N. Karve: Probing Chaos in Classical Systems

The interplay between chaos and thermalization in weakly non-integrable systems is a rich and complex subject. Interest in this area is further motivated by a desire to develop a unified picture of chaos for both quantum and classical systems. In this talk, I will show how the adiabatic gauge potential (AGP) can be used as a sensitive probe of chaos in classical FermiPasta-Ulam-Tsingou (FPUT) and Toda systems [1]. By making a connection between the time variance of the AGP and long-time correlations of a generic observable, we demonstrate the process of distinguishing between near-integrable, weakly chaotic, and strongly chaotic regimes. Furthermore, we show that anomalous and normal diffusion of observables in phase space correspond to weak and strong chaos, respectively. This facilitates the computation of onset times of chaos, which we study in relation to thermalization times. Lastly, we discuss an extension of this probe to discrete maps in the context of the ergodic hypothesis.