Evolution with size in a locally periodic system: scattering and deterministic maps

In this paper, we study the evolution of the wavefunction with the system size in a locally periodic structure. In particular, we analyse the dependence of the wavefunction with the number of unit cells, which also reflects information about its spatial behaviour in the system. We reduce the problem...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 46; no. 23; pp. 235101 - 12
Main Authors Domínguez-Rocha, V, Martínez-Mares, M
Format Journal Article
LanguageEnglish
Published IOP Publishing 14.06.2013
Subjects
Bands
Chaos theory
Decay
Equivalence
Evolution
Mathematical analysis
Mean free path
Wavefunctions
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Summary:In this paper, we study the evolution of the wavefunction with the system size in a locally periodic structure. In particular, we analyse the dependence of the wavefunction with the number of unit cells, which also reflects information about its spatial behaviour in the system. We reduce the problem to a nonlinear map and find an equivalence of its energy regions of single periodicity and weak chaos, with the forbidden and allowed bands of the fully periodic system, respectively. At finite size the wavefunction decays exponentially with the system size, as well as in space, when the energy lies inside a region of single periodicity, while for energies in the weak chaotic region it never decays. At the transition between those regions the wavefunction still decays but in a q-exponential form; we find that the decay length is a half of the mean free path, which is larger than the lattice constant.
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/46/23/235101