Estimation of tunneling times using Nelson's quantum stochastic process

为了估计中子自旋回波实验中测量的隧穿时间，必须考虑标准Nelson: s量子随机过程的半整数自旋自由度。本文利用Wigner函数在晶格相空间上构造了一个量子随机过程。由偶格点组成的晶格表示半整数自旋空间。Cohendet等人在1987年考虑了奇格的问题。在第一篇论文中，我们证明了Wigner函数在偶格上存在偶，这与Cohendet等人之前的论文相反。合理的维格纳函数满足的条件有无穷多个解，它们都是由一个维格纳函数通过正交变换得到的。在第二篇论文中，我们提出了保证Wigner函数在晶格上沿倾斜线的正确边际分布的一个条件。在此条件下，当格是奇格时，我们得到无歧义的Wigner函数。在第三篇论文中，我们利用第一篇和第二篇论文中表述的维格纳函数构造了一个量子马尔可夫过程。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。

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.