  Highly excited many-particle states in quantum systems such as nuclei, atoms,
quantum dots, spin systems, quantum computers etc., can be considered as
``chaotic'' superpositions of mean-field basis states (Slater determinants,
products of spin or qubit states). This is due to a very high level density of
many-body states that are easily mixed by a residual interaction between
particles (quasi-particles). For such systems, we have derived simple
analytical expressions for the time dependence of energy width of wave packets,
as well as for the entropy, number of principal basis components and inverse
participation ratio, and tested them in numerical experiments. It is shown that
the energy width $\Delta (t)$ increases linearly and very quickly saturates.
The entropy of a system increases quadratically, $S(t) \sim t^2$ at small
times, and after, can grow linearly, $S(t) \sim t$, before the saturation.
Correspondingly, the number of principal components determined by the entropy,
$N_{pc} \sim exp{(S(t))}$, or by the inverse participation ratio, increases
exponentially fast before the saturation. These results are explained in terms
of a cascade model which describes the flow of excitation in the Fock space of
basis components. Finally, a striking phenomenon of damped oscillations in the
Fock space at the transition to an equilibrium is discussed.
