Defining classical and quantum chaos through adiabatic transformations

Abstract We present a unified formalism which identifies chaos in both quantum and classical systems in an equivalent manner by means of adiabatic transformations . The complexity of adiabatic transformations which preserve classical time-averaged trajectories (quantum eigenstates) in response to Hamiltonian deformations serves as a measure of chaos. This complexity is quantified by the (properly regularized) fidelity susceptibility or, more generally, by the geometric tensor. Physically this measure quantifies (i) long time instabilities of physical observables due to small changes in the Hamiltonian of the system and (ii) irregularity of physical observables contained in low frequency noise. Our exposition…