Stochastic theory of accelerated detectors in a quantum field

We analyze the statistical mechanical properties of n detectors in arbitrary states of motion interacting with one another via a quantum field. We use the open system concept and the influence functional method to calculate the influence of quantum fields on detectors in motion, and the mutual influence of detectors via fields. We discuss the difference between self and mutual impedance, advanced and retarded noise, and the relations between noise-correlations and dissipation-propagation. The mutual effects of detectors on one another can be studied from the Langevin equations derived from the influence functional, as it contains the back reaction of the held on the system self-consistently. We show the existence of general fluctuation-dissipation relations, and for trajectories without event horizons, correlation-propagation relations, which succinctly encapsulate these quantum statistical phenomena. These findings serve to clarify some existing confusions on the accelerated detector problem. The general methodology presented here could also serve as a platform to explore the quantum statistical properties of particles and fields, with practical applications in atomic and optical physics problems.