The rate profile described in Eq. 43 is a Gaussian function centered at ω 0 with respect to cavity frequency ω c . The numerical value of these broadening factors at T = 300 K is 72 σ = 30.83 cm -1 . As a comparison, α = 5.3 cm -1 when τ c = 1 ps. Second, under the limit when the broadening caused by J ν (ω) is much smaller than the one caused by J eff (ω), which means that α σ (for example, when τ c → 0 or α → ∞), the Gaussian function is much narrower than J eff (ω), such that we can approximate G(ω -ω 0 ) as a single δ-function, G(ω -ω 0 ) ≈ δ(ω -ω 0 ). Then the k VSC expression in Eq. 41 becomes