Characterization of short necklace states in the logarithmic transmission spectra of localized systems.

High transmission plateaus exist widely in the logarithmic transmission spectra of localized systems. Their physical origins are short chains of coupled localized states embedded inside the localized system, which are dubbed as 'short necklace states'. In this work, we define the essential quantities and then, based on these quantities, we investigate the properties of the short necklace states statistically and quantitatively. Two different approaches are utilized and their results agree very well. In the first approach, the typical plateau-width and the typical order of short necklace states are obtained from the correlation function of the logarithmic transmission. In the second approach, we investigate the statistical distribution of the peak/plateau-width measured in the logarithmic transmission spectra. A novel distribution is found, which can be exactly fitted by the summation of two Gaussian distributions. These two distributions are the results of sharp peaks of localized states and the high plateaus of short necklace states. The center of the second distribution also tells us the typical plateau-width of short necklace states. With increasing system length, the scaling property of the typical plateau-width is very special since it hardly decreases. The methods and quantities defined in this work can be widely used in Anderson localization studies.