发表机构
University of Waterloo; Perimeter Institute for Theoretical Physics; Jiangxi Normal University（滑铁卢大学; 佩里默理论物理研究所; 江西师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导了常曲率时空中Unruh-DeWitt探测器的解析响应函数，区分了场谱与几何效应，并在德西特空间给出了单能隙纠缠检验，在BTZ黑洞中分析了对数增长。
AI 中文摘要
我们推导了与实质量子、共形耦合的无质量标量场耦合的Unruh-DeWitt探测器的解析响应函数，以区分场谱和全局几何效应与相互作用协议效应。对于闵可夫斯基、反德西特和德西特时空中的高斯开关静态探测器对，我们获得了时空维度$\mathcal D=d+1\ge3$下的领头阶激发概率和双探测器相干性。时间有序相干性要求不同的空间世界线；局部响应和单激发相干性也允许重合。对于等红移探测器对，高斯开关将时间有序相干性的能隙依赖性分离出来。在德西特空间中，KMS细致平衡确定了使非局域相干性与局部激发之比最大化的能隙，从而为领头阶纠缠的存在提供了一个单能隙检验，并将任何纠缠能隙限制在一个有界区间内。当纠缠存在时，并发性本身在较小的正能隙处达到峰值。在三维BTZ黑洞中，一个积分勒让德级数给出了径向内落探测器的尖锐开关响应。一个均匀的像求和估计建立了奇点附近的对数增长，并利用覆盖AdS响应确定了其系数。一个足够光滑的单调起始消除了有限时间起始毛刺，但留下了正的对数系数；累积的领头阶响应保持有限。独立的数值计算检验了解析表达式、其收敛性质以及这些物理区别。
英文摘要
We derive analytic response functions for Unruh--DeWitt detectors coupled to real, massless, conformally coupled scalar fields, to distinguish the effects of the field spectrum and global geometry from those of the interaction protocol. For Gaussian-switched static pairs in Minkowski, anti-de Sitter, and de Sitter spacetimes, we obtain the leading-order excitation probabilities and two-detector coherences in spacetime dimension $\mathcal D=d+1\ge3$. Time-ordered coherence requires distinct spatial worldlines; the local response and single-excitation coherence also admit coincidence. For equal-redshift pairs, Gaussian switching separates the gap dependence of the time-ordered coherence. In de Sitter space, KMS detailed balance fixes the gap that maximizes the ratio of nonlocal coherence to local excitation, giving a single-gap test for the existence of leading-order entanglement and restricting any entangling gaps to one bounded interval. When entanglement is present, the concurrence itself peaks at a smaller positive gap. In the three-dimensional BTZ black hole, an integrated Legendre series gives the sharply switched response of a radially infalling detector. A uniform image-sum estimate establishes logarithmic growth near the singularity and determines its coefficient from the covering-AdS response. A sufficiently smooth monotone onset removes the finite-time onset glitches but leaves a positive logarithmic coefficient; the accumulated leading-order response remains finite. Independent numerical calculations test the analytic expressions, their convergence properties, and these physical distinctions.
Comments22 pages, 9 figures
