AI 中文总结
该研究通过分析链上受监测长程量子行走的首次探测返回概率，发现跳跃衰减指数$\alpha=1$处存在连续相变，区分常返与瞬态行为，并揭示由投影测量导致的非幺正临界现象。
AI 中文摘要
在量子行走中，首次探测返回概率（FDRP）刻画了显著特征，决定了量子行走是瞬态的还是常返的。我们研究了链上量子行走的FDRP，其中初始位置被探测器以频闪方式监测，且行走者可在位置之间进行长程跳跃。我们假设跳跃强度随距离$d$按$d^{-\alpha}$衰减，且$\alpha\geq 0$，并证明幂律指数$\alpha$关键性地决定了FDRP的行为。$\alpha=1$的值通过总探测概率中的连续相变将常返（$\alpha<1$）与瞬态（$\alpha>1$）量子行走区分开来。对于$\alpha<1$，强长程跳跃导致局域化，产生单位总探测概率。相反，对于$\alpha>1$，长程行走是瞬态的，返回概率随时间按$t^{-\beta}$代数衰减。相关的衰减指数$\beta$作为$\alpha$的函数呈现非解析点。这些奇异性并非仅由低能谱决定，而是由投影测量引起的红外与紫外能量模式之间的干涉所致，标志着非幺正动力学固有的临界行为的出现。这些动力学仅通过调节长程指数$\alpha$来控制，因此可以在原子和分子系统中进行实验探测。
英文摘要
In a quantum walk, the first-detection return probability (FDRP) characterizes salient features, determining whether the quantum walk is transient or recurrent. We study the FDRP of quantum walks on a chain where the initial site is stroboscopically monitored by a detector and the walker performs long-range hopping between sites. We assume that the hopping strength decays with the distance $d$ as $d^{-α}$ and $α\geq 0$ and show that the power-law exponent $α$ critically determines the behavior of the FDRP. The value $α=1$ separates recurrent ($α<1$) from transient ($α>1$) quantum walks through a continuous phase transition in the total detection probability. For $α<1$, strong long-range hopping induces localization, resulting in unit total detection probability. Instead, for $α>1$ the long-range walk is transient and the return probability decays algebraically as a function of time as $t^{-β}$. The associated decay exponent $β$ features nonanalytic points as a function of $α$. Such singularities are not exclusively determined by the low-energy spectrum, but are caused by the interference between infrared and ultraviolet energy modes induced by projective measurements, signalling the emergence of critical behavior intrinsic to the non-unitary dynamics. These dynamics are solely controlled by tuning the long-range exponent $α$ and can thus be experimentally probed in atomic and molecular systems.
Comments27 pages (7 main text + 20 supplemental material), 10 figures (3 figures + 7 supplemental figures)
