Manuscript Em03-A@1 · Em03-A-v1.tex · remark · 6d54627d

Remark: Greybody weighting is not exact KMS thermality

Outgoing observables, rate normalization, and error bounds › Scattering of the quantum channels · lines 984–1001

The full outgoing current has spectral covariance

C_{out} (s) = \int_{0}^{\infty} \frac{ω}{4 π} [(1 + Γ_{ℓ} (ω) n_{H} (ω)) e^{- i ω s} + Γ_{ℓ} (ω) n_{H} (ω) e^{i ω s}] d ω .

Its negative-to-positive spectral ratio is

\frac{Γ _{ℓ} n _{H}}{1 + Γ _{ℓ} n _{H}},

not generally $e^{- β_{H} ω}$ . The appropriate statement is a greybody-weighted emission law, not global thermal equilibrium.

Displayed formulas in this passage

unlabeled · line 986
$C_{out} (s) = \int_{0}^{\infty} \frac{ω}{4 π} [(1 + Γ_{ℓ} (ω) n_{H} (ω)) e^{- i ω s} + Γ_{ℓ} (ω) n_{H} (ω) e^{i ω s}] d ω .$
unlabeled · line 995
$\frac{Γ _{ℓ} n _{H}}{1 + Γ _{ℓ} n _{H}},$