论文标题
耗散量子系统中具有完全散装的对应关系的点间隙拓扑
Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
论文作者
论文摘要
从拓扑的角度研究了通过阻尼振荡器建模的耗散量子系统的光谱和动力学特性。与自然在开放边界条件下的物理晶格系统不同，Fock空间的界限性质有界限为理解和验证在半实力边界条件下的非弱者皮肤模式的独特设置，而在实际物理晶格中难以捉摸。提出了基于liouvillian超级操作机的复杂光谱的拓扑表征，可以鉴定出相关的拓扑保护皮肤模式的完整集，从而反映了逼真的材料中通常不存在的点间隙拓扑的完整散装对应关系。此外，即使量子系统纯粹是耗散性的，我们也会发现具有指数扩增的异常皮肤模式。我们的结果表明，目前对非拓扑拓扑问题的研究可以极大地受益于量子开放系统的研究，反之亦然。
The spectral and dynamical properties of dissipative quantum systems, as modeled by a damped oscillator in the Fock space, are investigated from a topological point of view. Unlike a physical lattice system that is naturally under the open boundary condition, the bounded-from-below nature of the Fock space offers a unique setting for understanding and verifying non-Hermitian skin modes under semi-infinity boundary conditions that are elusive in actual physical lattices. A topological characterization based on the complex spectra of the Liouvillian superoperator is proposed and the associated complete set of topologically protected skin modes can be identified, thus reflecting the complete bulk-boundary correspondence of point-gap topology generally absent in realistic materials. Moreover, we discover anomalous skin modes with exponential amplification even though the quantum system is purely dissipative. Our results indicate that current studies of non-Hermitian topological matter can greatly benefit research on quantum open systems and vice versa.
