# Distribution of zeros of the S-matrix of chaotic cavities with localized losses and Coherent Perfect Absorption: non-perturbative results

## TL;DR

This paper uses Random Matrix Theory to analyze the distribution of zeros of the scattering matrix in chaotic cavities with localized losses, providing non-perturbative insights into optimal absorption for coherent perfect absorption (CPA).

## Contribution

It extends the analysis of scattering matrix zeros beyond weak coupling, offering a non-perturbative approach applicable to any absorption strength and validating predictions with simulations.

## Key findings

- Derived the density of zeros for any absorption strength.
- Identified the optimal loss for CPA realization.
- Validated theoretical predictions with numerical simulations.

## Abstract

We employ the Random Matrix Theory framework to calculate the density of zeroes of an $M$-channel scattering matrix describing a chaotic cavity with a single localized absorber embedded in it. Our approach extends beyond the weak-coupling limit of the cavity with the channels and applies for any absorption strength. Importantly it provides an insight for the optimal amount of loss needed to realize a chaotic coherent perfect absorbing (CPA) trap. Our predictions are tested against simulations for two types of traps: a complex network of resonators and quantum graphs.