关于量子态连续系综展开的一个注记

具有有界耦合项的双线性薛定谔方程部分包围能控的一个充分条件

A Sufficient Condition for Partial Ensemble Controllability of Bilinear Schrödinger Equations with Bounded Coupling Terms

本文给出了无限维希尔伯特空间中一类双线性保守量子系统部分近似系综能控的一个充分条件。证明依赖于经典的几何和平均控制技术应用于有限维近似的无限维系统。结果与线性分子的平面旋转说明。

Quantum Joule Expansion of One-Dimensional Systems

We investigate the Joule expansion of nonintegrable quantum systems that contain bosons or spinless fermions in one-dimensional lattices. A barrier initially confines the particles to be in half of the system in a thermal state described by the canonical ensemble and is removed at time $t = 0$. We investigate the properties of the time-evolved density matrix, the diagonal ensemble density matrix and the corresponding canonical ensemble density matrix with an effective temperature determined by the total energy conservation using exact diagonalization. The weights for the diagonal ensemble and …

关于冯·诺依曼投影仪测量指针态、弱值和干涉的注记

A Note Concerning von Neumann Projector Measurement Pointer States, Weak Values, and Interference

众所周知，指针状态|Φ>是由对处于预选态的量子系统系综进行的投影算符A的冯·诺依曼测量产生的|取决于A|我的意思是。这里显示指针状态|从对也是后选择的系综执行的这样的测量获得的α取决于A -的弱值，而不管测量相互作用强度。研究还发现，虽然空间分布|A>表现出干扰，A的幂等性禁止干扰|Φ>。这是根据welcher Weg信息解释的。

几乎对角随机矩阵的维里展开

Virial expansion for almost diagonal random matrices

研究了具有高斯独立随机元的厄米特随机矩阵$\hat H$的能级统计特性，其中$H_{i\geq j}$是具有$ <|H_{ii}|^{2} > \sim 1$和$<|H_{i\neq j}|^{2} >= b {\cal F}(|i-j|) \ll 1$的概对角随机矩阵的一般系综.我们执行的频谱形状因子$K(τ) = 1 + b K_{1}(τ) + b^{2} K_{2}(τ) + ... $在$b \ll 1$的权力与系数$K_{m}(τ)$，考虑到（m+1）能级的相互作用的定期扩展。为了计算$K_{m}(τ)$，我们开发了一种基于Trotter公式和图边用（m+1）种颜色着色的组合问题的图解技术。对于一般函数${\cal F}(|i-j|)$，在高斯正交系综（GOE）、高斯酉系综（GUE）以及它们之间的交叉（几乎酉高斯系综）中，得到了$K_{1}(τ)$和$K_{2}(τ)$的无穷级数表达式. Rosenzweig-Porter和幂律带状矩阵合奏被认为是作为例子。

Spectral form factors and late time quantum chaos

This is a collection of notes that are about spectral form factors of standard ensembles in the random matrix theory, written for the practical usage of current study of late time quantum chaos. More precisely, we consider Gaussian Unitary Ensemble (GUE), Gaussian Orthogonal Ensemble (GOE), Gaussian Symplectic Ensemble (GSE), Wishart-Laguerre Unitary Ensemble (LUE), Wishart-Laguerre Orthogonal Ensemble (LOE), and Wishart-Laguerre Symplectic Ensemble (LSE). These results and their physics applications cover a three-fold classification of late time quantum chaos in terms of spectral form factors…

关于量子熵的一个注记

A note on quantum entropy

增量信息，如量子熵所测量的，当两个集合结合时，增量信息正在增加。这一结果已被Lieb和Ruskai证明，它是证明量子熵强次可加性的基础。我们提出了一个真正的基本证明这一事实的背景下，更广泛的家庭矩阵熵介绍陈和Tropp。