Wave Scattering through Classically Chaotic Cavities in the Presence of Absorption: An Information-Theoretic Model

TL;DR

This paper introduces an information-theoretic model for wave transport in chaotic cavities with absorption, predicting statistical distributions of scattering coefficients and comparing well with simulations under strong absorption.

Contribution

It develops a maximum-entropy model for the S-matrix distribution considering absorption, extending previous analytical results to regimes with partial absorption.

Findings

Model agrees with analytical results for strong absorption

Distribution of transmission and reflection becomes Rayleigh for strong absorption

Model fails to accurately predict behavior at moderate and weak absorption

Abstract

We propose an information-theoretic model for the transport of waves through a chaotic cavity in the presence of absorption. The entropy of the S-matrix statistical distribution is maximized, with the constraint $<Tr SS^{\dagger}> =\alpha n$: n is the dimensionality of S, and $0\leq \alpha \leq 1, \alpha =0(1)$ meaning complete (no) absorption. For strong absorption our result agrees with a number of analytical calculations already given in the literature. In that limit, the distribution of the individual (angular) transmission and reflection coefficients becomes exponential -Rayleigh statistics- even for n=1. For $n\gg 1$ Rayleigh statistics is attained even with no absorption; here we extend the study to $\alpha <1$. The model is compared with random-matrix-theory numerical simulations: it describes the problem very well for strong absorption, but fails for moderate and weak absorptions. Thus, in the latter regime, some important physical constraint is missing in the construction of the model.