Winding Numbers, Complex Currents, and Non-Hermitian Localization
无序系统与神经网络
2009-10-31 v2 统计力学
超导电性
摘要
The nature of extended states in disordered tight binding models with a constant imaginary vector potential is explored. Such models, relevant to vortex physics in superconductors and to population biology, exhibit a delocalization transition and a band of extended states even for a one dimensional ring. Using an analysis of eigenvalue trajectories in the complex plane, we demonstrate that each delocalized state is characterized by an (integer) winding number, and evaluate the associated complex current. Winding numbers in higher dimensions are also discussed.
引用
@article{arxiv.cond-mat/9801111,
title = {Winding Numbers, Complex Currents, and Non-Hermitian Localization},
author = {Nadav M. Shnerb and David R. Nelson},
journal= {arXiv preprint arXiv:cond-mat/9801111},
year = {2009}
}
备注
4 pages, 2 figures