Abstract:
The problem of how best to detect chaotic dynamics in many-body systems is an old puzzle. Recently, sensitive probes of chaos in quantum systems have been proposed based on the response of eigenstates to Hamiltonian perturbations. In this talk, I will extend this formalism to many-body systems with a classical limit, where eigenstates are replaced with time-averaged trajectories. We will see that the low-frequency asymptotics of spectral functions can sharply predict the onset of chaos; moreover, the scaling of a related fidelity-susceptibility is predictive of ergodicity (thermalization). I will apply these probes to a family of few-particle spin models and comment on their scaling properties in the classical limit. Based on arxiv:2401.01927.