论文标题
微波网络中的边缘开关转换
The edge switch transformation in microwave networks
论文作者
论文摘要
我们研究了在边缘开关操作之前和之后，四个Vertex微波网络的共振光谱模拟了两个量子图，并在边缘开关操作之前和之后具有部分违反的时间反转不变性。我们通过实验表明，在边缘开关操作下，保留时间逆转对称性的微波网络的光谱是级别的1级交错，即$ν_{n-r} \ leq \tildeν_{n} {n} \ leq leq leq leq leq leq n+r} $ Aizenman，H。Schanz，U。Smilansky和S. Warzel，Acta Phys。 pol。 a {\ bf 132}，1699（2017）]。在这里，我们用$ \ {ν_{n} \} _ {n = 1}^{\ infty} $和$ \ {\tildeν_{n} \} _ {我们证明了光谱移位$Δn$的实验分布$ p（Δn）$接近理论。此外，我们通过实验表明，对于具有部分违反时间逆转对称性的四个vertex网络，光谱是级别1的交错。我们的实验结果补充了对具有违反时间反转对称性的量子图进行的数值计算。在这种情况下，边缘开关转换还导致级别1交错的光谱。此外，我们证明，对于模拟图形的微波网络，违反的时间反向对称性频谱移位$Δn$的实验分布$ p（Δn）$在实验中与数值不确定同意。
We investigated the spectra of resonances of four-vertex microwave networks simulating both quantum graphs with preserved and with partially violated time-reversal invariance before and after an edge switch operation. We show experimentally that under the edge switch operation the spectra of the microwave networks with preserved time reversal symmetry are level-1 interlaced, i.e., $ν_{n-r}\leq \tilde ν_{n}\leq ν_{n+r}$, where $r=1$, in agreement with the recent theoretical predictions of [M. Aizenman, H. Schanz, U. Smilansky, and S. Warzel, Acta Phys. Pol. A {\bf 132}, 1699 (2017)]. Here, we denote by $\{ν_{n}\}_{n=1}^{\infty}$ and $\{\tilde ν_{n}\}_{n=1}^{\infty}$ the spectra of microwave networks before and after the edge switch transformation. We demonstrate that the experimental distribution $P(ΔN)$ of the spectral shift $ΔN$ is close to the theoretical one. Furthermore, we show experimentally that in the case of the four-vertex networks with partially violated time reversal symmetry the spectra are level-1 interlaced. Our experimental results are supplemented by the numerical calculations performed for quantum graphs with violated time-reversal symmetry. In this case the edge switch transformation also leads to the spectra which are level-1 interlaced. Moreover, we demonstrate that for microwave networks simulating graphs with violated time-reversal symmetry the experimental distribution $P(ΔN)$ of the spectral shift $ΔN$ agrees within the experimental uncertainly with the numerical one.
