Experimental investigation of distributions of the off-diagonal elements of the scattering and the Wigner's $\hat K$ matrices for networks with broken time reversal invariance
我们提出了一个广泛的实验研究的散射矩阵$\hat S$和Wigner的反应$\hat K$ -矩阵的非对角元素的实部和虚部的分布与破缺时间（$T$）反转不变性的开放微波网络。为了打破$T$不变性，应用了微波法拉第循环器。将散射矩阵$\hat S$非对角元实部和虚部的实验分布与超对称随机矩阵理论[A. Nock，S. Kumar，H.- J. Sommers和T. Guhr，Annals of Physics { \bf 342}，103-132（2014）]。此外，我们还证明了实验结果与最近在随机矩阵理论（RMT）的高斯幺正系综框架内得到的Wigner反应$\hat K$ -矩阵的非对角元素实部和虚部分布的预测非常一致[S. B. Fedeli和Y. V. Fyodorov，J. Phys. A：Math. Theor. { \bf 53}，165701（2020）]。这两种理论都包括损耗作为可调参数，因此很好地适应了实验验证。
英文摘要：
We present an extensive experimental study of the distributions of the real and imaginary parts of the off-diagonal elements of the scattering matrix $\hat S$ and the Wigner's reaction $\hat K$-matrix for open microwave networks with broken time ($T$) reversal invariance. Microwave Faraday circulators were applied in order to break $T$-invariance. The experimental distributions of the real and imaginary parts of the off-diagonal entries of the scattering matrix $\hat S$ are compared with the theoretical predictions from the supersymmetry random matrix theory [A. Nock, S. Kumar, H.-J. Sommers, and T. Guhr, Annals of Physics {\bf 342}, 103-132 (2014)]. Furthermore, we show that the experimental results are in very good agreement with the recent predictions for the distributions of the real and imaginary parts of the off-diagonal elements of the Wigner's reaction $\hat K$-matrix obtained within the framework of the Gaussian unitary ensemble of random matrix theory (RMT) [S. B. Fedeli and Y. V. Fyodorov, J. Phys. A: Math. Theor. {\bf 53}, 165701 (2020)]. Both theories include losses as tunable parameters and are therefore well adapted to the experimental verification.
Coherent-state path integral calculation of the Wigner function
We consider a set of operators hat{x}=(hat{x}_1,..., hat{x}_N) with diagonal representatives P(n) in the space of generalized coherent states |n>; hat{x}=int dn P(n) |n><n|. We regularize the coherent-state path integral as a limit of a sequence of averages <.>_L over polygonal paths with L vertices {n_1...L}. The distribution of the path centroid bar{P}=(1/L) sum_{i=1} ^{L}P(n_i) tends to the Wigner function W(x), the joint distribution for the operators: W(x)= lim_{L->infinity} <delta(x-bar{P})>_{L}. This result is proved in the case where the Hamiltonian commutes with hat{x}. The Wigner fun…
Cat-States in the Framework of Wigner-Heisenberg Algebra
详细介绍了单参数广义Wigner-Heisenberg代数（WHA）。结果表明，WHA验证了变形对易规则$[\hat{x}, \hat{p}_λ] = i(1 + 2λ\hat{R})$，也突出了赝谐振子（PHO）的动力学对称性。\textbf{The present article is devoted to the study of new cat-states}是由$λ$变形的薛定谔相干态建立的，根据Barut-Girardello方案，它被定义为广义湮灭算符的本征态。特别关注获得薛定谔猫态的极限情况。通过对$λ-$形变正则对$( \hat{x}, \hat{p}_λ)$的Mandel参数和正交压缩的计算，研究了这些态的非经典特征和量子统计性质.结果表明，这些国家最小化的不确定性关系的每对$su(1,1)$组件。
Time Reversal and n-qubit Canonical Decompositions
对于n是偶数个量子比特和v是酉演化，酉群的矩阵分解v=k1 a k2是明确可计算的，并且允许研究并发纠缠单调的动力学。该并发正则分解（CCD）的边因子k1和k2是并发对称的，因此动力学问题归结为对因子a的考虑。在这项工作中，我们提供了一个显式的数值算法计算v=k1 k2为n奇数。此外，在奇数情况下，我们将单调性提升为双参数函数，从而允许奇数量子比特中的并发动力学理论。一般化也可以使用CCD来研究，再次导致大多数酉的最大并发能力。关键的技术是考虑自旋翻转作为一个时间反演对称运营商在维格纳的公理化，原来的CCD推导可以重述完全在这个时间反演。在途中，我们观察到Kramers的非简并性：任何时间反演对称n-量子比特哈密顿量的非简并本征态的存在要求（i）n偶数和（ii）所述本征态的最大并发。我们提供了如何应用这项工作的例子来研究自旋链哈密顿纠缠的运动学和动力学。
