Quantum walks in artificial electric and gravitational fields

•The continuous limit of quantum walks on the line is investigated systematically through a new method.•In all cases but one, the continuous limit coincides with the propagation of a Dirac fermion.•Inhomogeneities in the walk transcribe as artificial electric and gravitational fields.•New, state of the art simulations of a quantum walk propagating in an artificial electric field.•New, state of the art simulations of a quantum walk propagating in and around an artificial black hole.

The continuous limit of quantum walks (QWs) on the line is revisited through a new, recently developed method. In all cases but one, the limit coincides with the dynamics of a Dirac fermion coupled to an artificial electric and/or relativistic gravitational field. All results are carefully discussed and illustrated by numerical simulations. Possible experimental realizations are also addressed.