The geometric mean density of states and its application to one-dimensional nonuniform systems

By using the measure of the ratio R of the geometric mean of the local density of states (LDOS) and the arithmetic mean of LDOS, the localization properties can be efficiently characterized in one-dimensional nonuniform single-electron and two-interacting-particle (TIP) systems. For single-electron systems, the extended and localized states can be distinguished by the ratio R. There are sharp transitions in the ratio R at mobility edges. For TIP systems, the localization properties of particle states can also be reflected by the ratio R. These results are in accordance with what obtained by other methods. Therefore, the ratio R is a suitable quantity to characterize the localization properties of particle states for these 1D nonuniform systems.