Statistics of a simple transmission mode on a lossy chaotic background

TL;DR

This paper derives the joint distribution of reflection and transmission in a lossy chaotic system using random matrix theory, revealing a symmetry controlled by the ratio of spreading to escape width.

Contribution

It introduces a novel analytical framework for understanding the statistics of wave scattering in complex, lossy environments using the strength function formalism.

Findings

Distribution exhibits symmetry between reflection and transmission sectors.

Symmetry is governed by the ratio of spreading to escape width.

Provides insights into total losses at arbitrary coupling.

Abstract

Scattering on a resonance state coupled to a complicated background is a typical problem for mesoscopic quantum many-body systems as well as for wave propagation in the presence of a complex environment. On average, such a simple mode acquires an effective damping, the so-called "spreading" width, due to mixing with the background states. Modeling the latter by random matrix theory and employing the strength function formalism, we derive the joint distribution of the reflection and total transmission at arbitrary absorption in the background. The distribution is found to possess a remarkable symmetry between its reflection and transmission sectors, which is controlled by the ratio of the spreading to escape width. This in turn results in a symmetry relation between the marginal densities, despite the absence of the flux conservation at finite absorption. As an application, we study the statistics of total losses in the system at arbitrary coupling to the background.