We investigate the effect of spatial compactification on the transition rate of an inertial or accelerated Unruh–Dewitt detector coupled to an untwisted or twisted massless quantum scalar field. Four typical cases of the detector’s motion in the compactified Minkowski spacetime are considered respectively. Our results indicate that the detector’s transition rates are crucially dependent on the spatial compactification length, the magnitude and direction of detector’s velocity, the detector’s acceleration, and the field structure. As these factors change, the detector’s spontaneous emission and absorption processes can be enhanced or weakened at different degrees. In particular, when the compact length is small, the behavior of transition rate in the case of the twisted field is quite distinct from that of the untwisted field. Notably, when the detector moves at a constant velocity with nonzero components along the compact and non-compact directions, our study finds that the spontaneous emission rate depends on the component of velocity along the non-compact direction besides that along the compact direction. This is in sharp contrast with the case of the free Minkowski spacetime. Moreover, for the uniformly accelerated detector along the non-compact direction, the spatial compactification clearly modifies both the spontaneous emission and absorption rates, as the modifying factors depend on the compact length and the detector’s acceleration. Our work indirectly but comprehensively examines the nonequivalence of inertial frames in the compactified Minkowski spacetime, and meanwhile provides a theoretical way to identify the orientation and the size of the compact spatial dimension.

我们研究了空间压缩对惯性或加速Unruh-Dewitt检测器与未扭曲或扭曲的无质量量子标量场耦合的跃迁速率的影响。分别考虑了压缩的Minkowski时空中探测器运动的四种典型情况。我们的结果表明，探测器的跃迁速率关键取决于空间压缩长度，探测器速度的大小和方向，探测器的加速度以及场结构。随着这些因素的变化，检测器的自发发射和吸收过程可以不同程度地增强或减弱。特别地，当紧密长度较小时，在扭转场的情况下转变速率的行为与未扭转场的情况相当不同。尤其，我们的研究发现，当探测器以恒定的速度沿紧实方向和非紧实方向移动时具有非零分量时，自发发射率还取决于沿紧实方向的速度分量。这与自由Minkowski时空情况形成鲜明对比。此外，对于沿非紧凑方向均匀加速的探测器，空间压缩显然会修改自发发射率和吸收率，因为修改因素取决于紧凑长度和探测器的加速度。我们的工作间接但全面地研究了压缩的Minkowski时空中惯性系的不等价性，