Non-Hermitian delocalization and eigenfunctions

Recent literature on delocalization in non-Hermitian systems has stressed\ncriteria based on sensitivity of eigenvalues to boundary conditions and the\nexistence of a non-zero current. We emphasize here that delocalization also\nshows up clearly in eigenfunctions, provided one studies the product of left-\nand right-eigenfunctions, as required on physical grounds, and not simply the\nsquared modulii of the eigenfunctions themselves. We also discuss the right-\nand left-eigenfunctions of the ground state in the delocalized regime and\nsuggest that the behavior of these functions, when considered separately, may\nbe viewed as ``intermediate'' between localized and delocalized.\n