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The article discusses a research conducted by A. Eisfeld and colleagues on the unconventional disorder scalings of the Half Width at Half Maximum (HWHM) and the non universality of localization length (LL). It explains the use of unconventional HWHM and demonstrates that non universality of LL is due to segmentation by outliers.

The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D limits. It is found that the scaling relation is universal and independent of the temperature, disorder, and noise parameters, and the essential order parameter is the ratio between the localization length in 2D and the circumference of the tube. Phenomenological and quantitative expressions for transport properties as functions of disorder and noise are obtained and applied to real systems: In the natural chlorosomes found in light-harvesting bacteria the exciton transfer dynamics is predicted to be in the 2D limit, whereas a family of synthetic molecular aggregates is found to be in the homogeneous limit and is independent of dimensionality.

We show that the Peierls instability can result in softening of acoustic phonons with small wave vectors and suggest that this unusual transition takes place in carbon nanotubes, resulting in a static twist deformation of the nanotube lattice. The topological excitations in the ordered phase are immobile and propagate only in pairs.