Delocalization in an Open One-Dimensional Chain in an Imaginary Vector Potential

We calculate the moments of transmittance, [T-n], through an open disordered 1D system with an imaginary vector potential, ih. It turns out that the critical 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 different. They also differ from the corresponding curves for [lnT] and that of the 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 in localized eigenstates of the non-Hermitian model.