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In a previous paper, the distribution of resonance poles in the complex planeof the wavenumber $k$ associated to the multiple scattering of a quantumparticle in a random point field was numerically discovered. This distributionpresented two distinctive structures: a set of peaks at small $k$ when thewavelength is larger than the interscatterer distance, and a band almostparallel to the real axis at larger $k$. In this paper, a detailed theoreticalstudy based on wave transport theory is proposed to explain the origin of thesestructures and to predict their location in the complex $k$ plane. First, it isshown that the peaks at small $k$ can be understood using an effective waveequation for the average wave function over the disorder. Then, that the bandat large $k$ can be described by the Bethe-Salpeter equation for the squaremodulus of the wavefunction, which is derived from the diagrammatic method.This study is supported by careful comparisons with numerical simulations. Thelargest simulations revealed the presence of quantum scars in the bulk of thedisordered medium.

Effective medium approach of the resonance distribution in a random point field