REAL EIGENVALUES IN THE NON-HERMITIAN ANDERSON MODEL

• 成果类型: Article
• 署名作者: Goldsheid, Ilya; Sodin, Sasha
• 署名单位: University of London; Queen Mary University London; Tel Aviv University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1383
• 发表日期: 2018
• 页码: 3075-3093
• 关键词: tight-binding model; density-of-states; RANDOM MATRICES; large disorder; localization; bernoulli; delocalization; PRODUCTS; THEOREMS; Spacings

摘要

The eigenvalues of the Hatano-Nelson non-Hermitian Anderson matrices, in the spectral regions in which the Lyapunov exponent exceeds the non-Hermiticity parameter, are shown to be real and exponentially close to the Hermitian eigenvalues. This complements previous results, according to which the eigenvalues in the spectral regions in which the non-Hermiticity parameter exceeds the Lyapunov exponent are aligned on curves in the complex plane.