Random Matrix Theory of Resonances: an Overview

TL;DR

This paper reviews how Random Matrix Theory models the statistical properties of resonances and eigenfunctions in quantum chaotic scattering systems, especially focusing on complex poles and decaying states.

Contribution

It provides an overview of applying RMT to analyze resonance poles and non-orthogonal eigenfunctions in quantum chaotic scattering, highlighting recent advances and challenges.

Findings

RMT effectively describes eigenfrequency statistics in chaotic scattering.

Analysis of resonance poles reveals universal statistical patterns.

Understanding non-orthogonal eigenfunctions remains a complex challenge.

Abstract

Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated eigenfunctions remains one of the pillars of theoretical understanding of quantum chaotic systems. In a scattering system coupling to continuum via antennae converts real eigenfrequencies into poles of the scattering matrix in the complex frequency plane and the associated eigenfunctions into decaying resonance states. Understanding statistics of these poles, as well as associated non-orthogonal resonance eigenfunctions within RMT approach is still possible, though much more challenging task.