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arXiv · 0905.2489

Spectral Curves and Localization in Random Non-Hermitian Tridiagonal Matrices

L. G. Molinari·G. N. Lacagnina
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Abstract

Eigenvalues and eigenvectors of non-Hermitian tridiagonal periodic random matrices are studied by means of the Hatano-Nelson deformation. The deformed spectrum is annular-shaped, with inner radius measured by the complex Thouless formula. The inner bounding circle and the annular halo are stuctures that correspond to the two-arc and wings observed by Hatano and Nelson in deformed Hermitian models, and are explained in terms of localization of eigenstates via a spectral duality and the Argument principle.

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L. G. Molinari, G. N. Lacagnina. 2009-05-18. Spectral Curves and Localization in Random Non-Hermitian Tridiagonal Matrices. https://doi.org/10.1088/1751-8113%2F42%2F39%2F395204

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