科研之友
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摘要
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.
- 出版日期2013-7
