Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect
The energy spectrum of bosonic excitations from a condensate is given by the spectrum of a non-Hermitian Hamiltonian constructed from a bosonic Bogoliubov-de Gennes (BdG) Hamiltonian in general even though the system is essentially Hermitian. In other words, two types of non-Hermiticity can coexist: one from the bosonic BdG nature and the other from the open quantum nature. In this paper, we propose boundary-dependent dynamical instability. We first define the bosonic dissipative BdG Hamiltonian in terms of Green's function in Nambu space and discuss the correct particle-hole symmetry of the corresponding non-Hermitian Hamiltonian. We then construct a model of the boundary-dependent dynamical instability so that it satisfies the correct particle-hole symmetry. In this model, an anomalous term that breaks the particle number conservation represents the non-Hermiticity of the BdG nature, while a normal term is given by a dissipative Hatano-Nelson model. Thanks to the competition between the two types of non-Hermiticity, the imaginary part of the spectrum can be positive without the help of the amplification of the normal part and the particle-hole band touching that causes the Landau instability. This leads to the boundary-dependent dynamical instability under the non-Hermitian skin effect, -strong dependence of spectra on boundary conditions for non-Hermitian Hamiltonians-, of the Bogoliubov spectrum.
Selection Rule for Topological Amplifiers in Bogoliubov de Gennes Systems
动力学不稳定性是玻色子系统的一个固有特征，它由Bogoliubov de Geenes（BdG）哈密顿量描述。由于它会导致BdG系统崩溃，因此通常认为应该避免。最近，已经有很多努力来利用这种不稳定性的好处，创建一个拓扑放大器，具有稳定的体带，但不稳定的边缘模式，可以以指数快速填充。我们提出了一个定理，用于确定稳定的状态与能量足够远离零，在一个非常规的交换子之间的数量守恒部分和数量nonconserving部分的BdG哈密顿量。我们将该定理应用于Galilo等人[Phys. Rev. Lett，115，245302（2015）]的模型的推广，用于通过淬灭过程在蜂窝晶格中的相互作用自旋1原子系统中创建拓扑放大器。我们用这个模型来说明如何消失的非常规换向器选择系统的对称性，使其体状态是稳定的（弱）配对相互作用。我们发现，只要保持时间反演对称性，我们的系统可以像一个拓扑放大器，即使在现场交错的潜力，打破反演对称性的存在。
