Quasi-stationary solutions in non-Hermitian systems

TL;DR

This paper investigates quasi-stationary solutions in non-Hermitian systems, revealing their non-perturbative transition to eigenstates and identifying robust zero-energy modes in a non-Hermitian SSH model.

Contribution

It introduces the concept of quasi-stationary solutions in non-Hermitian lattices and analyzes their properties and transitions, expanding understanding of non-Hermitian skin effects.

Findings

Quasi-stationary solutions are approximately time-independent states.

Transition from quasi-stationary states to eigenstates is non-perturbative.

Identifies robust zero-energy modes in a non-Hermitian SSH model.

Abstract

Eigenstates exhibit localization at an open edge in a non-Hermitian lattice due to non-Hermitian skin effect. We here explore another interesting feature of non-Hermitian skin effect and predict quasi-stationary solutions, which are approximately time-independent. We show that the transition from such states to eigenstates is dramatically non-perturbative. We discuss that mathematically extending the boundary of a long non-Hermitian lattice to infinity can lead to nontrivial solution. We consider a non-Hermitian variant of the Su-Schrieffer-Heeger (SSH) model and predict non-topological but robust quasi-stationary zero energy modes.