Eigenvalues and localization of eigenvectors of non-Hermitian tridiagonal periodic random matrices are studied by means of the Hatano-Nelson deformation. The support of the spectrum undergoes a disk to annulus transition, with inner radius measured by the complex Thouless formula. The inner bounding circle and the annular halo are stuctures that correspond to the two-arcs 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. This disk-annulus transition is reminiscent of Feinberg and Zee's transition observed in full complex random matrices.
Disk-annulus transition and localization in random non-Hermitian tridiagonal matrices / L. G. Molinari, G. Lacagnina. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 42:39(2009), pp. 395204.395204.1-395204.395204.9.
Disk-annulus transition and localization in random non-Hermitian tridiagonal matrices
L. G. MolinariPrimo
;
2009
Abstract
Eigenvalues and localization of eigenvectors of non-Hermitian tridiagonal periodic random matrices are studied by means of the Hatano-Nelson deformation. The support of the spectrum undergoes a disk to annulus transition, with inner radius measured by the complex Thouless formula. The inner bounding circle and the annular halo are stuctures that correspond to the two-arcs 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. This disk-annulus transition is reminiscent of Feinberg and Zee's transition observed in full complex random matrices.File | Dimensione | Formato | |
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