Non-Hermitian Delocalization and Eigenfunctions

Details Non-Hermitian Delocalization and Eigenfunctions Non-Hermitian Delocalization and Eigenfunctions

1998-05-15

arxiv.org/abs/cond-mat/9805195v1

Phys. Rev. B 58, 8384--8390 (1998)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 11 figures included

Scientific paper

10.1103/PhysRevB.58.8384

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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