ONE-PARAMETER SCALING IN WEAKLY DISORDERED ONE-DIMENSIONAL SYSTEMS

This work is concerned with the statistical properties of the transmission coefficient t of a 1D disordered system. Previous studies have shown that in the long-length limit the quantity In \t\(-2) has a Gaussian distribution. It has also been shown for a number of specific cases (including the Anderson model, the random phase model, the Gaussian random potential model, and certain structural dynamic systems) that for weak disorder the distribution depends upon a single parameter, in the sense that the variance is equal to twice the mean value. By using a variant of the transfer matrix technique developed by Pendry, it is shown here that this one-parameter scaling is in fact a general property of weakly disordered 1D systems of a certain class, regardless of the details of the adopted model.