AI 中文总结
本文从谱视角推导单缺陷紧束缚链的占据概率、位移等解析结果，揭示均方位移非单调性的谱起源，且数值计算验证了临界缺陷强度与最小化均方位移的缺陷强度高度吻合。
AI 中文摘要
我们分析存在单个 onsite 缺陷时，近邻紧束缚链的时间演化。近期 Acharya 等人在《J. Stat. Mech. (2026) 043102》一文中指出，此类缺陷会产生非平凡的输运行为，作者们采用受经典随机游走方法启发的缺陷技术，得到了占据概率、平均位移及均方位移（MSD）的精确解析表达式。本文采用谱分解方法推导相同结果，从久期方程出发，得到本征值的自洽条件并构造对应的归一化本征向量，该方法自然地将希尔伯特空间分为暗子空间（其态在缺陷处振幅为零，不受影响）和亮子空间（其态因缺陷发生修改），利用本征值分解，我们揭示了 MSD 非单调性的谱起源。有限链的数值计算表明，解析估计的临界缺陷强度与最小化 MSD 的缺陷强度高度吻合。
英文摘要
We analyze the time evolution of the nearest-neighbour tight-binding chain in the presence of a single onsite defect. Such a defect was shown to generate non-trivial transport behavior recently in the article \textit{Acharya et al J. Stat. Mech. (2026) 043102}. The authors have used a defect technique inspired by classical random walk methods to obtain exact analytical expressions for the occupation probability and subsequently the mean and mean-squared displacement (MSD). Here we derive the same results using a spectral decomposition approach. Starting from the secular equation, we obtain the self-consistency condition for the eigenvalues and construct the corresponding normalized eigenvectors. This approach naturally separates the Hilbert space into dark subspace, whose states have zero amplitude at the defect site and remain unaffected, and bright subspaces, whose states get modified because of the defect. Using this eigenvalue decomposition, we provide a spectral origin of non-monotonicity in the MSD. Numerical calculations for finite chains show that the analytically estimated critical defect strength is in excellent agreement with the defect strength that minimizes the MSD.
Comments14 pages, 2 figures
