Discrete-time quantum walks: continuous limit and symmetries

Understand

The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated.

• A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks do.
• All families (1-jets) admitting a continuous limit are identified.
• The continuous limit is described by a Dirac-like equation or, alternately, a couple of Klein-Gordon equations.