Early-time signatures of quantum many-body scars in survival probability decay.

The presence of quantum many-body scars in a model is usually probed by looking at late-time manifestations after the system has been prepared in a fine-tuned initial state that has high overlap with the scarred eigenstates. In particular, one looks for coherent oscillations that remain for time-scales far beyond the natural time-scales for thermalization. Because of decoherence however, these timescales are hard to reach in current cold-atom experiments. Using a simple toy-model, we show that for initial states whose overlap with scars is significantly separated from the rest of the spectrum, the finite-size scaling of the survival probability decay rate at very early times is determined entirely by the scars. This quantity has the benefit of being easily accessible experimentally. Taking as an example the paradigmatic PXP model, we illustrate this fact numerically using the forward-scattering approximation and provide evidences for the robustness of this probe.