Dynamical realization of the κγ-vacuum

Identify a concrete physical system and boundary condition that dynamically generate the κγ-vacuum, whose Wightman function contains non-stationary, phase-dependent terms; specifically, determine whether an accelerating mirror with time-dependent reflectivity or alternative boundary conditions can reproduce the κγ-vacuum’s richer non-stationary correlation structure on future right null infinity.

Background

This paper establishes that the κ-plane-wave vacuum is physically and operationally equivalent to the quantum state produced by an accelerating Carlitz–Willey mirror at future null infinity, matching Bogoliubov structures, Wightman kernels, and Unruh–DeWitt detector responses at temperature T=κ/(2π). It further derives the full class of mirror trajectories that reproduce the same asymptotic thermal kernel, identifying the single-exponential Carlitz–Willey trajectory as uniquely yielding a constant, stationary flux.

Beyond this, the authors highlight a more general κγ-vacuum that introduces non-stationary, phase-dependent terms in its Wightman function. Unlike the κ-plane-wave case realized by the Carlitz–Willey mirror, the physical mechanism for producing the κγ-vacuum’s richer, time-dependent correlations is not yet known. The open question is whether a suitably modified mirror (e.g., with time-dependent reflectivity) or different boundary conditions could serve as a dynamical realization. This would extend the kinematic-to-dynamic bridge constructed in the paper to a broader class of deformed vacua.