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

I. Marquez-Martin , G. Di Molfetta (1, 2) , A. Perez

1 AMU - Aix Marseille Université
2 ECM - École Centrale de Marseille

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 [Phys. Lett. B 125, 136 (1983)PYLBAJ0370-269310.1016/0370-2693(83)91253-4]. 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” dimensions.

Mots clés: higher-dimensional; fermion: confinement; dimension: 2; field theory: scalar; membrane model; external field; localization; domain wall; lattice; noise

Domaines: Physique Générale [physics.gen-ph]; Physique des Hautes Energies - Phénoménologie [hep-ph]; Physique des Hautes Energies - Théorie [hep-th]

I. Marquez-Martin, G. Di Molfetta, A. Perez. Fermion confinement via Quantum Walks in 2D+1 and 3D+1 spacetime. Physical Review A, 2017, 95 (4), pp.042112. ⟨10.1103/PhysRevA.95.042112⟩. ⟨hal-01554870⟩