Effective-medium approach to the resonance distribution of wave scattering in a random point field

• URL: http://arxiv.org/abs/2309.00542v3
• Date: Sat, 8 Jun 2024 11:06:20 GMT
• Title: Effective-medium approach to the resonance distribution of wave scattering in a random point field
• Authors: David Gaspard, Jean-Marc Sparenberg,
• Abstract summary: Distribution of resonance poles in the complex plane of the wavenumber $k$ associated to the scattering of a quantum particle was numerically discovered. This paper proposes a theoretical study based on wave transport theory to explain the origin of these structures and to predict their distribution in the complex $k$ plane.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a previous paper [Phys. Rev. A 105, 042205 (2022)], the distribution of resonance poles in the complex plane of the wavenumber $k$ associated to the multiple scattering of a quantum particle in a random point field was numerically discovered. This distribution presented two distinctive structures: a set of peaks at small $k$ when the wavelength is larger than the interscatterer distance, and a band almost parallel to the real axis at larger $k$. In this paper, a theoretical study based on wave transport theory is proposed to explain the origin of these structures and to predict their distribution in the complex $k$ plane. First, it is shown that the peaks at small $k$ can be understood using the effective wave equation for the average wavefunction over the disorder. Then, that the band at large $k$ can be described by the Bethe-Salpeter equation for the square modulus of the wavefunction. This study is supported by careful comparisons with numerical simulations.

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