Noise-Enhanced Self-Healing Dynamics in Non-Hermitian Systems

TL;DR

This paper explores how stochastic noise can enhance self-healing in non-Hermitian systems, revealing that noise can both prolong and stabilize wave profile recovery through different mechanisms.

Contribution

It systematically analyzes the constructive role of noise in non-Hermitian self-healing, introducing Lyapunov exponent analysis and perturbation theory for different noise regimes.

Findings

Weak noise prolongs the self-healing window by aligning Lyapunov exponents.

Strong noise stabilizes profile recovery via effective drift-diffusion dynamics.

Analytical frameworks elucidate noise-induced enhancements in non-Hermitian systems.

Abstract

Self-healing is the ability of a wave packet to spontaneously restore its spatial profile after scattering. As an emergent feature of non-unitary dynamics, it has attracted significant interest in non-Hermitian physics. Here, we systematically investigate how stochastic noise influences edge self-healing. Counterintuitively, we find that noise can constructively enhance this dynamical process. Weak noise prolongs the self-healing window by aligning the finite-time Lyapunov exponent of the reference state with the maximum imaginary part of the energy spectrum. Remarkably, strong noise universally stabilizes asymptotic profile recovery across the entire spectrum by inducing an effective non-unitary drift-diffusion dynamics. We analytically elucidate these distinct mechanisms using a general finite-time Lyapunov exponent analysis, complemented by a dedicated perturbation theory for the strong-noise regime. Our results provide concrete guidance for realizing robust non-Hermitian dynamics in realistic noisy environments.