Semiclassical theory of chaotic quantum resonances

TL;DR

This paper develops a semiclassical framework to describe quantum resonances in chaotic open systems, highlighting the role of quantum diffraction and Ehrenfest time in decay mechanisms.

Contribution

It introduces boundary conditions for semiclassical propagation that unify deterministic escape and probabilistic decay based on trajectory times.

Findings

Quantum diffraction is crucial for resonance formation.

Boundary conditions depend on Ehrenfest time.

Unified description of decay mechanisms in chaotic systems.

Abstract

States supported by chaotic open quantum systems fall into two categories: a majority showing instantaneous ballistic decay, and a set of quantum resonances of classically vanishing support in phase space. We present a theory describing these structures within a unified semiclassical framework. Emphasis is put on the quantum diffraction mechanism which introduces an element of probability and is crucial for the formation of resonances. Our main result are boundary conditions on the semiclassical propagation along system trajectories. Depending on whether the trajectory propagation time is shorter or longer than the Ehrenfest time, these conditions describe deterministic escape, or probabilistic quantum decay.