Delocalization in an open one-dimensional chain in an imaginary vector potential

We calculate the moments of transmittance, [T-n], through an open disordere d 1D system with an imaginary vector potential, ih. It turns out that the c ritical curves on the complex energy plane, C-n, where an exponential decay of the appropriate quantity is changed by a power-law one, are all differe nt. They also differ from the corresponding curves for [lnT] and that of th e averaged one-particle Green's function; the latter defines the density of states support for the open system. This results from the absence of self- averaging in disordered 1D systems and reflects higher-order correlations i n localized eigenstates of the non-Hermitian model.