A stochasticity threshold in holography and the instability of AdS

We give strong numerical evidence that a self-interacting probe scalar field in AdS, with only a few modes turned on initially, will undergo fast thermalization only if it is above a certain energetic threshold. Below the threshold the energy stays close to constant in a few modes for a very long time instead of cascading quickly. This indicates the existence of a Strong Stochasticity Threshold (SST) in holography. The idea of SST is familiar from certain statistical mechanical systems, and we suggest that it exists also in AdS gravity. This would naturally reconcile the generic nonlinear instability of AdS observed by Bizon and Rostworowski, with the Fermi-Pasta-Ulam-Tsingou-like quasiperiodicity noticed recently for some classes of initial conditions. We show that our simple setup captures many of the relevant features of the full gravity-scalar system.