Effective-medium approach to the resonance distribution of wave scattering in a random point field
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914833204510720 |
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| author | Gaspard, David Sparenberg, Jean-Marc |
| author_facet | Gaspard, David Sparenberg, Jean-Marc |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_00542 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effective-medium approach to the resonance distribution of wave scattering in a random point field Gaspard, David Sparenberg, Jean-Marc Quantum Physics 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. |
| title | Effective-medium approach to the resonance distribution of wave scattering in a random point field |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2309.00542 |