本文研究了混合型相空间中台球混沌本征态的量子局域化，在将规则本征态和混沌本征态分离后，在微扭曲的圆形台球区域中，尽管扩散不是正态的，但经典输运时间仍然足够大.在具有离散能谱的量子系统中，Heisenberg时间$t_H =2π\hbar/ΔE$（$ΔE$是平均能级间距）是一个重要的时间尺度，经典输运时间尺度$t_T$与Heisenberg时间尺度$t_H$的比值（参数$α=t_H/t_T$）决定了混沌本征态的局域化程度，其度量$A$是基于信息熵的.我们发现，$A$是线性相关的归一化逆参与率。混沌本征态的局部化也反映在最近能级之间的分数幂律排斥中，在这个意义上，在距离$S$上找到连续能级的概率密度类似于小$S$的$\propto S^β$，其中$0\leqβ\leq1$和$β=1$对应于完全扩展的状态。我们表明，水平排斥指数$β$是经验的$α$的有理函数，和平均值$\langle A \rangle$作为$α$的函数也很好地近似由有理函数。在这两种情况下，平均曲线周围的经验数据都有一些分散，这是由于$A$实际上有一个分布，通常具有相当复杂的结构，但在极限$α\rightarrow \infty$中，β分布很好地描述了$α\rightarrow \infty$。与其他系统一样，当$α$从$0$变为$\infty$时，$β$从$0$变为$1$。$β$是$\langle A \rangle$的函数，类似于量子踢旋转器和体育场台球。
英文摘要：
We study the quantum localization in the chaotic eigenstates of a billiard with mixed-type phase space, after separating the regular and chaotic eigenstates, in the regime of slightly distorted circle billiard where the classical transport time in the momentum space is still large enough, although the diffusion is not normal. In quantum systems with discrete energy spectrum the Heisenberg time $t_H =2π\hbar/ΔE$, where $ΔE$ is the mean level spacing, is an important time scale.The classical transport time scale $t_T$ in relation to the Heisenberg time scale $t_H$ (their ratio is the parameter $α=t_H/t_T$) determines the degree of localization of the chaotic eigenstates, whose measure $A$ is based on the information entropy. We show that $A$ is linearly related to normalized inverse participation ratio. The localization of chaotic eigenstates is reflected also in the fractional power-law repulsion between the nearest energy levels in the sense that the probability density to find successive levels on a distance $S$ goes like $\propto S^β$ for small $S$, where $0\leqβ\leq1$, and $β=1$ corresponds to completely extended states. We show that the level repulsion exponent $β$ is empirically a rational function of $α$, and the mean $\langle A \rangle$ as a function of $α$ is also well approximated by a rational function. In both cases there is some scattering of the empirical data around the mean curve, which is due to the fact that $A$ actually has a distribution, typically with quite complex structure, but in the limit $α\rightarrow \infty$ well described by the beta distribution. Like in other systems, $β$ goes from $0$ to $1$ when $α$ goes from $0$ to $\infty$. $β$ is a function of $\langle A \rangle$, similar to the quantum kicked rotator and the stadium billiard.
Dynamical localization of chaotic eigenstates in the mixed-type systems: spectral statistics in a billiard system after separation of regular and chaotic eigenstates
Analysis of resonant population transfer in time-dependent elliptical quantum billiards
导出了具有振荡边界的椭圆量子台球瞬时本征态间布居数转移的费米黄金法则。因此，最近观察到的瞬时本征态之间的共振布居转移[F。Lenz等人，New J. Phys.，{ \bf 13}，103019，2011]以及说明当驱动频率与后者的平均差匹配时发生这些转变的经验标准。作为第二个主要结果，提供了判断哪些共振在一定持续时间的相应实验中是可分辨的标准。我们的分析是补充三种不同的驱动法律的数值模拟。相应的共振谱与这两个准则的预测是一致的。
Experimental study of coupled quantum billiards with integrable and chaotic classical dynamics and test of a special Rosenzweig-Porter model
Lanzhou University（兰州大学）；Institute for Basic Science（韩国基础科学研究院）；Qilu Normal University（齐鲁工业大学）；University of Electronic Science and Technology of China（电子科技大学）；Korea University of Science and Technology (UST)（韩国科学技术院）
Partial time-reversal invariance violation in a flat, superconducting microwave cavity with the shape of a chaotic Africa billiard
我们报告的实验实现的平面，超导微波谐振器，微波台球，与部分违反时间反转（T）不变性，诱导插入铁氧体到腔体和磁化它与外部磁场垂直的谐振器平面。为了防止Meissner-Ochsenfeld效应引起的排斥，我们使用了一个腔，腔的顶板和底板由铌（一种II型超导体）制成，并将其冷却到液氦温度T LHe '4K。空洞的形状就像一个混乱的非洲台球。超导性使得精确确定共振频率的完整序列以及共振的宽度和强度成为可能，这是明确检测T不变性违反的不可或缺的先决条件，特别是当它仅部分违反时。这允许第一次从谐振频率的波动特性和强度分布中精确地指定T不变性违反的大小，这实际上敏感地依赖于它，从而提供了最合适的测量。为此，我们推导出了后者的解析表达式，这是有效的孤立共振的范围内，从没有T不变性违反完全违反。
Thermodynamic Uncertainty Relations in Chaotic Andreev Billiards
Universidade Estadual Paulista（圣保罗州立大学）；Laboratório Nacional de Luz Síncrotron, Centro Nacional de Pesquisa em Energia e Materiais（巴西国家同步辐射光源实验室，国家能源与材料研究中心）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）
