  We study numerically the effects of short- and long-range correlations on the
localization properties of the eigenstates in a one-dimensional disordered
lattice characterized by a random non-Hermitian Hamiltonian, where the
imaginary part of the on-site potential is random. We calculate participation
number versus strengths of disorder and correlation. In the short-ranged case
and when the correlation length is sufficiently small, we find that there
exists a critical value of the disorder strength, below which enhancement and
above which suppression of localization occurs as the correlation length
increases. In the region where the correlation length is larger, localization
is suppressed in all cases. A similar behavior is obtained for long-range
correlations as the disorder strength and the correlation exponent are varied.
Unlike in the case of a long-range correlated real random potential, no
signature of the localization transition is found in a long-range correlated
imaginary random potential. In the region where localization is enhanced in the
presence of long-range correlations, we find that the enhancement occurs in the
whole energy band, but is strongest near the band center. In addition, we find
that the anomalous localization enhancement effect occurs near the band center
in the long-range correlated case.
