Stochastic Theory of Accelerated Detectors in a Quantum Field

TL;DR

This paper develops a stochastic framework for analyzing the statistical mechanics of multiple accelerated detectors interacting via a quantum field, revealing fluctuation-dissipation and correlation-propagation relations.

Contribution

It introduces a comprehensive influence functional approach to study mutual and self effects of detectors in arbitrary motion, clarifying quantum statistical phenomena in accelerated systems.

Findings

Existence of fluctuation-dissipation relations for accelerated detectors.

Derivation of correlation-propagation relations for trajectories without horizons.

Framework applicable to quantum statistical analysis in atomic and optical physics.

Abstract

We analyze the statistical mechanical properties of n-detectors in arbitrary states of motion interacting with each other 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 and advanced and retarded noise. The mutual effects of detectors on each other can be studied from the Langevin equations derived from the influence functional, as it contains the backreaction of the field 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 in 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.