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One-dimensional three-state quantum walks: Weak limits and localization

机译：一维三态量子行走：局限性和局限性

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摘要

We investigate one-dimensional three-state quantum walks. We find a formula for the moments of the weak limit distribution via a vacuum expectation of powers of a self-adjoint operator. We use this formula to fully characterize the localization of three-state quantum walks in one dimension. The localization is also characterized by investing the eigenvectors of the evolution operator for the quantum walk. As a byproduct we clarify the concepts of localization differently used in the literature. We also study the continuous part of the limit distribution. For typical examples we show that the continuous part is the same kind as that of two-state quantum walks. We provide with explicit expressions for the density of the weak limits of some three-state quantum walks.
机译：我们研究一维三态量子行走。通过对自伴算子的幂的真空期望，我们找到了弱极限分布时刻的公式。我们使用该公式来全面表征一维三态量子步态的定位。定位的特征还在于，将演化算子的​​特征向量用于量子步态。作为副产品，我们阐明了文献中使用的本地化概念。我们还研究极限分布的连续部分。对于典型的例子，我们证明了连续部分与二态量子行走是相同的。我们为某些三态量子步态的弱极限的密度提供了明确的表达式。

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