We demonstrate analytically and numerically that in isolated quantum systems of many interacting
particles, the number of 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 �� 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 1/��. 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.