where ∆ x = ν L | R|ν L is the transition dipole matrix element, and n(ω) = 1/(e βω -1) is the Bose-Einstein distribution function. Note that J eff (ω) explicitly contains ω c , thus giving the ω c dependence of k VSC . Furthermore, the term G(ω -ω 0 ) in Eq. 41 is an inhomogeneous broadening function for the quantum vibration frequency ω 0 , with a variance of (cf. Eq. A6)