AI 中文总结
该研究对比三种局域温度相同但起源不同的双原子-标量场耦合情形的交叉谱，揭示其谱与关联的差异及重合条件，对相关时空与真空的量子特性研究有重要意义。
AI 中文摘要
我们研究两个相同的两能级原子与四维无质量共形耦合标量场的弱耦合，对比三种局域温度相同但物理起源不同的情形：德西特时空Bunch–Davies真空中的随动原子、闵可夫斯基真空中横向分离的匀加速原子、闵可夫斯基热浴中的静止原子。我们首先推导三种情形下的双原子交叉谱，再从零分离极限统一得到单原子局域谱。当a=H且β=2π/H时，三种情形下的完整局域Wightman核与局域谱完全相同。有限分离时，真实热浴产生sinc(ΩL)空间因子，而德西特时空与横向加速真空产生双曲几何因子。长距离极限下，德西特时空与横向加速真空的交叉关联按L⁻²衰减，闵可夫斯基热浴的交叉关联仅按L⁻¹衰减；当a=H且分离瞬时匹配时，德西特与横向加速真空的交叉谱重合。固定实验设置时，德西特空间中两个随动原子的物理分离随宇宙膨胀演化，而匀加速与热闵可夫斯基构型中被拉回的交叉关联是定态的。
英文摘要
We study the weak coupling of two identical two-level atoms to a four-dimensional massless conformally coupled scalar field and compare three settings with the same local temperature but different physical origins: comoving atoms in the Bunch--Davies vacuum of de Sitter spacetime, transversely separated uniformly accelerated atoms in the Minkowski vacuum, and static atoms in a Minkowski thermal bath. We first derive the two-atom cross spectra in the three settings and then obtain the single-atom local spectra uniformly from the zero-separation limit. When $a=H$ and $β=2π/H$, the complete local Wightman kernels and local spectra are identical in all three cases. At finite separation, a genuine thermal bath produces a $\sinc(ΩL)$ spatial factor, whereas de Sitter spacetime and the transversely accelerated vacuum produce a hyperbolic geometric factor. In the long-distance limit, the cross correlations in de Sitter spacetime and the transversely accelerated vacuum decay as $L^{-2}$, whereas those in the Minkowski thermal bath decay only as $L^{-1}$. The de Sitter and transversely accelerated vacuum cross spectra coincide when $a=H$ and the separations are instantaneously matched. For a fixed experimental setup, the physical separation between the two comoving atoms in de Sitter space evolves with cosmic expansion, whereas the pulled-back cross correlations in the uniformly accelerated and thermal Minkowski configurations are stationary.
