Relaxation process in a regime of quantum chaos

We show that the quantum relaxation process in a classically chaotic open dynamical system is characterized by a quantum relaxation time scale $t_q.$ This scale is much shorter than the Heisenberg time and much larger than the Ehrenfest time: $t_q\propto g^{\alpha }$ where $g$ is the conductance of the system and the exponent $\alpha$ is close to $\frac{1}{2}$. As a result, quantum and classical decay probabilities remain close up to values $P\sim \exp \left(-\sqrt{g}\right)$ similarly to the case of open disordered systems.