Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics

• URL: http://arxiv.org/abs/2104.09896v1
• Date: Tue, 20 Apr 2021 11:12:03 GMT
• Title: Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics
• Authors: Liang Mao, Tianshu Deng and Pengfei Zhang
• Abstract summary: We study the evolution of wave-packets in non-Hermitian systems. Surprisingly, we find that in the thermodynamical limit, the Green's function does not depend on boundary conditions.
• Score: 7.660448224829509
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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