2011/11/09 by Giuseppe Di Molfetta, Fabrice Debbasch
Physics and Astronomy · Mathematics · #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.4764876
published as Journal of Mathematical Physics 53.12 (2012): 123302
arxiv created 2011/11/09 · arxiv updated 2017/04/25
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. Variational principles leading to these equations are also discussed, together with local invariance properties.