Universal non-Hermitian transport in disordered systems

TL;DR

This paper reveals universal wave propagation behaviors in disordered non-Hermitian systems, showing how non-Hermiticity enables transport despite localization, with results depending on the imaginary-part density of states.

Contribution

It introduces a universal framework for understanding non-Hermitian wave transport in disordered systems, highlighting new scaling laws and the influence of the imaginary-part density of states.

Findings

Logarithmically suppressed sub-ballistic transport in three classes of imaginary-part density of states.

Two types of subdiffusion with exponents depending on spatial dimensions.

Fundamental differences between Hermitian and non-Hermitian Anderson localization.

Abstract

In disordered Hermitian systems, localization of energy eigenstates prohibits wave propagation. In non-Hermitian systems, however, wave propagation is possible even when the eigenstates of Hamiltonian are exponentially localized by disorders. We find in this regime that non-Hermitian wave propagation exhibits novel universal scaling behaviors without Hermitian counterpart. Furthermore, our theory demonstrates how the tail of imaginary-part density of states dictates wave propagation in the long-time limit. Specifically, for the three typical classes, namely the Gaussian, the uniform, and the linear imaginary-part density of states, we obtain logarithmically suppressed sub-ballistic transport, and two types of subdiffusion with exponents that depend only on spatial dimensions, respectively. Our work highlights the fundamental differences between Hermitian and non-Hermitian Anderson localization, and uncovers unique universality in non-Hermitian wave propagation.