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) proportional to g(alpha) where g is the conductance of the system and the exponent alpha is close to 1/2. As a result, quantum and classical decay probabilities remain close up to values P similar to exp(-root g) similarly to the case of open disordered systems.