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For an open quantum system with classically chaotic
counterpart, the classical survival probability is ρcl(t)= exp(-t/τD), with classical dwell
time τD. This behavior has been observed in various disciplines, either directly, as in atom billiards or indirectly in the spectral regime of Ericson fluctuations in electron or microwave cavities and in atomic photo-ionization. I will address the quantum survival probability ρ(t) which exhibits deviations from its classical counterpart and compute semiclassically quantum corrections to the exponential classical decay. I will show that semiclassics confirms existing predictions in the limit of random matrix theory (RMT) and, going beyond RMT, compute so-called Ehrenfest time effects and compare with numerical wave packet simulations. The semiclassical calculation sheds in particular light on the underlying dynamical mechanism for quantum decay and related phenomena in photo-ionization and -dissociation, for which we compute cross section correlations. We find that for the computation of ρ(t), specific pairs of interfering, correlated classical paths play a key role. In particular, besides the usual loop orbit diagrams, a new class of correlated trajectory pairs, 'one-leg-loops', proves relevant. Moreover, these orbits ensure unitarity in problems involving semiclassical time propagation along open trajectories inside a system and allow us to establish a semiclassical version of the continuity equation. |
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