The time- and temperature-dependent drift mobility μd for dispersive transients in disordered solids is μd(T,t) = LEtT in terms of distance L, field E and transit time tT. Since current I ∝ tsu−(1−α) for t <Tand 0<α<1 by Scher-Montroll theory for hopping among localized states, it follows that μd(T) = α[μd(T,t)]α (LEτ)1−α where τ≈ 10−13s is estimated. Further μd(T) ∝ exp (−Δ0KT) and the activation energy Δ0 is time independent. On this basis Δ for the carbazole polymers is ca. zero, that for a-Se is ca. 0.05 eV, and that for a-As2Se3 is 0.35 eV rather than 0.5, 0.3 and 0.6 eV respectively on a phenomenological basis for μd(T,t). Trap-controlled hopping transport may be excluded. Time-resolved optical studies of excess carrier recombination supplement mobility measurements in a-Si:H and a-As2Se3 as well as other systems. Combined results suggest a dielectric response mechanism in which the time-dependent hopping frequency of localized carriers ν ∝ tα−1 arises from distortion of the medium at localization sites. This is satisfied by Δ(T,t) = Δ0+(1−α)KTT ln(t/τ) where τ is the mean initial localization time of the carrier, 10−13−10−12s, Δio is the height of the barrier at T, and 0<α<l. Consequently ν = ν0(t/τ)α−1 exp(frsol|−Δ0/KT) which applies also to bimolecular recombination.