Boundary condition independence of non-Hermitian Hamiltonian dynamics

Non-Hermitian skin effect, namely that the eigenvalues and eigenstates of a non-Hermitian tight-binding Hamiltonian have significant differences under open or periodic boundary conditions, is remarkable phenomenon systems. Inspired by presence we study evolution wave-packets in systems, which can be determined using single-particle Green's function. Surprisingly, find thermodynamical limit, function does not depend on despite effect. We proffer general proof for this statement arbitrary dimension with finite hopping range, an explicit illustration Su-Schrieffer-Heeger model. also explore its applications non-interacting quantum systems described master equation, where demonstrate density matrix independent condition.