Entropic analysis of the localization-delocalization transition in one dimensional correlated lattice.
In this work, propagation of acoustic waves in one-dimensional binary chain with different types of correlations in elasticity distribution is studied. By using the transfer-matrix method, we numerically calculated the localization length $\xi$. Secondly, we applied entropic analysis to investigate and quantify the localization-delocalization transition in correlated chains in terms of the scaling exponent $\alpha$ and discuss its relation to the order-disorder levels in the structure of the chain. The results demonstrate that there is an upper and lower threshold entropic scaling with respect to the size of the chain which separates three localization-delocalization phases, i.e., delocalized band, localized band/ delocalized modes (mixed) and purely localized modes. Above the upper threshold all states are localized while below the lower threshold an extended band exists.
Publisher URL: http://arxiv.org/abs/1811.04617