Discrete Time Quantum Walks Continuous Limit in 1 + 1 and 1 + 2 Dimension
The continuous limit of discrete-time quantum walks with time- and space-dependent coefficients is investigated in 1 + 1 and 1 + 2 dimensions. 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. In 1 + 1 dimensions, the continuous limit is always described by a Dirac equation or, alternately, a couple of Klein-Gordon equations. In 1 + 2 dimensions, the wave equation describing the continuous limit is not always identical to a Dirac equation and some
1-jets for which both equations coincide are exhibited.
Keywords: CONTINUOUS LIMIT; CONTINUOUS QUANTUM WALK; DIRAC EQUATION; DISCRETE TIME QUANTUM WALK; KLEIN GORDON EQUATION; LOW DIMENSION PHYSIC
Document Type: Research Article
Publication date: 01 July 2013
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