Quasi-stationary solutions in non-Hermitian systems

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.