Amplification or reduction of backscattering in a coherently amplifying or absorbing disordered chain

We study localization properties of a one-dimensional disordered system characterized by a random non-hermitean hamiltonian where both the randomness and the non-hermiticity arises in the local site-potential; its real part being random, and a constant imaginary part implying the presence of either a coherent absorption or amplification at each site. While the two-probe transport properties behave seemingly very differently for the amplifying and the absorbing chains, the logarithmic resistance u=ln(1+R4) where R4 is the 4-probe resistance gives a unified description of both the cases. It is found that the ensemble-averaged increases linearly with length indicating exponential growth of resistance. While in contrast to the case of Anderson localization (random hermitean matrix), the variance of u could be orders of magnitude smaller in the non-hermitean case, the distribution of u still remains non-Gaussian even in the large length limit.