  We argue that the dynamics of particle imbalance in quadratic fermionic
models is, for the majority of initial many-body product states in site
occupation basis, virtually indistinguishable from the dynamics of survival
probabilities of single-particle states. We then generalize our statement to a
similar relationship between the non-equal time and space density correlation
functions in many-body states and the transition probabilities of
single-particle states at nonzero distances. Finally, we study the equal time
connected density-density correlation functions in many-body states, which
exhibit certain qualitative analogies with the survival and transition
probabilities of single-particle states. Our results are numerically tested for
two paradigmatic models of single-particle localization: the 3D Anderson model
and the 1D Aubry-Andr\'e model. This work gives affirmative answer to the
question whether it is possible to measure features of the single-particle
survival and transition probabilities by the dynamics of observables in
many-body states.
