The generalized localization lengths in one-dimensional systems with correlated disorder

The scale-invariant properties of wave functions in finite samples of one-dimensional random systems with correlated disorder are analysed. The random-dimer model and its generalizations are considered and the wave functions are compared. Generalized entropic localization lengths are introduced in order to characterize the states and compared with their behaviour for exponential localization. An acceptable agreement is obtained; however, the exponential form seems to be an oversimplification in the presence of correlated disorder. According to our analysis, in the case of the random-dimer model and the two new models the possibility of power-law localization cannot be ruled out.