Scaling in one-dimensional localized absorbing systems

The single-parameter scaling ~SPS! hypothesis is the cornerstone of the current understanding of the localization phenomena. It was originally formulated in terms of the scaling behavior of the conductance of disordered conductors, where it was suggested that when the length, L, of a disordered conductor increases, the evolution of the conductance, g(L), is determined by a single parameter, g itself. For onedimensional ~1D! systems the Landauer’s formula expresses the electron conductance in terms of electron reflection, R(L), and transmission, T(L), coefficients as g(L) 5T(L)/R(L), and thereby allows considering of electron transport on an equal footing with, for example, propagation of light. It was recognized later that SPS must be understood in terms of properties of the entire distribution of g ~or T), and that the most appropriate quantity to deal with is