量子场中运动镜的非平衡动力学：影响泛函和朗之万方程
Nonequilibrium dynamics of moving mirrors in quantum fields: Influence functional and Langevin equation
摘要：
利用Schwinger-Keldysh方法研究了在量子场中运动的具有完全反射的镜面的非平衡动力学。在反射镜位移的一阶展开的线性响应范围内，通过影响泛函方法积分出量子场，得到粗粒度的有效作用量。导出了半经典朗之万方程，发现该方程包含两个层次的反反应效应：由镜面运动引起的辐射反应和由量子场涨落通过涨落-耗散关系引起的反反应耗散.虽然线性响应理论中的涨落和耗散定理是模型无关的，但从第一性原理推导的研究表明，所得到的定理也是{ \it无关}的调节器，用来处理来自量子场的短距离发散.因此，当引入正则化方法来计算耗散和涨落效应时，必须满足该定理，因为计算结果是在计算结束时采用短距离极限获得的。真空涨落对运动反射镜的反反应效应很难检测到，而热涨落的反反应效应则可以检测到。
英文摘要：
We employ the Schwinger-Keldysh formalism to study the nonequilibrium dynamics of the mirror with perfect reflection moving in a quantum field. Within the regime of linear response in terms of a first order expansion of the mirror's displacement, the coarse-grained effective action is obtained by integrating out quantum fields with the method of influence functional. The semiclassical Langevin equation is derived, and is found to involve two levels of backreaction effects on the dynamics of mirrors: radiation reaction induced by the motion of the mirror and backreaction dissipation arising from fluctuations in quantum fields via a fluctuation-dissipation relation. Although the theorem of fluctuation and dissipation in linear response theory is of model independence, the study from the first principles derivation shows that the obtained theorem is also {\it independent} of the regulators introduced to deal with short-distance divergences from quantum fields. Thus, when the method of regularization is introduced to compute the dissipation and fluctuation effects, this theorem must be fulfilled as the results are obtained by taking the short-distance limit in the end of calculations. The backreaction effects from vacuum fluctuations on moving mirrors are found to be hardly detected while those effects from thermal fluctuations may be detectable.
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