The Unruh effect states that a uniformly linearly accelerated observer with proper acceleration $a$ experiences Minkowski vacuum as a thermal state in the temperature $T_{\mathrm{\text{lin}}}=a/(2\pi )$, operationally measurable via the detailed balance condition between excitation and de-excitation probabilities. An observer in uniform circular motion experiences a similar Unruh-type temperature~$T_{\mathrm{\text{circ}}}$, operationally measurable via the detailed balance condition, but $T_{\mathrm{\text{circ}}}$ depends not just on the proper acceleration but also on the orbital radius and on the excitation energy. We establish analytic results for $T_{\mathrm{\text{circ}}}$ for a massless scalar field in $3+1$ and $2+1$ spacetime dimensions in several asymptotic regions of the parameter space, and we give numerical results in the interpolating regions. In the ultrarelativistic limit, we verify that in $3+1$ dimensions $T_{\mathrm{\text{circ}}}$ is of the order of $T_{\mathrm{\text{lin}}}$ uniformly in the energy, as previously found by Unruh, but in $2+1$ dimensions $T_{\mathrm{\text{circ}}}$ is significantly lower at low energies. We translate these results to an analogue spacetime nonrelativistic field theory in which the circular acceleration effects may become experimentally testable in the near future. We establish in particular that the circular motion analogue Unruh temperature grows arbitrarily large in the near-sonic limit, encouragingly for the experimental prospects, but the growth is weaker in effective spacetime dimension $2+1$ than in $3+1$.

中文翻译：

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用于3 + 1和2 + 1尺寸圆周运动的Unruh和模拟Unruh温度

Unruh效应表明，具有适当加速度的均匀线性加速的观察者 $\mathrm{一种}$ 经历Minkowski真空作为温度中的热态 ${Ť}_{\mathrm{\text{林}}}=\mathrm{一种}/（2\pi ）$可以通过激发和消磁概率之间的详细平衡条件进行操作上的测量。匀速圆周运动的观察者会经历类似的Unruh型温度〜${Ť}_{\mathrm{\text{圆}}}$，可以通过详细的余额条件进行操作上的衡量，但 ${Ť}_{\mathrm{\text{圆}}}$不仅取决于适当的加速度，还取决于轨道半径和激励能量。我们为建立分析结果${Ť}_{\mathrm{\text{圆}}}$ 在一个无质量的标量场 $3+\mathrm{1个}$ 和 $2+\mathrm{1个}$参数空间的几个渐近区域中的时空维度，我们在插值区域中给出数值结果。在超相对论极限中，我们验证了$3+\mathrm{1个}$ 尺寸 ${Ť}_{\mathrm{\text{圆}}}$ 大约是 ${Ť}_{\mathrm{\text{林}}}$ 能量均匀地分布，如Unruh先前发现的那样， $2+\mathrm{1个}$ 尺寸 ${Ť}_{\mathrm{\text{圆}}}$在低能量时明显更低。我们将这些结果转换为模拟时空非相对论场论，其中圆形加速度效应可能在不久的将来通过实验进行测试。我们特别确定，圆周运动模拟物Unruh温度在接近声速极限时任意增大，这对于实验前景是令人鼓舞的，但在有效时空维度上该增长较弱$2+\mathrm{1个}$ 比在 $3+\mathrm{1个}$。