Non-Hermitian delocalization and eigenfunctions

Naomichi Hatano and David R. Nelson
Phys. Rev. B 58, 8384 – Published 1 October 1998
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Abstract

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.

  • Received 15 May 1998

DOI:https://doi.org/10.1103/PhysRevB.58.8384

©1998 American Physical Society

Authors & Affiliations

Naomichi Hatano

  • Theoretical Division, MS-B262, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

David R. Nelson

  • Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138

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Issue

Vol. 58, Iss. 13 — 1 October 1998

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