Enhancement of non-escape probability in open chaotic system due to quantum localization induced by periodic orbits

We study semiclassically the quantum non-escape probability of a wavepacket initially localized in spatial region Ω, in an open system with fully chaotic classical limit. We show that at time t, the classically diffusive exponential decay is suppressed in leading order of ℏ by the quantum localization due to periodic orbits of period 2t that are passing through Ω. Each contributing periodic orbit is weighted by the probability density of the initial wave packet along the periodic orbit and a prefactor which counts the stability of the periodic orbit. We argue that the periodic orbits correction will give non-trivial fluctuations superimposed on the monotonic exponential decay at small time and gives arise to anomalous slow decay at large time.