Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov?de Gennes Hamiltonian and its application to non-Hermitian skin effect
Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov?de Gennes Hamiltonian and its application to non-Hermitian skin effect
复制标题
玻色子格林函数的边界依赖性动力学不稳定性：耗散 Bogoliubov?de Gennes 哈密顿量及其在非厄米集肤效应中的应用
DOI：
10.1103/physrevb.105.224301
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发表时间：
2022
影响因子：
3.7
通讯作者：
Okuma Nobuyuki
中科院分区：
文献类型：
--
作者：
Hudson Thomas;van Meurs Patrick;Peletier Mark;R. Oizumi and H. Inaba;Okuma Nobuyuki
凝聚体的玻色子激发能谱由非厄米哈密顿量的谱给出，该非厄米哈密顿量一般由玻色子Bogoliubov-de Gennes（BdG）哈密顿量构造，即使该系统本质上是厄米哈密顿量。换句话说，两种类型的非厄米性可以共存：一种来自玻色子BdG性质，另一种来自开放量子性质。在本文中，我们提出了边界相关的动力学不稳定性。首先在Nambu空间中用绿色函数定义了玻色耗散BdG哈密顿量，并讨论了相应的非厄米哈密顿量的正确的粒子-空穴对称性。然后，我们构建了一个模型的边界相关的动力学不稳定性，使它满足正确的粒子-空穴对称性。在这个模型中，打破粒子数守恒的反常项表示BdG性质的非厄米性，而正常项由耗散的Hatano-Nelson模型给出。由于两种非厄米性之间的竞争，光谱的虚部可以是正的，而不需要正常部分的放大和导致朗道不稳定性的粒子-空穴带接触的帮助。这将导致边界相关的动力学不稳定性下的非厄米趋肤效应的非厄米哈密顿边界条件的Bogoliubov谱的谱的强依赖性。
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.