$(1+3)$ D运动探测器-量子场系统中的涨落-耗散和关联-传播关系
Fluctuation-Dissipation and Correlation-Propagation Relations in $(1+3)$D Moving Detector-Quantum Field Systems
摘要：
涨落耗散关系（FDR）是描述系统与环境相互作用本质的强有力的关系。FDR帮助我们理解的这类性质的问题包括量子场过程的反作用，如早期宇宙学或量子黑洞中时空动力学的粒子产生。不太熟悉的，但同样重要的相关传播关系（CPR）的相关性的随机力在不同的检测器的延迟和先进的部分在现场传播的辐射。在这里，我们分析了一个系统的$N$均匀加速Unruh-DeWitt检测器的内部自由度（idf）是最小的耦合到一个真正的，无质量的，标量场在4D闵可夫斯基空间，扩展以前的工作在2D的导数耦合。利用影响泛函理论，我们导出了描述idfs非平衡动力学的随机方程。我们发现后的检测器场动力学已达到平衡的存在的FDR和CPR的检测器，结合起来，形成一个{ \it广义}波动耗散矩阵关系我们明确显示的能量流的检测器系统的组成部分之间的系统和量子场环境之间的。这种功率平衡锚定广义FDR。我们期望这种矩阵关系能为解释相对论量子信息中的一些基本问题提供一个有用的框架，例如保证能量平衡的自洽性和跟踪探测器-光场系统中的量子信息传递.
英文摘要：
The fluctuation-dissipation relations (FDR) are powerful relations which can capture the essence of the interplay between a system and its environment. Challenging problems of this nature which FDRs aid in our understanding include the backreaction of quantum field processes like particle creation on the spacetime dynamics in early universe cosmology or quantum black holes. The less familiar, yet equally important correlation-propagation relations (CPR) relate the correlations of stochastic forces on different detectors to the retarded and advanced parts of the radiation propagated in the field. Here, we analyze a system of $N$ uniformly-accelerated Unruh-DeWitt detectors whose internal degrees of freedom (idf) are minimally coupled to a real, massless, scalar field in 4D Minkowski space, extending prior work in 2D with derivative coupling. Using the influence functional formalism, we derive the stochastic equations describing the nonequilibrium dynamics of the idfs. We show after the detector-field dynamics has reached equilibration the existence of the FDR and the CPR for the detectors, which combine to form a {\it generalized} fluctuation-dissipation matrix relation We show explicitly the energy flows between the constituents of the system of detectors and between the system and the quantum field environment. This power balance anchors the generalized FDR. We anticipate this matrix relation to provide a useful guardrail in expounding some basic issues in relativistic quantum information, such as ensuring the self-consistency of the energy balance and tracking the quantum information transfer in the detector-field system.
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