Chaos-based Potentials in the One-dimensional Tight-binding Model Probed by the Inverse Participation Ratio

Weslley Florentino de Oliveira; Giancarlo Queiroz Pellegrino

doi:10.1007/s40314-017-0561-7

paper

Chaos-based Potentials in the One-dimensional Tight-binding Model Probed by the Inverse Participation Ratio

arXiv:1712.07729 · doi:10.1007/s40314-017-0561-7

Abstract

Chaos-based potentials are defined and implemented in the one-dimensional tight-binding model as a way of simulating disorder-controlled crystalline lattices. In this setting, disorder is handled with the aid of the chaoticity parameter. The inverse participation ratio $(I P R)$ probes the response of the system to three different such potentials and shows consistent agreement with results given by the Lyapunov exponent $L y$ : the greater $L y (r)$ for the chaotic sequence as a function of the chaoticity parameter $r$ , the greater the asymptotic value $I P R (r)$ for the large-system ground state.

18 pages, 7 figures, article accepted for publication in Computational and Applied Mathematics