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 a remarkable phenomenon of non-Hermitian systems. Inspired by the presence of the non-Hermitian skin effect,...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Mao, Liang, Deng, Tianshu, Zhang, Pengfei
Format: Article
Language:English
Subjects:
Boundary conditions
Eigenvalues
Eigenvectors
Evolution
Green's functions
Skin effect
Wave packets
Online Access:Get full text
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Summary: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 a remarkable phenomenon of non-Hermitian systems. Inspired by the presence of the non-Hermitian skin effect, we study the evolution of wave-packets in non-Hermitian systems, which can be determined using the single-particle Green's function. Surprisingly, we find that in the thermodynamical limit, the Green's function does not depend on boundary conditions, despite the presence of skin effect. We proffer a general proof for this statement in arbitrary dimension with finite hopping range, with an explicit illustration in the non-Hermitian Su-Schrieffer-Heeger model. We also explore its applications in non-interacting open quantum systems described by the master equation, where we demonstrate that the evolution of the density matrix is independent of the boundary condition.
ISSN:2331-8422
DOI:10.48550/arxiv.2104.09896