Abstract
We consider $N$ uniformly-accelerating Unruh-DeWitt detectors whose internal degrees of freedom are coupled to a massless scalar field in $(1+1)$D Minkowski space. We use the influence functional formalism to derive the Langevin equations governing the nonequilibrium dynamics of the internal degrees of freedom and show explicitly that the system relaxes in time and equilibrates. We also show that once the equilibrium condition is established a set of fluctuation-dissipation relations (FDR) and correlation-propagation relations (CPR) emerges for the detectors, extending earlier results of [1] which discovered these relations for the quantum field. Although similar in form to the FDRs commonly known from linear response theory, which assumes an equilibrium condition a priori, their physical connotations are dissimilar from that of a nonequilibrium origin. We show explicitly that both sets of relations are needed to guarantee the balance of energy flow in and out of the system in dynamical equilibrium with the field. These results are helpful to investigations of quantum information and communications of detectors in space experiments and inquiries of theoretical issues in black holes and cosmology.
Highlights
Fluctuation-dissipation relations (FDRs) are fundamental relations established in statistical mechanics with wideranging implications in many areas of physics, theoretical and applied
We show that once the equilibrium condition is established a set of fluctuation-dissipation relations (FDRs) and correlation-propagation relations emerges for the detectors, extending earlier results of Raval, Hu, and Anglin [Stochastic theory of accelerated detectors in quantum fields, Phys
The major findings in our investigation are as follows: (1) We examine the nonequilibrium dynamics of the system during the relaxation process, and show that the system’s achievement of dynamical equilibration is a necessary condition for the existence of the system’s FDR/correlation-propagation relations (CPRs)
Summary
Fluctuation-dissipation relations (FDRs) are fundamental relations established in statistical mechanics with wideranging implications in many areas of physics, theoretical and applied. RHA observed that this cancellation follows from the dissipative properties of the accelerated detector and its free uncoupled dynamics It does not explicitly involve the fluctuations of the field. They point out that this cancellation comes about because of the existence of a correlation-propagation relation (CPR) This set of more general relations between the correlations of various detectors and the radiation mediated by them is derived from the FDR for the accelerated detector. The remaining terms, which contribute to the excitation of the probe, are shown to represent correlations of the free field across the future horizon of the accelerating detector In this problem, the dissipative properties of either detector remain unchanged by the presence of the other. The stochastic force acting on the probe plays a nontrivial role
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