We study numerically the localization properties of a two-channel quasi-one-dimensional Anderson model with uncorrelated diagonal disorder within the nearest-neighbor tight-binding approximation. We calculate and analyze the disorder-averaged transmittance and the Lyapunov exponent. We find that the localization of the entire system is enhanced by increasing the interchain hopping strength t̃. From the numerical investigation of the energy dependence of the Lyapunov exponent for many different interchain hopping strengths, we find that apart from the band center anomaly, which usually occurs in strictly one-dimensional disordered systems, additional anomalies appear at special spectral points. They are found to be associated with the interchain hopping strength and occur at E = ± t̃/2 and ± t̃. We find that the anomalies at E = ± t̃ are associated with the π-coupling occurring within one energy band and those at E = ± t̃/2 are associated with the π-coupling occurring between two different energy bands. Despite having a similar origin, these two anomalies have distinct characteristics in their dependence on the strength of disorder. We also show that for a suitable range of parameter values, effectively delocalized states are observed in finite-size systems.

We study numerically the localization properties of eigenstates in a onedimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the on-site potential. We calculate the averaged participation number, the Shannon entropy and the structural entropy as a function of other parameters. We show that, in the presence of an imaginary random potential, all eigenstates are localized in the thermodynamic limit and strong anomalous Anderson localization occurs at the band center. In contrast to the usual localization anomalies where a weaker localization is observed, the localization of the eigenstates near the band center is strongly enhanced in the present non-Hermitian model. This phenomenon is associated with the occurrence of a large number of strongly-localized states with pure imaginary energy eigenvalues.

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