Sparse one-dimensional discrete Dirac operators II: Spectral properties

Sparse one-dimensional discrete Dirac operators II: Spectral properties

We study spectral properties of some discrete Dirac operators with nonzero potential only at some sparse and suitably randomly distributed positions. As observed in the corresponding Schrödinger operators, we determine the Hausdorff dimension of its spectral measure and identify a sharp spectral tra...

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Veröffentlicht in:Journal of mathematical physics 2011-07, Vol.52 (7), p.073501-073501-21
Hauptverfasser: Carvalho, S. L., de Oliveira, C. R., Prado, R. A.
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Mathematical methods in physics
Mathematics
Physics
Quantum physics
Schrodinger equation
Sciences and techniques of general use
Spectrum analysis
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Zusammenfassung:We study spectral properties of some discrete Dirac operators with nonzero potential only at some sparse and suitably randomly distributed positions. As observed in the corresponding Schrödinger operators, we determine the Hausdorff dimension of its spectral measure and identify a sharp spectral transition from point to singular continuous.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3600536