Winding Numbers, Complex Currents, and Non-Hermitian Localization

Details Winding Numbers, Complex Currents, and Non-Hermitian Localization Winding Numbers, Complex Currents, and Non-Hermitian Localization

1998-01-12

arxiv.org/abs/cond-mat/9801111v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.80.5172

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.

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