Fermion confinement via Quantum Walks in 2D+1 and 3D+1 spacetime

TL;DR

This paper models fermion confinement in higher-dimensional spacetime using quantum walks with position-dependent coins, mimicking brane-world scenarios, and demonstrates localization in one dimension while allowing free movement in others.

Contribution

It introduces a novel quantum walk model that simulates fermion confinement via scalar field interactions inspired by brane-world theories.

Findings

Fermions become localized in one dimension due to the coin's spatial dependence.

The quantum walk allows free movement along the other dimensions.

The model effectively mimics brane-world fermion confinement mechanisms.

Abstract

We analyze the properties of a two and three dimensional quantum walk that are inspired by the idea of a brane-world model put forward by Rubakov and Shaposhnikov [1]. In that model, particles are dynamically confined on the brane due to the interaction with a scalar field. We translated this model into an alternate quantum walk with a coin that depends on the external field, with a dependence which mimics a domain wall solution. As in the original model, fermions (in our case, the walker), become localized in one of the dimensions, not from the action of a random noise on the lattice (as in the case of Anderson localization), but from a regular dependence in space. On the other hand, the resulting quantum walk can move freely along the "ordinary" dimension.