  The response of a quantum system in a pure state to an external force is
investigated by reconsidering the standard statistical approach to quantum
dynamics on the light of the statistical description of equilibrium based on
typicality. We prove that the response of the large majority of quantum pure
states subjected to the same arbitrary external perturbation tends to be close
to the statistical response as the dimension of the Hilbert space increases.
This is what we can term dynamical typicality. The theoretical analysis is
substantiated by numerical simulations of the response of a spin system to a
sudden quench of the external magnetic field. For the considered system we show
that not only the system relaxes toward a new equilibrium state after the
quench of the Hamiltonian but also that such a new equilibrium is compatible
with the description of a thermal equilibrium.
