Stability of Equilibrium Distribution in Chaotic and Non-Chaotic Systems

While chaos in classical systems is traditionally defined through the sensitivity of a system to changes in its initial conditions, this notion of sensitivity does not translate to quantum systems. Various alternative measures of quantum chaos have been proposed, such as the system's spectral statistics, out-of-time-ordered correlators (OTOCs), and the sensitivity to adiabatic deformations. In this talk, we show that chaos in any dynamical system (either classical or quantum) can be quantified through the stability of the system's equilibrium distribution. Using the framework developed by David Ruelle, we show that the linear response of a system under a quench allows us to differentiate between weak and strong chaos. Surprisingly, the strongest sensitivity is observed in weakly chaotic systems. We discuss how this notion of chaos relates to other traditional definitions.