  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.

Quantum Physics;High Energy Physics - Phenomenology;High Energy Physics - Theory