Characterization of Spectrum and Eigenvectors of the Schrödinger Operator with Chaotic Potentials

Authors

  • Weslley Florentino de Oliveira Instituto Federal do Norte de Minas Gerais - IFNMG
  • Giancarlo Queiroz Pellegrino Centro Federal de Educação Tecnológica de Minas Gerais - CEFETMG

DOI:

https://doi.org/10.5540/tema.2014.015.02.0203

Abstract

Chaotic sequences are sequences generated by chaotic maps. A particle moving in a one-dimensional space has its behavior modeled according to the time-independent Schrödinger equation. The tight-binding approximation enables the use of chaotic sequences as the simulation of quantum potentials in the discretized version of the Schrödinger equation. The present work consists of the generation and characterization of spectral curves and eigenvectors of the Schrödinger operator with potentials generated by chaotic sequences, as  well as their comparison with the curves generated by periodic, peneperiodic and random sequences. This comparison is made by calculating in each case the inverse participation ratio as a function of the system size.

Author Biographies

Weslley Florentino de Oliveira, Instituto Federal do Norte de Minas Gerais - IFNMG

Professor Mestre do departamento de Matemática do IFNMG câmpus Pirapora.

Giancarlo Queiroz Pellegrino, Centro Federal de Educação Tecnológica de Minas Gerais - CEFETMG

Professor doutor do Departamento de Física e Matemática do CEFETMG

References

Ashcroft, N. W.; Mermin, N. D. Solid State Physics, Rinehart & Winston, Philadelphia, 1976.

Anderson, P. W. Absence of diffusion in certain random lattices. Physical Review, v. 109, pp. 1942–1958, (1958).

Oliveira, C. R. Private communication, 2002.

Hilborn, R. C. Chaos and Nonlinear Dynamics, Oxford University Press, Oxford, 2000.

Monthus, C.; Garel, T. Anderson localization of phonons in dimension d=1, 2, 3: Finite-size properties of the inverse participation ratios of eigenstates. Physical Review B, v. 81, pp. 224208–1 – 224208–9, (2010).

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Published

2014-09-06

How to Cite

Oliveira, W. F. de, & Pellegrino, G. Q. (2014). Characterization of Spectrum and Eigenvectors of the Schrödinger Operator with Chaotic Potentials. Trends in Computational and Applied Mathematics, 15(2). https://doi.org/10.5540/tema.2014.015.02.0203

Issue

Vol. 15 No. 2 (2014)

Section

Original Article

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