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arXiv · 1902.02017

Continuous limits of linear and nonlinear quantum walks

Masaya Maeda·Akito Suzuki
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Abstract

In this paper, we consider the continuous limit of a nonlinear quantum walk (NLQW) that incorporates a linear quantum walk as a special case. In particular, we rigorously prove that the walker (solution) of the NLQW on a lattice $\delta \mathbb Z$ uniformly converges (in Sobolev space $H^s$) to the solution to a nonlinear Dirac equation (NLD) on a fixed time interval as $\delta\to 0$. Here, to compare the walker defined on $\delta\mathbb Z$ and the solution to the NLD defined on $\mathbb R$, we use Shannon interpolation.

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Masaya Maeda, Akito Suzuki. 2019-02-06. Continuous limits of linear and nonlinear quantum walks. https://doi.org/10.1142/s0129055x20500087

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