权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Estimation of tunneling times using Nelson's quantum stochastic process

使用尼尔森量子随机过程估计隧道时间

基本信息

批准号：
13640400
负责人：
HASHIMOTO Takaaki
金额：
$ 2.24万
依托单位：
Fukui University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640400/
关键词：
quantum stochastic process half integer spin space Wigner function Nelson's method tunneling time

项目摘要

We have to take into account the half integer spin degree of freedom to the standart Nelson : s quantum stochastic process to estimate the tunneling time measured in the neutron spin echo experiments. In this research, we construct a quantum stochastic process using the Wigner function on a lattice phase space. The lattice composed of even lattice points represents a half integer spin space. The problem has been considered by Cohendet et al. in 1987 for odd lattice. In the first paper, we show that the Wigner functions do exit even on the even lattice contrary to the previous paper by Cohendet et al. There are infinitely many solution satisfying the conditions which reasonable Wigner function should respect and all of them are derived from one Wigner function by a orthogonal transformation. In the second paper, we propose a condition which ensures the correct marginal distributions of the Wigner function along tilted lines on a lattice. Under this condition we get the Wigner function without ambiguity if the lattice is odd. In the third manuscript we construct a quantum Markov process using the Wigner function formulated in the first and second paper. Introducing so-called ghost variables both on even and odd lattices, it is show that we can make the same kind of discussion as Cohendet et al.

在中子自旋回波实验中，为了估计隧道时间，必须考虑标准纳尔逊量子随机过程的半整数自旋自由度。在本研究中，我们利用格点相空间上的Wigner函数构造了一个量子随机过程。由偶数格点组成的格表示半整数自旋空间。Cohendet等人在1987年对奇格考虑了这个问题。在第一篇文章中，我们证明了Wigner函数在偶数格上确实存在，与Cohendet等人的前一篇文章相反，存在无穷多个满足合理Wigner函数所应满足的条件的解，并且这些解都是由一个Wigner函数通过正交变换导出的.在第二篇论文中，我们提出了一个条件，确保正确的边缘分布的维格纳函数沿着倾斜线上的一个格子。在此条件下，我们得到的维格纳函数没有二义性，如果格是奇数。在第三稿中，我们构造了一个量子马尔可夫过程使用的维格纳函数制定的第一和第二篇论文。在偶格和奇格上引入所谓的鬼变量，表明我们可以进行与Cohendet等人相同的讨论。