Statistics and scaling in one-dimensional disordered systems

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Abstract
The authors present a new calculation of the statistical cumulants of -ln mod t mod 2 and Theta where t= mod t mod exp(i Theta ) is the transmission of a one-dimensional (1D) disordered system. They find that both variables are normally distributed in the long-length limit, and that in general the distributions obey a two-parameter scaling. However, it does not follow that the distributions of mod t mod 2 or 1/ mod t mod 2 are log-normal. They find that mod t mod 2 is never log-normal while 1/ mod t mod 2 is so only for weak disorder. For the 1D Anderson model they show that there is a crossover to a single-parameter scaling in the weak-disorder limit.