1998/05/15 by Naomichi Hatano, David R. Nelson · 311 citations
Mathematics · Physics and Astronomy · #Delocalized electron #Eigenfunction #Eigenvalues and eigenvectors #Geometry #Ground state #Hermitian matrix #Mathematical analysis #Mathematics #Physics #Product (mathematics) #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quantum, superfluid, helium dynamics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.58.8384
published in Physical review. B, Condensed matter 58(13), 8384-8390 (American Physical Society) · 8 pages, 11 figures included
arxiv created 1998/05/15 · openalex publication_date 1998/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Recent literature on delocalization in non-Hermitian systems has stressed criteria based on sensitivity of eigenvalues to boundary conditions and the existence of a nonzero current. We emphasize here that delocalization also shows up clearly in eigenfunctions, provided one studies the product of left and right eigenfunctions, as required on physical grounds, and not simply the squared modulii of the eigenfunctions themselves. We also discuss the right and left eigenfunctions of the ground state in the delocalized regime and suggest that the behavior of these functions, when considered separately, may be viewed as ``intermediate'' between localized and delocalized.