强相互作用下两硬核玻色子在具有少量缺陷点的一维晶格中的量子行走

doi:10.3969/j.issn.1007-5461.2026.05.013

摘要/Abstract

摘要： 本文深入研究了在强的长程和短程相互作用下, 两个硬核玻色子在具有缺陷点的一维晶格势阱中的量子行走。通过在晶格中部分格点上附加一定强度的局域势能来模拟晶格中的缺陷点, 并假定初始时刻两粒子位于缺陷点左侧的相邻晶格格点中。研究表明, 在这一封闭量子系统中, 晶格中缺陷点的存在以及粒子间的强相互作用会导致量子系统的希尔伯特空间分解为多个动力学上隔绝的简并态子空间。因此, 缺陷点的存在及其分布情况、缺陷点附加势能的强度、两粒子的初始状态以及粒子间相互作用能量的空间结构(长程或短程)均对两粒子量子行走的结果产生显著影响。特别是在强长程相互作用下, 当两粒子的相互作用能量与缺陷点的附加势能达到共振时, 两粒子被限定在缺陷点附近行走, 展现出局域化的量子行走特征; 而作为对比, 当两粒子的能量完全偏离共振条件时, 两粒子波函数被缺陷点的附加势垒部分或全部反射回晶格左半侧区域, 并在强相互作用下形成排斥束缚对, 在晶格中呈现弹道式的绑定行走。

关键词: 量子物理, 量子行走, 关联函数, 缺陷点, 长程相互作用

Abstract: The quantum walks of two hard-core Bosons in one-dimensional lattices with a small number of defects under strong long-range and short-range interactions are investigated in detail in this work. Specifically, a certain strength of potential energy is added to specific sites in the lattices to simulate the defect points, and it is assumed that the two particles are located in the adjacent lattice sites to the left of the defects at the initial moment. The study reveals that in this closed quantum system, the presence of defects in the lattices and the strong interaction energy between particles can cause the Hilbert space to decompose into many different dynamically isolated degenerate subspaces. Consequently, the existence and distribution of defect points, the strength of the additional potential energy of defect points, the initial states of the two particles, and the spatial structure of the interaction energy between particles (long-range or short-range) all have a significant impact on the dynamic evolution (quantum walks) of the two particles. Especially for strong long-range interactions, when the interaction energy between two particles reaches resonance with the additional potential energy of the defect points, which results in the two particles being restricted to the edge of the defects, exhibiting localized walking characteristics. By contrast, when the energy of the two particles completely deviates from the resonance condition, the twoparticle wavefunction is partially or completely reflected back to the left region of the lattice by the defects, and the two particles form a repulsive bound pair, exhibiting ballistic co-walking behavior in the lattice.

Key words: quantum physics, quantum walk, correlation function, defects, long-range interaction

中图分类号:

O469

李艳. 强相互作用下两硬核玻色子在具有少量缺陷点的一维晶格中的量子行走[J]. 量子电子学报, 2026, 43(5): 812-824.

LI Yan. Quantum walks of two strongly interacting hard‐core Bosons in one‐dimensional lattices with a small number of defects[J]. Chinese Journal of Quantum Electronics, 2026, 43(5): 812-824.

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