Zhang Weihua, Zhang Xiaodong, Che Jiongning, Lu Junjie, Miski-Oglu M, Dietz Barbara
Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China.
Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea.
Phys Rev E. 2022 Oct;106(4-1):044209. doi: 10.1103/PhysRevE.106.044209.
We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that are connected at vertices. On the bonds, they are governed by the one-dimensional Schrödinger equation with boundary conditions imposed at the vertices. The resulting transport properties through the vertices may be expressed in terms of a vertex scattering matrix. Quantum graphs with incommensurate bond lengths attracted interest within the field of quantum chaos because, depending on the characteristics of the vertex scattering matrix, its wave dynamic may exhibit features of a typical quantum system with chaotic counterpart. In distinction to microwave networks, which serve as an experimental model of quantum graphs with Neumann boundary conditions, the vertex scattering matrices associated with a waveguide system depend on the wave number and the wave functions can be determined experimentally. We analyze the spectral properties of microwave waveguide systems with preserved and partially violated time-reversal invariance, and the properties of the associated wave functions. Furthermore, we study properties of the scattering matrix describing the measurement process within the framework of random matrix theory for quantum chaotic scattering systems.
我们报告了用微波波导系统进行的实验，并证明在单个横向模式的频率范围内，它们可作为封闭和开放量子图的模型。这些量子图由在顶点处相连的键组成。在键上，它们由一维薛定谔方程控制，并在顶点处施加边界条件。通过顶点的传输特性可以用顶点散射矩阵来表示。具有不相称键长的量子图在量子混沌领域引起了关注，因为根据顶点散射矩阵的特性，其波动动力学可能表现出具有混沌对应物的典型量子系统的特征。与作为具有诺伊曼边界条件的量子图实验模型的微波网络不同，与波导系统相关的顶点散射矩阵取决于波数，并且波函数可以通过实验确定。我们分析了具有保留和部分违反时间反演不变性的微波波导系统的光谱特性以及相关波函数的特性。此外，我们在量子混沌散射系统的随机矩阵理论框架内研究了描述测量过程的散射矩阵的特性。
