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Chaos-based potentials in the one-dimensional tight-binding model probed by the inverse participation ratio

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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 \(\mathrm{Ly}\): the greater \(\mathrm{Ly}(r)\) 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.

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Notes

  1. To the best of the authors’ knowledge, this was first proposed by C. R. de Oliveira (personal communication, 2002).

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Acknowledgements

The authors thank sincerely Luciano Coutinho dos Santos and Luiz Argel Poveda Calvino for discussions on nonchaotic attractors. Also, the authors thank very much the anonymous Referees for their invaluable advice.

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Author notes

  1. Weslley Florentino de Oliveira

    Present address: Departamento de Ensino, IFNMG-Instituto Federal do Norte de Minas Gerais, Pirapora, MG, Brazil

Authors and Affiliations

  1. Programa de Pós-graduação em Modelagem Matemática e Computacional, CEFET-MG-Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG, Brazil

    Weslley Florentino de Oliveira

  2. Departamento de Matemática, CEFET-MG-Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG, Brazil

    Giancarlo Queiroz Pellegrino

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  1. Weslley Florentino de Oliveira
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Correspondence to Giancarlo Queiroz Pellegrino.

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Communicated by Jose Alberto Cuminato.

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de Oliveira, W.F., Pellegrino, G.Q. Chaos-based potentials in the one-dimensional tight-binding model probed by the inverse participation ratio. Comp. Appl. Math. 37, 3995–4006 (2018). https://doi.org/10.1007/s40314-017-0561-7

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  • DOI: https://doi.org/10.1007/s40314-017-0561-7

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