Anderson localization

The diffusion regime is characterized by spatially extended eigenstate that form a continuous in energy. When the disorder becomes high enough the transport doesn't become just more diffusive but there is a transition to a new transport regime where all eigenstates are exponentially confined.
In this new regime, known as Anderson localization, the standard diffusion is no more possible and the transport properties change dramatically.  One of the most macroscopic effect is that the Ohm's law cease to be valid: in fact the transmission do not decrease linearly with the system thickness (as it happens in the diffusive regime) but exponentially with a characteristic lenght scale ξ known as the localization length.

Necklace states
If two, spatially separated, modes are degenerate in energy they hibrid to form a miniband through the sample. The resulting state is extended over a large part of the sample and is characterized by a high transmission and  a large spectral width. In 1D systems it is known that such modes, albeit extremely rare, dominate the statistic of the transmission. There is still no evidence for the existance of Necklace modes in 2D and 3D.