广义不确定原理（GUP）对与量子标量场相互作用的加速原子兰姆移位的修正
Corrections induced by the GUP to the Lamb shift of an accelerated atom interacting with a quantum scalar field
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中文总结 AI 辅助
该研究在DDC形式体系下，分析了GUP对做惯性、匀加速、匀速圆周运动的两能级原子兰姆移位的修正，发现其修正项与运动类型、加速度及β相关，且匀速圆周运动的修正量更大。
中文摘要 AI 辅助
我们在DDC形式体系内研究了广义不确定原理（GUP）对与实无质量标量量子场相互作用的两能级原子兰姆移位的影响。针对做惯性运动、匀加速运动和匀速圆周运动的原子，我们分析了真空涨落与辐射反作用的各自贡献。我们首先推导了场沿三种运动类型原子轨迹的统计函数，将其表示为频率积分，随后利用这些函数计算辐射能级移位中的真空涨落和辐射反作用贡献。我们证明，两能级原子经GUP修正后的兰姆移位完全源自真空涨落，且获得了与β成正比的额外修正项。我们特别关注依赖加速度的GUP修正：对于匀加速原子，GUP修正包含热部分与非热部分；在低加速度下，热部分呈现非单调行为，当a/ω₀→0时，热部分与a⁴成正比；相比之下，非热部分呈非线性单调增长，在大加速度下超过热部分近两个数量级。对于做匀速圆周运动的原子，GUP修正完全为非热部分，且也呈现对加速度的非线性单调依赖，其随加速度的变化方向由β的符号决定（即随加速度陡增或陡减）。在相同β值下，匀速圆周运动原子的修正量大于匀加速运动原子的修正量，因为前者包含与a²和a³成正比的项，而后者仅包含与a²成正比的项。
英文摘要
We investigate the effect of the GUP on the Lamb shift of a two-level atom interacting with a real massless scalar quantum field, within the DDC formalism. For an atom undergoing inertial motion, uniform acceleration, and uniform circular motion, we analyze the separate contributions of vacuum fluctuations and radiation reaction. We first derive the statistical functions of the field along the atom's trajectories for the three types of motion, expressing them as frequency integrals, and then employ them to calculate the vacuum fluctuation and radiation reaction contributions to the radiative level shift. We show that the GUP-modified Lamb shift of the two-level atom arises entirely from vacuum fluctuations and acquires additional corrections proportional to $β$. We focus in particular on the acceleration-dependent GUP corrections. For a uniformly accelerated atom, the GUP corrections comprise thermal and nonthermal parts. At low accelerations, the thermal part exhibits nonmonotonic behavior, and is proportional to $a^4$ in the limit $a/ω_0 \to 0$; the nonthermal part, by contrast, grows nonlinearly and monotonically, exceeding the thermal part by nearly two orders of magnitude at large accelerations. For an atom in uniform circular motion, the GUP corrections are purely nonthermal and also display a nonlinear, monotonic dependence on acceleration, increasing or decreasing steeply according to the sign of $β$. For the same $β$, the corrections are larger in uniform circular motion than in uniformly accelerated motion, since the former involves terms proportional to both $a^2$ and $a^3$, whereas the latter contains only $a^2$ terms.
