Distribution of reflection eigenvalues in many-channel chaotic cavities with absorption

TL;DR

This paper analytically derives the distribution of reflection eigenvalues in large chaotic cavities with absorption, revealing independence from time-reversal symmetry and applicability to various openness levels, with implications for thermal emission.

Contribution

It provides a new analytical expression for the eigenvalue distribution of the reflection matrix in chaotic cavities with absorption, valid for large systems and arbitrary openness.

Findings

Eigenvalue distribution is independent of time-reversal symmetry.

Results are valid for finite absorption and arbitrary openness.

Application to thermal emission from random media is discussed.

Abstract

The reflection matrix R=S^{\dagger}S, with S being the scattering matrix, differs from the unit one, when absorption is finite. Using the random matrix approach, we calculate analytically the distribution function of its eigenvalues in the limit of a large number of propagating modes in the leads attached to a chaotic cavity. The obtained result is independent on the presence of time-reversal symmetry in the system, being valid at finite absorption and arbitrary openness of the system. The particular cases of perfectly and weakly open cavities are considered in detail. An application of our results to the problem of thermal emission from random media is briefly discussed.