Fluctuations and correlations in scattering on a resonance coupled to a chaotic background

TL;DR

This paper uses random matrix theory to analyze the complex statistical fluctuations and correlations in wave scattering involving a resonance coupled to a chaotic background, relevant for complex environments.

Contribution

It provides exact nonperturbative results for scattering statistics, including distributions of intensities and phases, at arbitrary coupling and absorption levels, advancing understanding of wave behavior in chaotic systems.

Findings

Intensities and phases show complex statistical correlations.

Distributions derived exactly for arbitrary coupling and absorption.

Correlations persist even under strong absorption.

Abstract

We discuss and briefly overview recent progress with studying fluctuations in scattering on a resonance state coupled to the background of many chaotic states. Such a problem arises naturally, e.g., when dealing with wave propagation in the presence of a complex environment. Using a statistical model based on random matrix theory, we obtain a number of nonperturbative results for various statistics of scattering characteristics. This includes the joint and marginal distributions of the reflection and transmission intensities and phases, which are derived exactly at arbitrary coupling to the background with finite absorption. The intensities and phases are found to exhibit highly non-trivial statistical correlations, which remain essential even in the limit of strong absorption. In the latter case, we also consider the relevant approximations and their accuracy. As an application, we briefly discuss the statistics of the phase rigidity (or mode complexness) in such a scattering situation.