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

TL;DR

This paper investigates how chaos-based potentials affect localization in a one-dimensional tight-binding model, using the inverse participation ratio and Lyapunov exponent to analyze the system's response to different chaotic potentials.

Contribution

It introduces a method to simulate disorder in crystalline lattices using chaos-based potentials and correlates the inverse participation ratio with the Lyapunov exponent to understand localization.

Findings

IPR increases with Lyapunov exponent for chaotic potentials

Chaos-based potentials effectively simulate disorder in 1D lattices

Results show consistent correlation between IPR and Lyapunov exponent

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.