Zhong Wnag

Institute for Advanced Study
Tsinghua University
China

Non-Hermitian skin effect and non-Bloch band theory: Topology and dynamics

Non-Hermitian operators provide a unifying language for many open systems. One of the counterintuitive features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely, that all the eigenstates are exponentially localized at the boundary of the system. It implies a dramatic departure from the standard Bloch band theory of Hermitiansystems, and causes failures of conventional topological invariants in predicting the topological edge modes. In this talk, I will introduce the basic idea of the recently proposed non-Bloch band theory of non-Hermitian systems. In the first part, it will be shown that the non-Bloch topological invariants defined in the generalized Brillouin zone faithfully predict the topological edge modes, embodying a generalized (non-Bloch) bulk-boundary correspondence. In the second part, I will show that the non-Hermitian skin effect has interesting consequences in the dynamics of open quantum systems governed by the master equation. Specifically, the non-Hermitian skin effect induces a "chiral damping" with novel long-time behaviors.

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