Quantum relaxation in open chaotic systems

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.