Statistical wave scattering through classically chaotic cavities in the presence of surface absorption

TL;DR

This paper models the statistical properties of wave scattering in chaotic cavities with surface absorption, providing analytical solutions and comparisons with numerical simulations for different universality classes.

Contribution

It introduces a new model for surface absorption in chaotic cavities and derives analytical distributions of the scattering matrix for specific cases.

Findings

Analytical distribution of S matrix for N=1 and Na=1 in orthogonal and unitary classes.

Model effectively simulates surface absorption via an absorbing mirror.

Results agree with numerical simulations and relate to existing volumetric absorption models.

Abstract

We propose a model to describe the statistical properties of wave scattering through a classically chaotic cavity in the presence of surface absorption. Experimentally, surface absorption could be realized by attaching an "absorbing patch" to the inner wall of the cavity. In our model, the cavity is connected to the outside by a waveguide with N open modes (or channels), while an experimental patch is simulated by an "absorbing mirror" attached to the inside wall of the cavity; the mirror, consisting of a waveguide that supports Na channels, with absorption inside and a perfectly reflecting wall at its end, is described by a subunitary scattering matrix Sa. The number of channels Na, as a measure of the geometric cross section of the mirror, and the lack of unitarity of Sa as a measure of absorption, are under our control: these parameters have an important physical significance for real experiments. The absorption strength in the cavity is quantified by the trace of the lack of unitarity. The statistical distribution of the resulting S matrix for N=1 open channel and only one absorbing channel, Na =1, is solved analytically for the orthogonal and unitary universality classes, and the results are compared with those arising from numerical simulations. The relation with other models existing in the literature, in some of which absorption has a volumetric character, is also studied.