Quantum decay of an open chaotic system: A semiclassical approach

– We study the quantum probability to survive in an open chaotic system in the framework of the van Vleck-Gutzwiller propagator and present the first such calculation that accounts for quantum interference effects. Specifically, we calculate quantum deviations from the classical decay after the break time t∗ for both broken and preserved time-reversal symmetry. The source of these corrections is identified in interfering pairs of correlated classical trajectories. In our approach the quantized chaotic system is modelled by a quantum graph. A fundamental source of physical information are time-resolved decay measurements in open quantum-mechanical systems. While the radioactive decay is a prominent paradigm, more recent experiments studied atoms in optically generated lattices and billiards [1–6], the ionization of molecular Rydberg states [7] and excitaton relaxation in semiconductor quantum dots and wires [8, 9]. Most of these examples, and also the complementary theoretical investigations of quantum decay [10–20], address the semiclassical regime of systems with chaotic classical limit. However, despite this broad interest there is no satisfactory semiclassical theory for the observed quantum dynamics. It is known from numerical studies and random-matrix theory (RMT) calculations [16–19] that the quantum survival probability P (t) follows the exponential classical decay Pcl(t) only up to a break time t∗. This break time scales with the number of open decay channels L and the classical lifetime tcl as t∗ ∼ √ L tcl [16]. For t > t∗, the quantum decay law is a universal function which depends only on L, tcl and the Heisenberg time tH and is qualitatively different from Pcl(t) [17–19]. Up to now, none of these results was accessible by semiclassical calculations and thus their applicability to individual chaotic systems remained a matter of speculation. In this letter we show that a systematic semiclassical expansion for the quantum decay can be based on the van Vleck-Gutzwiller propagator. Specifically, we obtain with this approach the above-mentioned features for the quantum probability to survive inside a quantized network (quantum graph), which is one of the standard models in quantum chaos [21, 22]. We identify the source of quantum deviations from the classical decay in the interference between certain pairs of correlated classical trajectories (inset of fig. 1). We have calculated the