发表机构
Universidade Federal do Paraná; Universidade Estadual de Ponta Grossa（巴拉那联邦大学; 蓬塔格罗萨州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将SQW框架扩展到能量依赖点相互作用晶格，构建了对应Kronig-Penney型点相互作用阵列的DTQW模型，分析其谱与动力学，揭示四类点相互作用的不同透射与纠缠行为。
AI 中文摘要
本工作将散射量子行走（SQW）框架扩展到能量依赖点相互作用的晶格中。这在硬币量子行走（CQW）形式体系内产生了一个与零范围势的散射矩阵直接相关的硬币算子。该模型因此提供了离散时间量子行走（DTQW）对Kronig-Penney型点相互作用周期阵列的模拟，其中行走者的波数作为硬币操作的连续、物理上透明的控制参数。我们分析了位置概率和纠缠的谱与动力学，得到特定能量和点相互作用下的不同结果。我们将谱结构与空间概率分布关联起来，并明确表征了每种点相互作用的长时间纠缠行为。透射模量决定了准能隙、带宽和最大群速度，同时也控制了所考虑初始态的长时间硬币-位置纠缠。四类一维点相互作用（δ、δ'、交叉型和不对称型）实现了定性不同的透射轮廓，并涵盖了全部行为范围，包括增强或强烈抑制的扩散以及振荡纠缠。
英文摘要
In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantum-walk (DTQW) analog of a periodic array of point interactions of the Kronig-Penney type, where the walker's wavenumber serves as a continuous, physically transparent control parameter for the coin operation. We analyze the spectra and the dynamics of position probability and entanglement, yielding distinct results for specific energies and point interactions. We relate the spectral structure to the spatial probability distribution and explicitly characterize the long-time entanglement behavior for each point interaction. The transmission modulus determines the quasienergy gap, bandwidth, and maximum group velocity, while also controlling the long-time coin-position entanglement for the initial state considered. The four families of one-dimensional point interactions ($δ$, $δ'$, crossed and asymmetric) realize qualitatively distinct transmission profiles and span the full range of behavior, including enhanced or strongly suppressed spreading and oscillatory entanglement.
Comments11 pages, 9 figures, comments are welcome
