Quantum relaxation and Poincare recurrences

We study the quantum relaxation process in open dynamical systems with completely chaotic or mixed classical phase space. We show that quantum effects modify the decay rate of Poincare recurrences P(t), In particular, the exponent p of the algebraic decay P(t) proportional to 1/t(P) is shown to have the universal value p=1 due to tunneling and localization effects. Experimental evidence of such decay should be observable in mesoscopic systems and cold atoms.