Localization in Highly Anisotropic Systems

The localization behavior of the Anderson model with anisotropic hopping integral t for weakly coupled planes and weakly coupled chains is investigated both numerically with the transfer-matrix method and analytically within the self-consistent theory of localization. It is found that the mobility edge is independent of the propagating direction. However, the correlation (localization) length in the extended (localized) side of the transition can be very different for the two directions. The critical disorder $W_c$ is found to vary from $t^{1/4}$ for weakly coupled planes to $t^{1/2}$ for weakly coupled chains.