# Fluctuations in an established transmission in the presence of a complex environment

## TL;DR

This paper introduces a new theoretical framework combining a transmitting channel with a chaotic background to analyze fluctuations in wave transport within complex environments, revealing key parameters that govern transmission behavior.

## Contribution

It develops a unified effective Hamiltonian approach using random matrix theory to derive exact results for transmission and reflection in complex scattering systems.

## Key findings

- Transmission sharply disappears when the spreading width exceeds the natural width.
- Transport is governed by absorption rate and the ratio of spreading to natural width.
- The approach highlights the chaotic background's role in dephasing scattering.

## Abstract

In various situations where wave transport is preeminent, like in wireless communication, a strong established transmission is present in a complex scattering environment. We develop a novel approach to describe emerging fluctuations, which combines a transmitting channel and a chaotic background in a unified effective Hamiltonian. Modeling such a background by random matrix theory, we derive exact non-perturbative results for both transmission and reflection distributions at arbitrary absorption that is typically present in real systems. Remarkably, in such a complex scattering situation, the transport is governed by only two parameters: an absorption rate and the ratio of the so-called spreading width to the natural width of the transmission line. In particular, we find that the established transmission disappears sharply when this ratio exceeds unity. The approach exemplifies the role of the chaotic background in dephasing the deterministic scattering.