Title: Braiding of dynamical eigenvalues of Hermitian bosonic Kitaev chains Show Chinese title

Title: 哈密顿玻色子基塔夫链的动力学本征值的编织

Abstract: In quantum mechanics, observables correspond to Hermitian operators, and the spectra are restricted to be real. However, the dynamics of the underlying fields may allow complex eigenvalues and therefore create the possibility of braiding structures. Here we study the braiding of dynamical eigenvalues in quantum systems by considering Hermitian bosonic Kitaev chains with multiple bands. The dynamics of the quantum fields in these systems are described by their dynamic matrices, which have complex eigenvalues. We show that there are symmetry constraints imposed on these dynamic eigenvalues. Despite these constraints, braiding is possible for frequencies within the effective gain and loss regions of the complex plane. We explicitly construct two- and three-strand braidings using the exceptional points found in the system and discuss possible implementations. Show Chinese abstract

Abstract: 在量子力学中，可观测量对应于厄米算符，其谱被限制为实数。 然而，底层场的动力学可能允许复数特征值，从而创造出编织结构的可能性。 在这里，我们通过考虑具有多带的厄米玻色子基塔耶夫链来研究量子系统中的动态特征值的编织。 这些系统中量子场的动力学由其动态矩阵描述，这些矩阵具有复数特征值。 我们表明，这些动态特征值受到对称性约束。 尽管存在这些约束，在复平面上的有效增益和损耗区域内的频率仍可以实现编织。 我们使用系统中发现的例外点显式构造了二股和三股编织，并讨论了可能的实现方式。