Directionality emergence and localization in a quantum random Lorentz gas

• URL: http://arxiv.org/abs/2603.12432v1
• Date: Thu, 12 Mar 2026 20:29:07 GMT
• Title: Directionality emergence and localization in a quantum random Lorentz gas
• Abstract summary: We study the propagation of a spherical wave through a two-dimensional random Lorentz gas composed of small fixed scatterers.<n>Inspired by the Mott problem, we investigate, on a schematic model, whether such a directional behavior can emerge purely from the multiscattering process.<n> Numerical simulations reveal the existence of a strongly directional regime within a specific wavenumber range.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The propagation of a spherical wave through a two-dimensional random Lorentz gas composed of small fixed scatterers is studied. Inspired by the Mott problem (how an initially isotropic quantum wave can give rise to a single particle-like track), we investigate, on a schematic model, whether such a directional behavior can emerge purely from the multiscattering process, without any explicit measurement or decoherence mechanism. Using the Foldy-Lax formalism, we derive the far-field angular behavior of the wavefunction, and introduce a directionality vector to quantify its anisotropy and identify its preferred direction. Numerical simulations reveal the existence of a strongly directional regime within a specific wavenumber range, which emerges from multiscattering with more than $100$ scatterers and which can be related to Anderson localization.

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