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

Weslley Florentino de Oliveira, Giancarlo Queiroz Pellegrino

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.

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References


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

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

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