  Using the supersymmetry technique, we analytically derive the recent result
of Casati, Maspero and Shepelyansky [cond-mat/9706103] according to which the
quantum dynamics of open chaotic systems follows the classical decay up to a
new quantum relaxation time scale $t_q\sim\sqrt{t_c t_H}$. This scale is larger
than the classical escape time $t_c$ but still much smaller than the Heisenberg
time $t_H$. For systems with orthogonal or unitary symmetry the quantum decay
is slower than the classical one while for the symplectic case there is an
intermediate regime in which the quantum decay is slightly faster.
