Evolving disorder in non-Hermitian lattices

TL;DR

This paper explores how evolving disorder in non-Hermitian lattices influences wave transport, revealing that disorder periodicity can suppress localization, induce diffusion, or modulate drift and localization effects, offering new control mechanisms.

Contribution

It introduces the concept of evolving disorder in non-Hermitian lattices and demonstrates its effects on transport phenomena, a novel approach compared to static disorder studies.

Findings

Short disorder periods suppress localization and promote diffusion.

Longer periods lead to jumpy wave evolution.

Disorder period influences drift velocity and localization in Hatano-Nelson lattices.

Abstract

The impact of disorder on wave transport has been extensively studied in Hermitian systems, where static randomness gives rise to Anderson localization. In non-Hermitian lattices, static disorder can lead to peculiar transport features, including jumpy wave evolution. By contrast, much less is known about how transport is modified when the on-site disorder evolves during propagation. Here we address this problem by investigating two pertinent non-Hermitian lattice models with disorder altered at regular intervals, characterized by a finite disorder period. In lattices with symmetric couplings and complex on-site disorder, short disorder periods suppress localization and give rise to diffusion-like spreading, while longer periods allow the emergence of jumps. In Hatano-Nelson lattices with real on-site disorder, the non-Hermitian skin effect asymptotically dominates regardless of the disorder strength, while the disorder period reshapes the drift velocity and modulates its competition with Anderson localization. These results establish evolving disorder as a novel way of tuning non-Hermitian transport.