On the correspondence between three nodes W states in quantum network theory and the oriented links in knot theory

The GHZ states and W states are two fundamental types of three qubits quantum entangled states. For finding the knotted pictures of three nodes W states, on the one side, we empty any one node, thus obtaining three degenerated twonode W states, then we find the nonzero submatrix of the corresponding covariance correlation tensor in quantum network theory. On the other side, excepting the linkage 41 corresponding to Bell bases, we conjecture that the another one possible oriented link(which is composed of two-component knots entangled with each other and has four crossings) would be the required knotted pictures of the two nodes W states, thence obtain the nonzero submatrix of the Alexander relation matrix in the theory of knot crystals for these knotted pictures. The equality of the two nonzero submatrices of different kinds thus verify the exactness of our conjecture. The superposition of three knotted pictures of two-node W states from different choices of the emptied node gives the knotted pictures of three-node W states, thus shows the correspondence between three-node W states in quantum network theory and the oriented links in knot theory. Finally we point out that there is an intimate and simple relationship between the knotted pictures of GHZ states and W states.     

含时三次幂势系统传播子的精确解

本文应用正则变换的方法，以一般的含时不变量为正则动量，求得含时三次幂势系统传播子的精确解表达式。     

Knotted pictures of the GHZ states on the surface of a trivial torus

By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three-qubit states on the surface of a trivial torus. Thus, we obtain eight knotted pictures 121 linkage on the ordinary plane.     

双磁通线Aharonov—Bohm散射系统的传播子

本文将对双磁通Aharonov-Bohm(以下简称A-B)效应以约束路径积分形式进行表述。首先应用多边形法在椭柱坐标上层开路径积分求得径向(?)传播子,然后再求属于同伦类的传播子,进而求得全传播子。     

有反平方势时各向同性变频率谐振子的AB效应

讨论的动力学系统为一受反平方势作用的各向同性变频率谐振子。文中给出了此动力学系统的阿哈罗诺夫·玻姆(AB)效应的传播子。此外,还给出了在常频率这一特殊情形下波函数的表达式     

纽结理论与量子混沌

讨论了纽结理论对量子混沌的应用，并揭示了量子系统中混沌解的拓扑结构。     

参数平移相关类的形不变势的多参数变形

证明了对参数平移相关的所有一维形不变势，都可以求得其多参数变莆而以ｑ作为变形参数。     

Knotted pictures of the GHZ states on the surface of trivial torus

By means of the method of torus knot theory, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of trivial torus from the knotted pictures of eight basic three-qubit states on the surface of trivial torus. Thus, we obtain eight knotted pictures 12₁ linkage on the ordinary plane.     

关于A-B效应和Oscillator系统

采用Feynman路径积分的方法,得到变频率Oscillator受平方反比势及单磁通A-B势扰动时的传播函数,以及常频率情况下的传播函数、波函数和能谱.     

在点正则变换下赫耳顿势映射于潘歇—推劳Ⅰ势

利用在点正则变换下形不变势的映射方法，我们从潘歇－推劳Ⅰ势的已知结果求得了赫耳顿势的束缚态能谱与本征函数。