantum system has been conjectured recently. It would be useful to develop a physical understanding of what prevents a system from violating this bound. In this article we suggest violation of this bound leads to instability. Our suggestion is based on careful scrutiny of the arguments that established the bound. We also present a physical system where this phenomenon is manifested. In the stable regime, along with incoherent metallic phase, the system exhibits another novel phase, where transport is controlled neither by quasi-particles nor by diffusion. At the phase transition, diffusion coefficient, butterfly velocity and Thouless time diverges.