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

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 $(IPR)$ probes the response of the system to three different such potentials and shows consistent agreement with results given by the Lyapunov exponent $Ly$: the greater $Ly(r)$ for the chaotic sequence as a function of the chaoticity parameter $r$, the greater the asymptotic value $IPR(r)$ for the large-system ground state.