We study the transport and spectral properties of a non-Hermitian one-dimensional disordered lattice, the diagonal matrix elements of which are random complex variables taking both positive (loss) and negative (gain) imaginary values: Their distribution is either the usual rectangular one or a binary pair-correlated one possessing, in its Hermitian version, delocalized states, and unusual transport properties. Contrary to the Hermitian case, all states in our non-Hermitian system are localized. In addition, the eigenvalue spectrum, for the binary pair-correlated case, exhibits an unexpected intricate fractallike structure on the complex plane and with increasing non-Hermitian disorder, the eigenvalues tend to coalesce in particular small areas of the complex plane, a feature termed "eigenvalue condensation". Despite the strong Anderson localization of all eigenstates, the system appears to exhibit transport not by diffusion but by a new mechanism through sudden jumps between states located even at distant sites. This seems to be a general feature of open non-Hermitian random systems. The relation of our findings to recent experimental results is also discussed.
Observation of Erratic Non-Hermitian Skin Localization and Transport
Nanjing University（南京大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；Politecnico di Milano（米兰理工大学）；IFISC (UIB-CSIC), Instituto de Fisica Interdisciplinary Sistemas Complejos（复杂系统跨物理研究所（巴伊拉大学-西班牙国家科研委员会））
