Complexity Measures in the Tight-Binding Model

The deformation of a wave packet is a significant topic in classical and quantum mechanics. Understanding this phenomenon is relevant in the study of various physical systems. In this work, we characterize the evolution of a highly localized wave packet in a tight-binding lattice. We investigate the behavior of the probability distribution associated with the wave packet and the accompanying complexity measures. We take information entropy, disequilibrium, disorder, and complexity measures to describe the localization-delocalization process from a highly localized initial pulse, showing the particles moving in a lattice. The main result is obtained from the entropy definition (Logarithmic and Linear) and the inverse of the participant ratio to describe the expected localization-delocalization process, evoking two definitions of Complexity: CLMC and CSDL.