  We discuss the behavior of fidelity for a classically chaotic quantum system
in the metallic regime. We show the existence of a critical value of the
perturbation below which the exponential decay of fidelity is determined by the
width of the Breit-Wigner distribution and above which the quantum decay
follows the classical one which is ruled by the Lyapunov exponent. The
independence of the decay {\it rate} from the perturbation strength derives
from the similarity of the quantum and classical relaxation process inside the
Heisenberg time scale.
