Statistics of a simple transmission mode on a lossy chaotic background

This work develops a general approach to quantify fluctuations in scattering on a simple mode coupled to a lossy chaotic background. The paper derives the exact joint distribution of reflection and total transmission at arbitrary absorption and establish a remarkable symmetry between fluctuations in reflection and transmission sectors. The results are further applied to study the statistics of total losses, which is relevant in a broader context of wave chaotic systems.