  Quantum systems whose classical counterparts are chaotic typically have
highly correlated eigenvalues and level statistics that coincide with those
from ensembles of full random matrices. A dynamical manifestation of these
correlations comes in the form of the so-called correlation hole, which is a
dip below the saturation point of the survival probability's time evolution. In
this work, we study the correlation hole in the spin-boson (Dicke) model, which
presents a chaotic regime and can be realized in experiments with ultracold
atoms and ion traps. We derive an analytical expression that describes the
entire evolution of the survival probability and allows us to determine the
timescales of its relaxation to equilibrium. This expression shows remarkable
agreement with our numerical results. While the initial decay and the time to
reach the minimum of the correlation hole depend on the initial state, the
dynamics beyond the hole up to equilibration is universal. We find that the
relaxation time of the survival probability for the Dicke model increases
linearly with system size.
