for a timescale τ such that 2π/E ≪ τ ≪ 1/Γ. The result of performing this moving average will subsequently be called the "time average" of the quantity, although it is important to understand that only the effects that the Edependent rapid oscillations have on the decay rates have been averaged out while any remaining time dependence is still present in the "time averaged" quantity. By using Im[ρ 01 ] 2 ≈ |ρ 01 | 2 sin 2 (Et) and sin 2 (Et) = 1 2 , the time average of Eq. A13 is expressed