Directionality emergence and localization in a quantum random Lorentz gas

TL;DR

This paper investigates how directional behavior can emerge from multiscattering of a quantum wave in a 2D Lorentz gas without measurement, revealing a strongly directional regime linked to Anderson localization.

Contribution

It demonstrates that pure multiscattering can induce directionality in quantum waves, without decoherence, through a schematic model and numerical simulations.

Findings

A directional regime emerges at specific wavenumbers.

Directionality is related to Anderson localization.

More than 100 scatterers are needed for strong directionality.

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.