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 the 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. 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.

我们在数值上研究了短期和长期相关性对一维无序晶格中本征态的定位特性的影响，该晶格的特征是随机的非Hermitian哈密顿量，其中现场势的虚部是随机的。我们计算参与人数与无序和相关强度的关系。在短距离情况下，当相关长度足够小时，我们发现存在一个无序强度的临界值，在该值以下，随着相关长度的增加，增强强度升高，而在该强度之上，则出现局部抑制。在相关长度较大的区域中，在所有情况下都抑制了定位。当无序强度和相关指数发生变化时，对于远程相关也会获得类似的行为。与远距离相关的实数随机电位不同，在远距离相关的虚数随机电位中未发现定位转变的信号。在存在长距离相关性的情况下定位增强的区域中，我们发现增强发生在整个能带中，但在带中心附近最强。另外，我们发现在远距离相关情况下，异常定位增强效应发生在带中心附近。