Spectral Curves and Localization in Random Non-Hermitian Tridiagonal Matrices
arXiv:0905.2489 · doi:10.1088/1751-8113/42/39/395204
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.
5 pages, 9 figures, typographical error corrected in references