From open quantum systems to open quantum maps

TL;DR

This paper demonstrates that analyzing the resolvent, scattering, and resonances of certain open quantum chaotic systems can be simplified by reducing the problem to the study of finite-dimensional open quantum maps derived from the classical Poincaré map.

Contribution

It introduces a method to connect the analysis of open quantum chaotic systems with finite-dimensional quantum maps, simplifying the study of their spectral properties.

Findings

Reduction of resolvent analysis to quantum maps

Application to scattering and resonances in chaotic systems

Provides a new framework for quantizing Poincaré maps

Abstract

For a class of quantized open chaotic systems satisfying a natural dynamical assumption, we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite dimensional operators obtained by quantizing the Poincar\'e map associated with the flow near the set of trapped trajectories.