Transport and spectral features in non-Hermitian open systems

TL;DR

This paper investigates the unique transport and spectral behaviors of a non-Hermitian disordered lattice, revealing all states are localized, eigenvalue condensation occurs, and transport proceeds via sudden jumps rather than diffusion.

Contribution

It uncovers the localization of all states in non-Hermitian disordered systems and describes a novel transport mechanism involving jumps between distant states.

Findings

All states are localized in the non-Hermitian system.

Eigenvalues form a fractallike structure and condense in the complex plane.

Transport occurs through sudden jumps, not diffusion.

Abstract

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.