Non-Hermitian Delocalization and Eigenfunctions

Naomichi Hatano; David R. Nelson

doi:10.1103/physrevb.58.8384

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arXiv · cond-mat/9805195

Non-Hermitian Delocalization and Eigenfunctions

Naomichi Hatano·David R. Nelson

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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 non-zero 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.

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Naomichi Hatano, David R. Nelson. 1998-05-15. Non-Hermitian Delocalization and Eigenfunctions. https://doi.org/10.1103/physrevb.58.8384

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