Conductor-insulator transition in the Anderson model of a disordered solid

Abstract

The theoretical approach to the Anderson transition, introduced by Götze and based on an approximative treatment of kinetic equations, is generalized and applied to the Anderson model of $d$-dimensional hypercubic lattice. The memory-function representation of density and current relaxation functions is used, where memory functions are approximated in a manner analogous to mode-coupling theories. Mobility edges, dc and ac conductivity, as well as the participation ratio and the localization length are discussed and calculated for special cases $d=2\mathrm{} \mathrm{and} 3$. A comparison with recent numerical experiment data is performed. The question of marginal dimensionalities is also considered.