Nathan Rose:Adiabatic Sensitivity in Classical Chaotic Systems

Two foundations of chaos theory are the Lyapunov spectrum and KAM theory, which describe dynamical instability of trajectories and the onset of ergodicity in perturbed integrable systems, respectively. Both of these theories lack a direct analogue in quantum theory and for many body systems, and so developing a physical understanding of chaos that can be consistently applied to all systems remains an open problem. Several recent works have probed quantum chaos by measuring how a system responds to an adiabatic parameter change. In my talk I will describe how to compute adiabatic sensitivity for classical Hamiltonian systems and show how this connects to known classical features of chaos. I will illustrate these properties with numerical simulations of low-dimensional systems. I will then present results of this method applied to the Fermi-Pasta-Ulam-Tsingou model, a many-body nonlinear system with weakly broken integrability. The connection between adiabatic sensitivity and the long-time decay of correlations makes this probe well suited to describe the complex dynamics arising from slow thermalization in this system. Overall this method originally developed for quantum systems is consistent with and naturally extends classical notions of chaos.