Chern numbers and localization by non-Hermitean operators
Mesoscale and Nanoscale Physics
2007-05-23 v1
Abstract
In Hermitean quantum mechanics, extended current-carrying states are distinguished from localized ones by their non-zero Chern number. We generalize the notion of Chern number to non-Hermitean localization problems such as tiltedflux lines in type-II superconductors with line defects and passive scalar transport in random vorticity fields. We find that the usualpoint eigenvalue degeneracies that occur in the Hermitean case are now loops bounding a branch cut sheet with the same quantized total Berry flux, and hence Chern number, as the original point. If a loop cuts the integration surface non-quantized contributions to the total flux result.
Cite
@article{arxiv.cond-mat/9909209,
title = {Chern numbers and localization by non-Hermitean operators},
author = {J. Miller and P. B. Weichman},
journal= {arXiv preprint arXiv:cond-mat/9909209},
year = {2007}
}