Numerical study of a universal distribution and non-universal distributions of resistance and transmission coefficient in 1-d disordered systems

A universal probability distribution of resistance and transmission coefficient in a one dimensional disordered system proposed by Mello from a macroscopic point of view is examined numerically from a microscopic point of view for some tightly binding disordered systems. Some universal relations between the cumulants are well observed at the band center energy E=0 in a weakly disordered system, while these are modified at the other energies E ≠ 0. They are modified even at E0 in the strongly disordered system. It is further found that the universal relations are broken in a modified Bernoulli system with an inverse-power law structural correlation.