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.

arXiv comment18 pages, 7 figures, article accepted for publication in Computational and Applied Mathematics

References in corpus (8)

• Fluctuations of the inverse participation ratio at the Anderson transition
• Strange Nonchaotic Attractors
• Generalized Inverse Participation Ratio as a Possible Measure of Localization for Interacting Systems
• Intermittency Route to Strange Nonchaotic Attractors
• Remarks on the Spectral Properties of Tight Binding and Kronig-Penney Models with Substitution Sequences
• Analytical results for Scaling Properties of the Spectrum of the Fibonacci Chain
• Quantum Return Probability for Substitution Potentials
• Persistent current and Drude weight in one-dimensional rings with substitution potentials