Symmetry and transport in disordered systems

The transfer matrix for a disordered system enables averages of integer powers of the resistance to be found, R
^N
; application of the symmetric group generalizes this formula to fractional and negative N, providing a powerful tool for the study of transport. Consequences for fluctuations in resistance, 1/f noise, and frequency response are discussed, as well as a new sort of state, of fractal dimension 1/2, which is responsible for transport in localized systems.