Transport and spectral features in non-Hermitian open systems

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.

Automated summary

The study focuses on the transport and spectral properties of a non-Hermitian one-dimensional disordered lattice, revealing that all states in the system are localized and the eigenvalue spectrum exhibits an intricate fractallike structure on the complex plane with eigenvalue condensation. Despite Anderson localization of all eigenstates, transport in the system seems to occur through sudden jumps between states rather than diffusion, suggesting a new mechanism for open non-Hermitian random systems.