# Numerical study of the transverse localization of waves in one-dimensional lattices with randomly distributed gain and loss: Effect of disorder correlations

## TL;DR

This study numerically investigates how short- and long-range correlations in a one-dimensional disordered lattice with random gain and loss influence wave localization, revealing critical disorder strengths and correlation effects on localization behavior.

## Contribution

It provides new insights into the effects of correlation length and disorder strength on wave localization in non-Hermitian lattices with imaginary disorder.

## Key findings

- Localization is enhanced or suppressed depending on disorder strength and correlation length.
- Long-range correlations suppress localization across the entire energy band.
- No localization transition signature is observed in long-range correlated imaginary potentials.

## Abstract

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.