Estimation of tunneling times using Nelson's quantum stochastic process
Project/Area Number 
13640400

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
物理学一般

Research Institution  Fukui University 
Principal Investigator 
HASHIMOTO Takaaki Applied Phys., Associate Prof., 工学部, 助教授 (30228415)

CoInvestigator(Kenkyūbuntansha) 
HORIBE Minoru Associate Prof., 工学部, 助教授 (90143932)
HAYASHI Akihisa Prof., 工学部, 教授 (80208610)

Project Period (FY) 
2001 – 2002

Project Status 
Completed (Fiscal Year 2002)

Budget Amount *help 
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 2001: ¥3,100,000 (Direct Cost: ¥3,100,000)

Keywords  quantum stochastic process / half integer spin space / Wigner function / Nelson's method / tunneling time 
Research Abstract 
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 socalled ghost variables both on even and odd lattices, it is show that we can make the same kind of discussion as Cohendet et al.

Report
(3 results)
Research Products
(8 results)