Semiclassical Mechanism for the Quantum Decay in Open Chaotic Systems

TL;DR

This paper develops a semiclassical framework to explain quantum decay in open chaotic systems, confirming predictions and revealing new trajectory-based mechanisms affecting decay and related phenomena.

Contribution

It introduces a novel semiclassical approach that accounts for interference effects and Ehrenfest time influences, advancing understanding of quantum decay in chaotic systems.

Findings

Confirmed random matrix theory predictions for decay rates

Identified key classical trajectory pairs influencing quantum decay

Established a semiclassical continuity equation for open systems

Abstract

We address the decay in open chaotic quantum systems and calculate semiclassical corrections to the classical exponential decay. We confirm random matrix predictions and, going beyond, calculate Ehrenfest time effects. To support our results we perform extensive numerical simulations. Within our approach we show that certain (previously unnoticed) pairs of interfering, correlated classical trajectories are of vital importance. They also provide the dynamical mechanism for related phenomena such as photo-ionization and -dissociation, for which we compute cross section correlations. Moreover, these orbits allow us to establish a semiclassical version of the continuity equation.