基于开放系统Green函数的广义Chern数
Generalized Chern numbers based on open system Green's functions
摘要：
我们提出了另一种方法来研究开放量子系统的拓扑结构，直接依赖于格林函数，避免了需要构建一个有效的非厄米哈密顿。我们定义了一个依赖于能量的陈数的基础上的本征态的逆格林函数矩阵的系统，其中包含，在自能，所有的信息的影响的环境，相互作用，增益或损失。我们明确地计算这个拓扑不变的系统组成的一个单一的二维狄拉克锥，并发现它是半整数量子化时，某些假设的阻尼。远离这些条件，不能或通常不考虑在非厄米哈密顿的形式主义，我们发现，这样的量化通常是失去和陈数消失，在特殊情况下，它可以改变为整数量化。
英文摘要：
We present an alternative approach to studying topology in open quantum systems, relying directly on Green's functions and avoiding the need to construct an effective non-Hermitian Hamiltonian. We define an energy-dependent Chern number based on the eigenstates of the inverse Green's function matrix of the system which contains, within the self-energy, all the information about the influence of the environment, interactions, gain or losses. We explicitly calculate this topological invariant for a system consisting of a single 2D Dirac cone and find that it is half-integer quantized when certain assumptions over the damping are made. Away from these conditions, which cannot or are not usually considered within the formalism of non-Hermitian Hamiltonians, we find that such a quantization is usually lost and the Chern number vanishes, and that in special cases, it can change to integer quantization.
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