AI 中文总结
该研究分离热涨落与辐射反作用贡献，探究热浴中引力极化两能级物体与无限引力狄利克雷边界的引力卡西米尔-波尔德相互作用，发现高温下其缩放规律及力的性质与真空不同，热引力子可主动调控该相互作用。
AI 中文摘要
我们通过分离热涨落（tf）和辐射反作用（rr）的贡献，研究了温度为T的热浴中，可被引力极化的两能级物体与无限引力狄利克雷边界之间的引力卡西米尔-波尔德相互作用。结果表明，相互作用势的辐射反作用（rr）贡献与温度无关，而热涨落（tf）贡献通常由热修正与极化效应之间的非平凡相互作用决定。此处，物体与边界的距离、物体的特征跃迁波长、引力子的热波长分别记为L、λ、β。与真空情形不同（真空下，当L≪λ时，相互作用势按L⁻⁵缩放；当L≫λ时，按L⁻⁶缩放，对应始终为排斥力），高温下会出现全新的行为。特别地，当βλ³的四次方根≪L≪λ，且物体在垂直于边界的平面内可极化时，会出现TL⁻¹的新缩放关系；当βλ的平方根≪L≪λ，且物体沿垂直于边界的轴可极化时，相互作用力会意外变为吸引力。在极高温度和大距离下，即当β≪λ≪L时，势会随距离L振荡，因此根据L的具体取值，可产生吸引力、排斥力甚至零力。本工作表明，热引力子可作为量子引力相互作用的主动控制机制，温度、极化构型及物体与边界的距离共同决定了相互作用力的大小、缩放规律甚至吸引或排斥的性质。
英文摘要
We have investigated, by separating the contributions from thermal fluctuations (tf) and the radiation reaction (rr), the gravitational Casimir-Polder interaction between a gravitationally polarizable two-level object and an infinite gravitational Dirichlet boundary in a thermal bath at a temperature $T$. The results indicate that the rr-contribution to the interaction potential is independent of the temperature, whereas the tf-contribution is generally governed by a nontrivial interplay between the thermal corrections and the polarization effect. Here, the object-to-boundary distance, the characteristic transition wavelength of the object and the thermal wavelength of gravitons are denoted by $L$, $λ$ and $β$, respectively. In contrast to the vacuum case, where the interaction potential scales as $L^{-5}$ for $L\llλ$ and $L^{-6}$ for $L\ggλ$, corresponding to an always repulsive force, qualitatively new behaviors emerge at high temperatures. Particularly, when $\sqrt[4]{βλ^3}\ll L\llλ$ and the object is polarizable within the plane perpendicular to the boundary, a novel scaling of $TL^{-1}$ arises; when $\sqrt{βλ}\ll L\llλ$ and the object is polarizable along the vertical-to-boundary axis, the interaction force becomes surprisingly attractive. At extremely high temperatures and large distances, i.e. when $β\ll λ\ll L$, the potential oscillates with the distance $L$ and thus an attractive or repulsive and even vanishing force can be resulted, depending on the exact values of $L$. Our work demonstrates that thermal gravitons can act as an active control mechanism for quantum gravitational interactions, and temperature, polarization configuration, and object-to-boundary distance jointly determine the magnitude, scaling law, and even the attractive or repulsive nature of the interaction force.
