Dielectric anomalies near the Anderson metal-insulator transition

The linear-response expressions for the dielectric constant and conductivity as functions of wave number and frequency are evaluated near the localization metal-insulator transition for noninteracting quasiparticles. New behavior is found in the microscopic range. The static dielectric constant from the insulating side is found to diverge with twice the exponent characterizing the vanishing of the conductivity from the metallic side. The dynamic structure factor follows easily from our expressions and we suggest that it can be measured, in principle, using high-frequency electromagnetic radiation.