Spectral Curves and Localization in Random Non-Hermitian Tridiagonal Matrices
Mathematical Physics
2009-09-14 v2 math.MP
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.
Cite
@article{arxiv.0905.2489,
title = {Spectral Curves and Localization in Random Non-Hermitian Tridiagonal Matrices},
author = {L. G. Molinari and G. N. Lacagnina},
journal= {arXiv preprint arXiv:0905.2489},
year = {2009}
}
Comments
5 pages, 9 figures, typographical error corrected in references