Discrete-time quantum walks: continuous limit and symmetries
Mathematical Physics
2017-04-25 v1 math.MP
Quantum Physics
Abstract
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.
Cite
@article{arxiv.1111.2165,
title = {Discrete-time quantum walks: continuous limit and symmetries},
author = {Giuseppe Di Molfetta and Fabrice Debbasch},
journal= {arXiv preprint arXiv:1111.2165},
year = {2017}
}