用移动半透明镜的真空涨落模拟黑洞坍缩
Black hole collapse simulated by vacuum fluctuations with a moving semi-transparent mirror
摘要：
在二维闵可夫斯基时空中的标量无质量粒子的创建-所预测的动态Casimir效应-的情况下，一个透明的镜子最初在休息，然后加速一些有限的时间，沿着一个轨迹，模拟黑洞崩溃（由沃克，Carlitz和Willey定义），最后以恒定的速度移动。当反射系数和透射系数是Barton、Calogeracos和Nicolaevici提出的模型[ $r(w)=-iα/(\w+iα)$和$s(w)=\w/(\w+iα)$，with $α\geq 0$ ]中的系数时，可以精确计算反射镜背面的Bogoliubov系数。这使我们能够证明，当$α$是非常大的（理想的情况下，完美的反射镜）的标量无质量粒子的热发射服从玻色-爱因斯坦统计辐射从镜子（一个黑体辐射），根据先前在文献中获得的结果。然而，当$α$是有限的（透明镜，一种物理上真实的情况）时，我们得到了一个惊人的结果：标量无质量粒子的热辐射服从费米-狄拉克统计。我们还证明了在二维无质量粒子的费米子模型中，统计量发生了相反的变化，即完全反射情况下的费米-狄拉克统计量将变为部分反射物理镜的玻色-爱因斯坦统计量。
英文摘要：
Creation of scalar massless particles in two-dimensional Minkowski space-time--as predicted by the dynamical Casimir effect--is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a trajectory that simulates a black hole collapse (defined by Walker, and Carlitz and Willey), and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [$r(w)=-iα/(\w+iα)$ and $s(w)=\w/(\w+iα)$, with $α\geq 0$], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when $α$ is very large (case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a black body radiation), in accordance with results previously obtained in the literature. However, when $α$ is finite (semitransparent mirror, a physically realistic situation) the striking result is obtained that the thermal emission of scalar massless particles obeys Fermi-Dirac statistics. We also show here that the reverse change of statistics takes place in a bidimensional fermionic model for massless particles, namely that the Fermi-Dirac statistics for the completely reflecting situation will turn into the Bose-Einstein statistics for a partially reflecting, physical mirror.
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