  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.
