  We demonstrate analytically and numerically that in isolated quantum systems
of many interacting particles, the number of many-body states participating in
the evolution after a quench increases exponentially in time, provided the
eigenstates are delocalized in the energy shell. The rate of the exponential
growth is defined by the width $\Gamma$ of the local density of states (LDOS)
and is associated with the Kolmogorov-Sinai entropy for systems with a well
defined classical limit. In a finite system, the exponential growth eventually
saturates due to the finite volume of the energy shell. We estimate the time
scale for the saturation and show that it is much larger than $\hbar/\Gamma$.
Numerical data obtained for a two-body random interaction model of bosons and
for a dynamical model of interacting spin-1/2 particles show excellent
agreement with the analytical predictions.
