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

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

Disordered Systems and Neural Networks 2018-01-25 v2

Authors: Weslley Florentino de Oliveira , Giancarlo Queiroz Pellegrino

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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.

Keywords

chaos-based potentials tight-binding model inverse participation ratio lyapunov exponent disorder crystalline lattices

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@article{arxiv.1712.07729,
  title  = {Chaos-based Potentials in the One-dimensional Tight-binding Model Probed by the Inverse Participation Ratio},
  author = {Weslley Florentino de Oliveira and Giancarlo Queiroz Pellegrino},
  journal= {arXiv preprint arXiv:1712.07729},
  year   = {2018}
}

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

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

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