Frequency dependence of low-temperature phononless conductivity in disordered systems

The frequency dependence of resonant phononless hopping conductivity in disordered systems with pointlike centers of localization in the low-temperature limit is considered within the framework of the pair approximation. It is shown that the existing theory that predicts the power-mode frequency dependence of the low-frequency phononless hopping conductivity $\sigma(\omega)$ and a transition from linear to quadratic dependence (crossover) when frequency increases may become invalid, and the quadratic frequency dependence may never manifest itself at all.