Comparison of two-atom cross spectra in de Sitter spacetime, uniformly accelerated Minkowski vacuum, and a thermal bath
- 1Wuyi University
Abstract
We compare two identical two-level atoms coupled to a four-dimensional massless conformally coupled scalar field in three settings: comoving geodesics in the de Sitter Bunch–Davies vacuum, transversely separated uniformly accelerated trajectories in the Minkowski vacuum, and static trajectories in a Minkowski thermal bath. When a=H a = H and β =2π /H, β = 2 π / H , their local Wightman kernels and spectra agree in both the excitation and de-excitation sectors. At finite separation, the thermal cross spectrum contains a sinc(Ω L) sinc ( Ω L ) factor, whereas the two vacuum settings share a hyperbolic geometric factor. At fixed nonzero gap, their large-distance spectral envelopes scale as L−1 L - 1 and L−2, L - 2 , respectively. For each fixed midpoint time T , the comoving de Sitter cross kernel equals the accelerated kernel with a=H a = H and L=r(T). L = r ( T ) . This equality concerns the full relative-time dependence at that midpoint; its Fourier transform is a Wigner-type cross spectrum and is not an instantaneous detector transition rate. We derive the corresponding negative-frequency spectra and express finite-time responses using smooth switching functions. Finite switching samples a range of midpoint times, so matching the two vacuum kernels at one midpoint does not generally match their cross responses over a measurement interval. These relations depend on the specified conformal scalar field and trajectory geometries.
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BibTeX
@article{huang2026comparison,
title = {{Comparison of two-atom cross spectra in de Sitter spacetime, uniformly accelerated Minkowski vacuum, and a thermal bath}},
author = {Zhiming Huang},
journal = {The European Physical Journal C},
year = {2026},
month = oct,
doi = {10.1140/epjc/s10052-026-16520-3},
url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16520-3},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Comparison of two-atom cross spectra in de Sitter spacetime, uniformly accelerated Minkowski vacuum, and a thermal bath
AU - Zhiming Huang
PY - 2026
DA - 2026/10/22
JO - The European Physical Journal C
DO - 10.1140/epjc/s10052-026-16520-3
UR - https://link.springer.com/article/10.1140/epjc/s10052-026-16520-3
AB - We compare two identical two-level atoms coupled to a four-dimensional massless conformally coupled scalar field in three settings: comoving geodesics in the de Sitter Bunch–Davies vacuum, transversely separated uniformly accelerated trajectories in the Minkowski vacuum, and static trajectories in a Minkowski thermal bath. When a=H a = H and β =2π /H, β = 2 π / H , their local Wightman kernels and spectra agree in both the excitation and de-excitation sectors. At finite separation, the thermal cross spectrum contains a sinc(Ω L) sinc ( Ω L ) factor, whereas the two vacuum settings share a hyperbolic geometric factor. At fixed nonzero gap, their large-distance spectral envelopes scale as L^−1 L - 1 and L^−2, L - 2 , respectively. For each fixed midpoint time T , the comoving de Sitter cross kernel equals the accelerated kernel with a=H a = H and L=r(T). L = r ( T ) . This equality concerns the full relative-time dependence at that midpoint; its Fourier transform is a Wigner-type cross spectrum and is not an instantaneous detector transition rate. We derive the corresponding negative-frequency spectra and express finite-time responses using smooth switching functions. Finite switching samples a range of midpoint times, so matching the two vacuum kernels at one midpoint does not generally match their cross responses over a measurement interval. These relations depend on the specified conformal scalar field and trajectory geometries.
SN - 1434-6044
SN - 1434-6052
ER -