Quantum versus classical decay laws in open chaotic systems

We study analytically the time evolution in decaying chaotic systems and discuss in detail the hierarchy of characteristic time scales that appeared in the quasiclassical region. There exist two quantum time scales: the Heisenberg time ${t}_{H}$ and the time ${t}_{q}{=t}_{H}/\sqrt{\ensuremath{\kappa}T}$ (with $\ensuremath{\kappa}\ensuremath{\gg}1$ and $T$ being the degree of resonance overlapping and the transmission coefficient, respectively) associated with the decay. If ${t}_{q}l{t}_{H}$ the quantum deviation from the classical decay law starts at the time ${t}_{q}$ and are due to the openness of the system. Under the opposite condition quantum effects in intrinsic evolution begin to influence the decay at the time ${t}_{H}.$ In this case we establish the connection between quantities which describe the time evolution in an open system and their closed counterparts.