Exponentially accelerated mirrors as a physical realization of the kappa plane-wave vacuum

Abstract

The kappa plane-wave vacuum is a family of kinematically defined quantum states whose thermal properties are well understood, but whose physical origin has remained obscure. In this paper we provide a concrete dynamical realization of this vacuum, showing that it is physically and operationally equivalent to the quantum state produced on future null infinity by a mirror following the Carlitz-Willey (CW) trajectory. The equivalence is established through a three-pronged analysis: we demonstrate that the two constructions share identical Bogoliubov squeeze parameters, identical nonlocal thermal kernels in their Wightman functions, and identical Planckian responses of an Unruh-DeWitt detector. This result anchors an abstract kinematic construction in a well-understood dynamical model, identifying the parameter $\kappa$ with the physical scale that governs the Carlitz-Willey trajectory. In the final part of the paper we characterize, within the moving-mirror framework, the complete class of mirror trajectories that reproduce the same asymptotic thermal kernel on $\mathscr I^+_R$, and show that only the purely exponential CW trajectory generates a constant, stationary flux.