Envelope and phase distribution of a resonance transmission through a complex environment

TL;DR

This paper derives exact statistical distributions for the transmission amplitude's envelope and phase in a complex environment modeled by chaotic states, accounting for absorption and coupling effects.

Contribution

It provides the first exact joint distribution of transmission intensity and phase for a resonance in a chaotic background, including absorption effects.

Findings

Exact joint distribution of transmission intensity and phase derived.

Distribution reveals correlations even at strong absorption.

Asymptotic expression approximates the distribution across all regimes.

Abstract

A transmission amplitude is considered for quantum or wave transport mediated by a single resonance coupled to the background of many chaotic states. Such a model provides a useful approach to quantify fluctuations in an established signal induced by a complex environment. Applying random matrix theory to the problem, we derive an exact result for the joint distribution of the transmission intensity (envelope) and the transmission phase at arbitrary coupling to the background with finite absorption. The intensity and phase are distributed within a certain region, revealing essential correlations even at strong absorption. In the latter limit, we obtain a simple asymptotic expression that provides a uniformly good approximation of the exact distribution within its whole support, thus going beyond the Rician distribution often used for such purposes. Exact results are also derived for the marginal distribution of the phase, including its limiting forms at weak and strong absorption.