1999/09/14 by J. Miller, Jonathan Miller, Miller, J. +3
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Mechanics and Applications #Radioactive Decay and Measurement Techniques #cond-mat.mes-hall
paper · pdf · doi:10.48550/arxiv.cond-mat/9909209
arxiv created 1999/09/14 · openalex publication_date 1999/09/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.