  Isolated chaotic many-body quantum systems can reach thermal equilibrium, but
it is not yet clear how long they take to do so. To answer this question, we
use exact numerical methods and analyze the entire evolution, from perturbation
to thermalization, of a paradigmatic disordered many-body quantum system in the
chaotic regime. We investigate how the thermalization time depends on the
system size and observables. We show that if dynamical manifestations of
spectral correlations in the form of the correlation hole ("ramp") are taken
into account, the time for thermalization scales exponentially with system
size, while if they are neglected, the scaling is better described by a power
law with system size, though with an exponent larger than expected for
diffusive transport.
