Chern numbers and localization by non-Hermitean operators

J. Miller; P. B. Weichman

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arXiv · cond-mat/9909209

Chern numbers and localization by non-Hermitean operators

J. Miller·P. B. Weichman

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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.

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J. Miller, P. B. Weichman. 1999-09-14. Chern numbers and localization by non-Hermitean operators. https://arxiv.org/abs/cond-mat/9909209

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